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General relativistic corrections are calculated for the quadrupole moment of a magnetically confined mountain on an accreting neutron star. The hydromagnetic structure of the mountain satisfies the general relativistic Grad–Shafranov equation supplemented by the flux-freezing condition of ideal magnetohydrodynamics, as in previous calculations of the magnetic dipole moment. It is found that the ellipticity, and hence the gravitational wave strain, are up to 12% greater than in the analogous Newtonian system. The direct contribution of the magnetic field to the nonaxisymmetric component of the stress-energy tensor is shown to be negligible in accreting systems such as low-mass X-ray binaries. [ABSTRACT FROM AUTHOR]

Although ultraluminous X-ray pulsars (ULXPs) are believed to be powered by super-Eddington accretion onto a magnetized neutron star (NS), the detailed structures of the inflow–outflow and magnetic fields are still not well understood. We perform general relativistic radiation magnetohydrodynamics (GR-RMHD) simulations of super-Eddington accretion flows onto a magnetized NS with dipole and/or quadrupole magnetic fields. Our results show that an accretion disk and optically thick outflows form outside the magnetospheric radius, while inflows aligned with magnetic field lines appear inside. When the dipole field is more prominent than the quadrupole field at the magnetospheric radius, accretion columns form near the magnetic poles, whereas a quadrupole magnetic field stronger than the dipole field results in the formation of a belt-like accretion flow near the equatorial plane. The NS spins up as the angular momentum of the accreting gas is converted into the angular momentum of the electromagnetic field, which then flows into the NS. Even if an accretion column forms near one of the magnetic poles, the observed luminosity is almost the same on both the side with the accretion column and the side without it, because the radiation energy is transported to both sides through scattering. Our model suggests that galactic ULXP Swift J0243.6+6124 has a quadrupole magnetic field of 2 × 1013 G and a dipole magnetic field of less than 4 × 1012 G. [ABSTRACT FROM AUTHOR]

In this paper, we study the next-to-leading order corrections in the mass multipole expansion, i.e. the mass octupole and current quadrupole, to gravitational wave production by close hyperbolic encounters of compact objects. We find that the signal is again, as in the simple quadrupole case, a burst event with the majority of the released energy occurring during the closest approach. In particular, we investigate the relative contribution to the power, both in the time and frequency domains, and total energy emitted by each order in the mass multipole expansion in gravitational waves. To do so, we include in the quadrupole term its first order post-Newtonian correction, giving this a contribution to the power of the same order as that of the mass octupole and the current quadrupole. We find specific configurations of systems where these corrections could be important and should be taken into account when analysing burst events. [ABSTRACT FROM AUTHOR]

Canonically, 'classic' tests of general relativity (GR) include perihelion precession, the bending of light around stars, and gravitational redshift; 'modern' tests have to do with, inter alia, relativistic time delay, equivalence principle tests, gravitational lensing, strong field gravity, and gravitational waves. The orthodoxy is that both classic and modern tests of GR afford experimental confirmation of that theory in particular. In this article, we question this orthodoxy, by showing there are classes of both relativistic theories (with spatiotemporal geometrical properties different from those of GR) and non-relativistic theories (in which the lightcones of a relativistic spacetime are 'widened') which would also pass such tests. Thus, (a) issues of underdetermination in the context of GR loom much larger than one might have thought, and (b) given this, one has to think more carefully about what exactly such tests in fact are testing. [ABSTRACT FROM AUTHOR]

Some authors have defended the claim that one needs to be able to define 'physical coordinate systems' and 'observables' in order to make sense of general relativity. Moreover, in Rovelli (Physical Review D,65(4), 044017 2002), Rovelli proposes a way of implementing these ideas by making use of a system of satellites that allows defining a set of 'physical coordinates', the GPS coordinates. In this article I oppose these views in four ways. First, I defend an alternative way of understanding general relativity which implies that we have a perfectly fine interpretation of the models of the theory even in the absence of 'physical coordinate systems'. Second, I analyze and challenge the motivations behind the 'observable' view. Third, I analyze Rovelli's proposal and I conclude that it does not allow extracting any physical information from our models that wasn't available before. Fourth, I draw an analogy between general relativistic spacetimes and Newtonian spacetimes, which allows me to argue that as 'physical observables' are not needed in Newtonian spacetime, then neither are they in general relativity. In this sense, I conclude that the 'observable' view of general relativity is unmotivated. [ABSTRACT FROM AUTHOR]

The present investigation examines the behaviour of compact relativistic objects characterised by static and spherically symmetric space–time for neutral anisotropic matter distribution. More specifically, we consider an equation of state (EoS), in which density and radial pressure are connected with each other quadratically. By smoothly matching the interior space–time with the exterior at the stellar surface, the appropriate values of the constant parameters for physically realistic solutions are obtained to model various compact stars. We explore the physical behaviour of compact stellar models SMC X-4, Vela X-1, CEN X-3, PSR J1614-2230, LMC X-4 and EXO 1785-248. Further, we describe several features of the compact stellar systems that exhibit physically acceptable attributes with no singularity. All important stability criteria, such as the energy conditions, causality conditions, Buchdhal condition and the adiabatic index are fulfilled by our neutral anisotropic compact star models. An in-depth comprehension of the physical characteristics of the proposed solution has been achieved through meticulous analytical and graphical examinations. By utilising this solution, the masses and radii of six compact stellar candidates mentioned above are optimised with the observed values obtained experimentally. The derived solution might be useful to enhance the understanding of the strong-field regimes and self-gravitating entities. [ABSTRACT FROM AUTHOR]

Primordial black holes (PBHs) may have formed through the gravitational collapse of cosmological perturbations that were generated and stretched during the inflationary era, later entering the cosmological horizon during the decelerating phase, if their amplitudes were sufficiently large. In this review paper, we will briefly introduce the basic concept of PBHs and review the formation dynamics through this mechanism, the estimation of the initial spins of PBHs and the time evolution of type II fluctuations, with a focus on the radiation-dominated and (early) matter-dominated phases. [ABSTRACT FROM AUTHOR]

In this work, we investigate spacetime and photon dynamics around a charged Hayward black hole, focusing on the effects of electric charge Q and the length factor l. Our analysis shows that the maximum charge for black hole existence decreases as l increases, vanishing at l / M ≃ 0.77 . The black hole has both inner and outer horizons, with the outer horizon shrinking and the inner horizon expanding as spacetime parameters increase. The spacetime curvature, measured by the Kretschmann scalar, is most pronounced when both parameters are small, resembling the Schwarzschild black hole. The electric charge strongly influences the curvature and photon sphere size, while the effect of the length factor is less significant. Additionally, the gravitational redshift of photons is more sensitive to the electric charge of the compact object than the length factor, diminishing as Q increases and with greater radial distance from the black hole. Overall, while both spacetime parameters affect black hole properties, the electric charge has a slightly stronger impact, especially on gravitational redshift and photon behavior. [ABSTRACT FROM AUTHOR]

This paper explores the optical approach to simplifying complex concepts in general relativity (GR) and nonlinear vacuum electrodynamics. The focus is on using optical analogies to simplify the understanding of spacetime curvature and interactions in strong gravitational and magnetic fields. We demonstrate how applying concepts of effective refractive index can facilitate the teaching and comprehension of GR optical effects, such as gravitational lensing and the behavior of light around massive objects. Additionally, the paper covers the application of optical analogies in the context of nonlinear vacuum electrodynamics, showing how strong magnetic fields affect light propagation. This interdisciplinary approach provides a more natural understanding and modeling of complex physical phenomena, making them better accessible for study and teaching. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of stationary trajectories of free particles. From a classical point of view, this appears to be an almost trivial problem: Free particles should follow straight lines as predicted by Newton's first law, and straight lines are indeed the stationary trajectories of the standard action integrals in the classical theory. In the following, however, a general relativistic approach is studied, and in this situation it is much less evident what action integral should be used. As it turns out, using the traditional Einstein–Hilbert principle gives us stationary states very much in line with the classical theory. But it is suggested that a different action principle, and in fact one which is closer to quantum mechanics, gives stationary states with a much richer structure: Even if these states in a sense can represent particles which obey the first law, they are also inherently rotating. Although we may still be far from understanding how general relativity and quantum mechanics should be united, this may give an interesting clue to why rotation (or rather spin, which is a different but related concept) seems to be the natural state of motion for elementary particles. [ABSTRACT FROM AUTHOR]

We present the Quantum Memory Matrix (QMM) hypothesis, which addresses the longstanding Black Hole Information Paradox rooted in the apparent conflict between Quantum Mechanics (QM) and General Relativity (GR). This paradox raises the question of how information is preserved during black hole formation and evaporation, given that Hawking radiation appears to result in information loss, challenging unitarity in quantum mechanics. The QMM hypothesis proposes that space–time itself acts as a dynamic quantum information reservoir, with quantum imprints encoding information about quantum states and interactions directly into the fabric of space–time at the Planck scale. By defining a quantized model of space–time and mechanisms for information encoding and retrieval, QMM aims to conserve information in a manner consistent with unitarity during black hole processes. We develop a mathematical framework that includes space–time quantization, definitions of quantum imprints, and interactions that modify quantum state evolution within this structure. Explicit expressions for the interaction Hamiltonians are provided, demonstrating unitarity preservation in the combined system of quantum fields and the QMM. This hypothesis is compared with existing theories, including the holographic principle, black hole complementarity, and loop quantum gravity, noting its distinctions and examining its limitations. Finally, we discuss observable implications of QMM, suggesting pathways for experimental evaluation, such as potential deviations from thermality in Hawking radiation and their effects on gravitational wave signals. The QMM hypothesis aims to provide a pathway towards resolving the Black Hole Information Paradox while contributing to broader discussions in quantum gravity and cosmology. [ABSTRACT FROM AUTHOR]

I propose a possible way to introduce the effect of temperature (defined through the virial theorem) into Einstein's theory of general relativity. This requires the computation of a path integral on a ten-dimensional flat space in a four-dimensional spacetime lattice. Standard path integral Monte Carlo methods can be used to compute this. [ABSTRACT FROM AUTHOR]

This paper delves into the impact of electromagnetic fields on isotropic spherical charged gravastar (CGS) systems within the framework of f (R , Σ , T) gravity. The investigation focuses on singularity-free exact systems of relativistic spheres with a specific equation of state (EoS), employing a suitable choice of the effective field for different regions of the gravastar. The exterior region considers the Reissner–Nordström spacetime, while the interior charged manifold is matched at the junction interface. By utilizing graphical representations, the study examines various physical characteristics of the spherical gravastar system in the presence of an electromagnetic field. The findings reveal that the electric charge plays a significant role in shaping the optimal length, energy content, entropy, EoS parameter of the stellar system, and the energy conditions of our system. Additionally, the stability of the system is also investigated. Here are some of the results obtained. It is determined that both the matter density and pressure remain constant within the interior region of the CGS. The EoS is always negative. Also, the energy conditions are violated in our cosmological system. [ABSTRACT FROM AUTHOR]

Recent observations from the James Webb Space Telescope have identified a population of massive galaxy sources (> 1 0 1 0 M ⊙ ) at z > 7 –10, formed less than 700 Myr after the Big Bang. Such massive galaxies do not have enough time to form within the standard cosmological model, and hence these observations pose a significant challenge. A number of possible solutions to this problem have been put forward. In this essay, we discuss two more theoretical and speculative possibilities. [ABSTRACT FROM AUTHOR]

Many previous works have studied gravitational lensing effects from Loop Quantum Gravity. So far, gravitational lensing effects from Loop Quantum Gravity have only been studied by choosing large quantum parameters much larger than the Planck scale. However, by construction, the quantum parameters of the effective models of Loop Quantum Gravity are usually related to the Planck length and, thus, are extremely small. In this work, by strictly imposing the quantum parameters as initially constructed, we study the true quantum corrections of gravitational lensing effects by five effective black hole models of Loop Quantum Gravity. Our study reveals several interesting results, including the different scales of quantum corrections displayed by each model and the connection between the quantum correction of deflection angles and the quantum correction of the metric. Observables related to the gravitational lensing effect are also obtained for all models in the case of SgrA* and M87*. [ABSTRACT FROM AUTHOR]

Particular Kottler spacetimes are analytically investigated. The investigated spacetimes are spherically symmetric nonrotating spacetimes endowed with a Schwarzschild solid-angle element. SchwarzschildNairiai spacetimes, Schwarzschild spacetimes with a linear term, and Schwarzschild spacetimes with a linear term and a cosmological constant are studied. The infinite-redshift surfaces are analytically written. To this aim, the parameter spaces of the models are analytically investigated, and the conditions for which the analytical radii are reconducted to the physical horizons are used to set and to constrain the parameter spaces. The coordinate-singularity-avoiding coordinate extensions are newly written. Schwarzschild spacetimes with a linear term and a cosmological constant termare analytically studied, and the new singularity-avoiding coordinate extensions are detailed. The new roles of the linear term and of the cosmological constant term in characterizing the Schwarzschild radius are traced. The generalized Schwarzschild–deSitter case and generalized Schwarzschild–anti-deSitter case are characterized in a different manner. The weak field limit is newly recalled. The embeddings are newly provided. The quantum implementation is newly envisaged. The geometrical objects are newly calculated. As a result, for the Einstein field equations, the presence of quintessence is newly excluded. The Birkhoff theorem is newly proven to be obeyed. [ABSTRACT FROM AUTHOR]

We examine the black-hole limits of the family of static and spherically symmetric solutions of the Einstein field equations for polytropic matter, that was presented in a previous paper. This exploration is done in the asymptotic sub-regions of the allowed regions of the parameter planes of that family of solutions, for a few values of the polytropic index n, with the limitation that n > 1 . These allowed regions were determined and discussed in some detail in another previous paper. The characteristics of these limits are examined and analyzed. We find that there are different types of black-hole limits, with specific characteristics involving the local temperature of the matter. We also find that the limits produce a very unexpected but specific type of spacetime geometry in the interior of the black holes, which we analyze in detail. Regarding the spatial part of the interior geometry, we show that in the black-hole limits there is a general collapse of all spatial distances to zero. Regarding the temporal part, there results an infinite overall red shift in the limits, with respect to the flat space at radial infinity, over the whole interior region. The analysis of the interior geometry leads to a very surprising connection with quantum-mechanical studies in the background metric of a naked Schwarzschild black hole. The nature of the solutions in the black-hole limits leads to the definition of a new type of singularity in General Relativity. We argue that the black-hole limits cannot actually be taken all the way to their ultimate conclusion, due to the fact that this would lead to the violation of some essential physical and mathematical conditions. These include questions of consistency of the solutions, questions involving infinite energies, and questions involving violations of the quantum behavior of matter. However, one can still approach these limiting situations to a very significant degree, from the physical standpoint, so that the limits can still be considered, at least for some purposes, as useful and simpler approximate representations of physically realizable configurations with rather extreme properties. [ABSTRACT FROM AUTHOR]

Gravity and electromagnetic interactions are the only fundamental physical interactions (outside the nuclear domain). In this work, we shall concentrate on Hamiltonians containing gravitational interaction, which according to general relativity must be retarded. In recent years, retarded gravity has explained many of the mysteries surrounding the "missing mass" related to galactic rotation curves, the Tully–Fisher relations, and gravitational lensing phenomena. Indeed, a recent paper analyzing 143 galaxies has demonstrated that retarded gravity will suffice to explain galaxies' rotation curves without the need to postulate dark matter for multiple types of galaxies. Moreover, it also demystified the "missing mass" related to galactic clusters and elliptic galaxies in which excess matter was derived through the virial theorem. Here, we give a mathematical criterion that specifies the cases in which retardation is important for gravity (and when it is not). The criterion takes the form of an inequality. [ABSTRACT FROM AUTHOR]

The Landauer principle establishes a lower bound in the amount of energy that should be dissipated in the erasure of one bit of information. The specific value of this dissipated energy is tightly related to the definition of entropy. In this article, we present a generalization of the Landauer principle based on the Tsallis entropy. Some consequences resulting from such a generalization are discussed. These consequences include the modification to the mass ascribed to one bit of information, the generalization of the Landauer principle to the case when the system is embedded in a gravitational field, and the number of bits radiated in the emission of gravitational waves. [ABSTRACT FROM AUTHOR]

In almost all countries, the Ministry of Public Education has introduced the topics of special and general relativity into the high school curriculum. For example, in Italy the teaching of so-called modern physics (quantum mechanics and relativity) was introduced in the last year of high school. The students are approximately 18 years old and, although the arguments are addressed in an introductory and qualitative way, they are also a topic for the final exam. Einstein's theory fascinates young students, but it is not always easy to explain the revolutionary effects it predicts. For this reason, we have organized a series of in-depth lessons trying to derive the space-time distortions in a way suitable for the young age of the students. In this frontline we summarize a derivation, suitable for high school pupils, regarding gravitational time dilation. [ABSTRACT FROM AUTHOR]

In this paper, we review the theoretical basis for generation of gravitational waves and the detection techniques used to detect a gravitational wave. To materialize this goal in a thorough way, we first start with a mathematical background for general relativity from which a clue for gravitational wave was conceived by Einstein. Thereafter, we give the classification scheme of gravitational waves such as (i) continuous gravitational waves, (ii) compact binary inspiral gravitational waves and (iii) stochastic gravitational wave. Necessary mathematical insight into gravitational waves from binaries is also dealt with which follows detection of gravitational waves based on the frequency classification. Ground-based observatories as well as space borne gravitational wave detectors are discussed in a length. We have provided an overview on the inflationary gravitational waves. In connection to data analysis by matched filtering there are a few highlights on the techniques, e.g. (i) random noise, (ii) power spectrum, (iii) shot noise and (iv) Gaussian noise. Optimal detection statistics for a gravitational wave detection is also in the pipeline of the discussion along with detailed necessity of the matched filter and deep learning. [ABSTRACT FROM AUTHOR]

An attempt to directly use the synchronous gauge ( g 0 λ = − δ 0 λ ) in perturbative gravity leads to a singularity at p 0 = 0 in the graviton propagator. This is similar to the singularity in the propagator for Yang–Mills fields A λ a in the temporal gauge ( A 0 a = 0). There the singularity was softened, obtaining this gauge as the limit at ε → 0 of the gauge n λ A λ a = 0 , n λ = (1 , − ε (∂ j ∂ j) − 1 ∂ k). Then the singularities at p 0 = 0 are replaced by negative powers of p 0 ± i ε , and thus we bypass these poles in a certain way. Now consider a similar condition on n λ g λ μ in perturbative gravity, which becomes the synchronous gauge at ε → 0. Unlike the Yang–Mills case, the contribution of the Faddeev–Popov ghosts to the effective action is nonzero, and we calculate it. In this calculation, an intermediate regularization is needed, and we assume the discrete structure of the theory at short distances for that. The effect of this contribution is to change the functional integral measure or, for example, to add nonpole terms to the propagator. This contribution vanishes at ε → 0. Thus, we effectively have the synchronous gauge with the resolved singularities at p 0 = 0 , where only the physical components g j k are active and there is no need to calculate the ghost contribution. [ABSTRACT FROM AUTHOR]

It is commonly accepted that superluminal travel may be used to facilitate time travel. This is a purely special-relativistic argument, using the fact that for observers in two frames of reference, separated by a spacelike interval, the non-causal (spacelike) future of one observer includes part of the causal past of the other. In this paper we provide a concrete realization of this argument in a curved general-relativistic spacetime, using warp drives as the means of faster-than-light travel. By generalizing the usual warp drive metric to allow for a non-unit lapse function, we allow the warp drive to switch between reference frames in a purely geometric way. With an additional modification allowing the warp drive to have compact support, this permits us to glue two warp drives together to construct a closed timelike geodesic, such that a test particle following the geodesics of the two warp drives travels back to its own past. This provides a precise mathematical model for the connection between faster-than-light travel and time travel in general relativity, and the first such model to be explicitly formulated using two warp drives. We also give a detailed discussion of weak energy condition violations in the non-unit-lapse warp drive. [ABSTRACT FROM AUTHOR]

We analyze the orbits of a unit mass body in a background Reissner–Nordstr o ¨ m (RN) black hole in d = (3 + 1) from the perspectives of Geometric Torsion (GT) modified gravity theory in (4 + 1) dimensional bulk. A 4-form flux in bulk GT theory in d = (4 + 1) has been shown to ensure a mass dipole correction to the (3 + 1) dimensional gravity theory by Gupta, Kar and Rang recently. We argue that the dipole correction contributes topologically to the known exact geometries in General Theory of Relativity (GTR). Furthermore, the topological correction has been identified with non-Newtonian potential underlying a B 2 ∧ F 2 coupling term to Einstein–Hilbert action. The winding numbers ensured by the BF coupling to d = (3 + 1) action in the framework presumably provide a clue towards a tunneling instanton in theory. [ABSTRACT FROM AUTHOR]

This is the third and final entry in a sequence of papers devoted to the formulation of a theory of self-gravitating anisotropic fluids in Newtonian gravity and general relativity. In the first paper we placed our work in context and provided an overview of the results obtained in the second and third papers. In the second paper we took the necessary step of elaborating a Newtonian theory, and exploited it to build anisotropic stellar models. In this third paper we elevate the theory to general relativity, and apply it to the construction of relativistic stellar models. The relativistic theory is crafted by promoting the fluid variables to a curved spacetime, and promoting the gravitational potential to the spacetime metric. Thus, the director vector, which measures the local magnitude and direction of the anisotropy, is now a four-dimensional vector, and to keep the number of independent degrees of freedom at three, it is required to be orthogonal to the fluid's velocity vector. The Newtonian action is then generalized in a direct and natural way, and dynamical equations for all the relevant variables are once more obtained through a variational principle. We specialize our relativistic theory of a self-gravitating anisotropic fluid to static and spherically symmetric configurations, and thus obtain models of anisotropic stars in general relativity. As in the Newtonian setting, the models feature a transition from an anisotropic phase at high density to an isotropic phase at low density. Our survey of stellar models reveals that for the same equations of state and the same central density, anisotropic stars are always less compact than isotropic stars. [ABSTRACT FROM AUTHOR]

We study the chaotic dynamics of spinless extended bodies in a wide class of spherically symmetric spacetimes, which encompasses black-hole scenarios in many modified theories of gravity. We show that a spherically symmetric pulsating ball may have chaotic motion in this class of spacetimes. The cases of the Reissner–Nordström and Ayón-Beato–García black holes are analyzed in detail. The equations of motion for the extended bodies are obtained according to Dixon's formalism, up to quadrupole order. Then, we use Melnikov's method to show the presence of homoclinic intersections, which imply chaotic behavior, as a consequence of our assumption that the test body has an oscillating radius. [ABSTRACT FROM AUTHOR]

This paper was a pioneering contribution to a symplectic description of the dynamics of spinning particles in general relativity which remained somewhat unnoticed. In particular, it introduced the pre-symplectic 2-form σ describing the dynamics of spinning particles coupled to an Einsteinian curved background. The method throws light on approaches to spinning black holes and neutron stars. [ABSTRACT FROM AUTHOR]

The gravitational interaction of (classical and quantum) spinning bodies is currently the focus of many works using a variety of approaches. This note is a comment on a short paper by Jean-Marie Souriau, now reprinted in the GRG Golden Oldies collection. Souriau's short 1970 note was a pioneering contribution to a symplectic description of the dynamics of spinning particles in general relativity which remained somewhat unnoticed. We explain the specificity of Souriau's approach and emphasize its potential interest within the current flurry of activity on the gravitational interaction of spinning particles. [ABSTRACT FROM AUTHOR]

Some aspects of atom-field interactions in curved spacetime are reviewed. Of great interest are quantum radiative and entanglement processes arising out of Rindler and black hole spacetimes, which involve the role of Hawking–Unruh and dynamical Casimir effects. Most of the discussion surrounds the radiative part of interactions. For this, we specifically reassess the conventional understandings of atomic radiative transitions and energy level shifts in curved spacetime. We also briefly outline the status quo of entanglement dynamics study in curved spacetime, and highlight literature related to some novel insights, like entanglement harvesting. On one hand, the study of the role played by spacetime curvature in quantum radiative and informational phenomena has implications for fundamental physics, notably the gravity-quantum interface. In particular, one examines the viability of the Equivalence Principle, which is at the heart of Einstein's general theory of relativity. On the other hand, it can be instructive for manipulating quantum information and light propagation in arbitrary geometries. Some issues related to nonthermal effects of acceleration are also discussed. [ABSTRACT FROM AUTHOR]

Aggregative moral theories face a series of devastating problems when we apply them in a physically realistic setting. According to current physics, our universe is likely infinitely large, and will contain infinitely many morally valuable events. But standard aggregative theories are ill-equipped to compare outcomes containing infinite total value. So, applied in a realistic setting, they cannot compare any outcomes a real-world agent must ever choose between. This problem has been discussed extensively, and non-standard aggregative theories proposed to overcome it. This paper addresses a further problem of similar severity. Physics tells us that, in our universe, how remotely in time an event occurs is relative. But our most promising aggregative theories, designed to compare outcomes containing infinitely many valuable events, are sensitive to how remote in time those events are. As I show, the evaluations of those theories are then relative too. But this is absurd; evaluations of outcomes must be absolute! So we must reject such theories. Is this objection fatal for all aggregative theories, at least in a relativistic universe like ours? I demonstrate here that, by further modifying these theories to fit with the physics, we can overcome it. [ABSTRACT FROM AUTHOR]

The limited velocity in a geometry of Lorentzian signature seem to prevent the universe to reach thermodynamic equilibrium as suggested by the cosmic microwave background. Thus it was suggested that the universe which was initially minuscule has reached a more considerable radius in a short duration by a process known as cosmic inflation. However, to drive such a process have led to the suggestion of an ad-hoc scalar field the inflaton, which has no purpose in nature other than driving the cosmic inflation field and then stopping it once the universe reached the right size. In a recent paper it was shown that rapid expansion can occur without postulating an inflation by following Hawking's suggestion and assuming that primordially the metric of the universe had an Euclidean signature, in which case velocity is not limited and thermalization and rapid expansion are derived without the need to assume an ad-hoc field. However, while in the previous work emphasis was put on the dynamics and physical statistics of the particles in a Euclidean space versus Lorentzian space in which both spaces were given. No mathematical model was given regarding the development of current Lorentzian space-time from the early Euclidean space-time, and how fundamental problems such as the space-time singularity and the homogeneity of the CMB can be solved in the hybrid Euclidean–Lorentzian picture. This lacuna is to be rectified in this paper. [ABSTRACT FROM AUTHOR]

Gravitational memory effects are predictions of general relativity that are characterized by an observable effect that persists after the passage of gravitational waves. In recent years, they have garnered particular interest, both due to their connection to asymptotic symmetries and soft theorems and because their observation would serve as a unique test of the nonlinear nature of general relativity. Apart from the more commonly known displacement and spin memories, however, there are other memory effects predicted by Einstein's equations that are associated with more subleading terms in the asymptotic expansion of the Bondi-Sachs metric. In this paper, we write explicit expressions for these higher memory effects in terms of their charge and flux contributions. Further, by using a numerical relativity simulation of a binary black hole merger, we compute the magnitude and morphology of these terms and compare them to those of the displacement and spin memory. We find that, although these terms are interesting from a theoretical perspective, due to their small magnitude they will be particularly challenging to observe with current and future detectors. [ABSTRACT FROM AUTHOR]

In this paper, I investigate the existence of the NUT charge through the KTN spacetime using shadow observations of Sgr A*. I report that the range of my constraint for the NUT charge is between −0.5 and 0.5 for Schwarzschild-like and very slowly rotating KTN black holes. This range extends to 1.5 for spins up to −2 and −1.5 for spins up to 2 based on Keck observations for both 40° and 10° viewing angles. For VLTI observations, Schwarzschild-like and very slowly rotating KTN black holes are excluded for a 40° viewing angle, and the NUT charge is constrained to a very narrow range for a 10° viewing angle. I report that the possibility of having KTN naked singularities in Sgr A* is small, considering the uncertainties in the shadow size. [ABSTRACT FROM AUTHOR]

We model compact objects of known stellar mass and radius made of isotropic matter within Einstein's gravity. The interior solution describing hydrostatic equilibrium we are using throughout the manuscript corresponds to the Tolman IV exact analytic solution obtained a long time ago. The three free parameters of the solutions are determined by imposing the matching conditions for objects of known stellar mass and radius. Finally, using well established criteria, it is shown that, contrary to the Kohler Chao solution, the Tolman IV solution is compatible with all requirements for well-behaved and realistic solutions, except for the relativistic adiabatic index that diverges at the surface of stars. The divergence of the index Γ may be resolved, including a thin crust assuming a polytropic equation of state, which is precisely the case seen in studies of neutron stars. To the best of our knowledge, we model here for the first time the recently discovered massive pulsar PSR J0740+6620 and the strangely light HESS compact object via the Tolman IV solution. The present work may be of interest to model builders as well as a useful reference for future research. [ABSTRACT FROM AUTHOR]

In relativity, the Newtonian concepts of velocity and acceleration are observer-dependent quantities that vary with the chosen frame of reference. It is well established that in the comoving frame, cosmic expansion is currently accelerating; however, in the rest frame, this expansion is actually decelerating. In this paper, we explore the implications of this distinction. The traditional measure of cosmic acceleration, denoted by q, is derived from the comoving frame and describes the acceleration of the scale factor a for a 3D space-like homogeneous sphere. We introduce a new parameter q E representing the acceleration experienced between observers within the light cone. By comparing q E to the traditional q using observational data from Type Ia supernovae (SN) and the radial clustering of galaxies and quasars (BAO)—including the latest results from DESI2024—our analysis demonstrates that q E aligns more closely with these data. The core argument of the paper is that Λ —regardless of its origin—creates an event horizon that divides the manifold into two causally disconnected regions analogous to conditions inside a black hole's interior, thereby allowing for a rest-frame perspective q E in which cosmic expansion appears to be decelerating and the horizon acts like a friction term. Such a horizon suggests that the universe cannot maintain homogeneity outside. The observed cosmological constant Λ can then be interpreted not as a driver of new dark energy or a modification of gravity but as a boundary term exerting an attractive force, akin to a rubber band, resisting further expansion and preventing event horizon crossings. This interpretation calls for a reconsideration of current cosmological models and the assumptions underlying them. [ABSTRACT FROM AUTHOR]

We study the impact of nonextensive entropy on the thermodynamics of various black hole configurations, utilizing both Tsallis and Kaniadakis statistical frameworks. Additionally, we explore the stability of these black holes using the framework of nonextensivity. Our analysis reveals that the nonextensive Kaniadakis entropy does not result in any stability for the black holes. In contrast, the nonextensive Tsallis entropy ensures the stability of various black hole configurations. [ABSTRACT FROM AUTHOR]

Our aim in this paper is two-fold. We establish a novel geometric characterization of the Robertson–Walker (RW) spacetime and, along the process, we find a canonical form of the RW metric associated to an arbitrary timelike curve and an arbitrary space frame. A known characterization establishes that a spacetime foliated by constant curvature leaves whose orthogonal flow (the cosmological flow) is geodesic, shear-free, and with constant expansion on each leaf, is RW. We generalize this characterization by relaxing the condition on the expansion. We show it suffices to demand that the spatial gradient and Laplacian of the cosmological expansion on a single arbitrary timelike curve vanish. In General Relativity these local conditions are equivalent to demanding that the energy flux measured by the cosmological flow, as well as its divergence, are zero on a single arbitrary timelike curve. The proof allows us to construct canonically adapted coordinates to the arbitrary curve, thus well-fitted to an observer with an arbitrary motion with respect to the cosmological flow. [ABSTRACT FROM AUTHOR]

A novel axially symmetric metric is proposed to solve the Einstein field equations. This provides an analytical solution within the matter in the equatorial plane for any galaxy density profile. The solution predicts the observed increase in rotational velocity up to the edge of the galaxy's bulge. However, beyond the bulge, the rotational velocity remains constant, which contradicts the observed peak curves. The existence of the Universe is then considered by approximating the gravitational fields within the galaxy as the sum of those generated by the galaxy and the Universe. The resulting solution explicitly includes a Universe frame-dragging term, aligning with the sixth version of Mach's principle proposed by Bondi and Samuel: "inertial mass is affected by the global distribution of matter". Neglecting the presence of the Universe, stars only have a relative rotation to the bulge, and their rotational velocities monotonically increase with the radial distance r to balance the increasing mass contained in distances < r. At larger distances, the bulge's attraction and its frame-dragging effect decrease, resulting in a constant rotational velocity. When the Universe is considered, stars also have a relative rotation to the non-rotating Universe and experience an additional centrifugal force at any distance from the bulge. This component induces a decrease in rotational velocity as the gravitational influence of the bulge diminishes with r. This model predicts the observed rotational velocity curves for the galaxies M31, M101, and M81 without requiring any dark matter halo or adjustable parameters. This success substantiates Mach's idea as an alternative to the dark matter halo theory. [ABSTRACT FROM AUTHOR]

This paper presents new relativistic composite polytropic models for compact stars by simultaneously solving Einstein field equations with the polytropic state equation to simulate the spherically symmetric, static matter distribution. Using a non-uniform polytropic index, we get the Tolman–Oppenheimer–Volkoff equation for the relativistic composite polytrope (CTOV). To analyze the star's structure, we numerically solve the CTOV equation and compute the Emden and mass functions for various relativistic parameters and polytropic indices appropriate for neutron stars. The calculation results show that, as the relativistic parameter approaches zero, we recover the well-known Lane-Emden equation from the Newtonian theory of polytropic stars; thus, testing the computational code by comparing composite Newtonian models to those in the literature yields good agreement. We compute composite relativistic models for the neutron star candidates Cen X-3, SAXJ1808.4-3658, and PSR J1614-22304. We compare the findings with various existing models in the literature. Based on the accepted models for PSR J1614-22304 and Cen X-3, the star's core radius is predicted to be between 50 and 60% percent of its total radius, while we found that the radius of the core of star SAXJ1808.4-3658 is around 30% of the total radius. Our findings show that the neutron star structure may be approximated by a composite relativistic polytrope, resulting in masses and radii that are quite consistent with observation. [ABSTRACT FROM AUTHOR]

This study focuses on dynamically exploring Marder-type spacetime containing viscous Ricci dark energy within the framework of general relativity theory. To find a solution of the field equations, we use the relation between metric potentials and the average scale factor a(t) = (sinhẞ₁t), this leads to a seamless transition of the Universe from its initial decelerating phase to the current accelerating phase. Here, we have obtained the cosmological parameters and wde - w'de plane for the derived model. Also, dynamical features of the derived cosmological model are analyzed through diagrams. [ABSTRACT FROM AUTHOR]

We develop a notion of causal order on a generic manifold as independent of the underlying differential and topological structure. We show that sufficiently regular causal orders can be recovered from a distinguished algebra of sets, which plays a role analogous to that of topologies and σ algebras. We then discuss how a natural notion of measure can be associated to the algebra of causal sets. [ABSTRACT FROM AUTHOR]

The possibility of using spin connection components as basic quantization variables of a conformal version of general relativity is studied. The considered model contains gravitational degrees of freedom and a scalar dilaton field. The standard tetrad formalism is applied. Properties of spin connections in this model are analyzed. Secondary quantization of the chosen variables is performed. The gravitational part of the model action turns out to be quadratic with respect to the spin connections. So at the quantum level, the model looks trivial, i.e., without quantum self-interactions. Meanwhile the correspondence to general relativity is preserved at the classical level. [ABSTRACT FROM AUTHOR]

A renormalized group improved Schwarzschild black hole spacetime contains two quantum correction parameters. One parameter γ represents the identification of cutoff of the distance scale, and another parameter Ω stems from nonperturbative renormalization group theory. The two parameters are constrained by the data from the shadow of M87* central black hole. The dynamics of electrically charged test particles around the black hole are integrable. However, when the black hole is immersed in an external asymptotically uniform magnetic field, the dynamics are not integrable and may allow for the occurrence of chaos. Employing an explicit symplectic integrator, we survey the contributions of the two parameters to the chaotic dynamical behavior. It is found that a small change of the parameter γ constrained by the shadow of M87* black hole has an almost negligible effect on the dynamical transition of particles from order to chaos. However, a small decrease in the parameter Ω leads to an enhancement in the strength of chaos from the global phase space structure. A theoretical interpretation is given to the different contributions. The term with the parameter Ω dominates the term with the parameter γ , even if the two parameters have same values. In particular, the parameter Ω acts as a repulsive force, and its decrease means a weakening of the repulsive force or equivalently enhancing the attractive force from the black hole. On the other hand, there is a positive Lyapunov exponent that is universally given by the surface gravity of the black hole when Ω ≥ 0 is small and the external magnetic field vanishes. In this case, the horizon would influence chaotic behavior in the motion of charged particles around the black hole surrounded by the external magnetic field. This point can explain why a smaller value of the renormalization group parameter would much easily induce chaos than a larger value. [ABSTRACT FROM AUTHOR]

The problem of formulating thermodynamics in a relativistic scenario remains unresolved, although many proposals exist in the literature. The challenge arises due to the intrinsic dynamic structure of spacetime as established by the general theory of relativity. With the discovery of the physical nature of information, which underpins Landauer's principle, we believe that information theory should play a role in understanding this problem. In this work, we contribute to this endeavour by considering a relativistic communication task between two partners, Alice and Bob, in a general Lorentzian spacetime. We then assume that the receiver, Bob, reversibly operates a local heat engine powered by information, and seek to determine the maximum amount of work he can extract from this device. As Bob cannot extract work for free, by applying both Landauer's principle and the second law of thermodynamics, we establish a bound on the energy Bob must spend to acquire the information in the first place. This bound is a function of the spacetime metric and the properties of the communication channel. [ABSTRACT FROM AUTHOR]

In this work, an exact solution of Einstein's field equations in isotropic coordinates for anisotropic matter distribution is obtained by considering a particular metric choice of metric potential g rr . To check the feasibility of the model, we have investigated all the physical characteristics of a realistic star. It is found that the model is potentially stable, and the adiabatic index is greater than 4 3 . The model has been analyzed for compact star 4U 1538-52. [ABSTRACT FROM AUTHOR]

It is well-known that the global structure of every space-time model for relativistic cosmology is observationally underdetermined. In order to alleviate the severity of this underdetermination, it has been proposed that we adopt the Cosmological Principle because the Principle restricts our attention to a distinguished class of space-time models (spatially homogeneous and isotropic models). I argue that, even assuming the Cosmological Principle, the topology of space remains observationally underdetermined. Nonetheless, I argue that we can muster reasons to prefer various topological properties over others. In particular, I favor the adoption of multiply connected universe models on grounds of (i) simplicity, (ii) Machian considerations, and (iii) explanatory power. We are able to appeal to such grounds because multiply connected topologies open up the possibility of finite universe models (consistent with our best data), which in turn avoid thorny issues concerning the postulation of an actually infinite universe. [ABSTRACT FROM AUTHOR]

We consider the hypothesis that the sources of dark energy (DE) could be black holes (BHs) or more exotic objects, such as naked singularities or gravastars. We propose a definition of the presence of DE in the Universe and a criterion for what can be considered the source of this dark energy. It is based on the idea of the accelerated expansion of the Universe, which requires antigravity caused by large negative pressure. A recently proposed hypothesis, that the mass of BHs increases with time according to the same law as the volume of the part of the Universe containing it and the population of BHs can mimic DE, is examined. We demonstrate the reasons why it cannot be accepted, even if all the assumptions on which this hypothesis is based are considered true. [ABSTRACT FROM AUTHOR]

We present the solution of the Einstein field equations, in the static and spherically symmetric case, for an incompressible fluid, that has constant proper energy density at each and every point of the volume where it exists, according to a set of local observers who are stationary with respect to the fluid at each point. In the general case the fluid exists within a spherically symmetric shell with an inner vacuum-matter interface at a radial position r 1 and an outer matter-vacuum interface at a radial position r 2 in the Schwarzschild coordinate system. Therefore, in the general case there is an inner vacuum region with a repulsive singularity at the origin, just like in all other similar shell solutions. We present the parameter plane of the problem, and show that there are limits of solutions that approach the configuration of black holes, with the formation of an event horizon at the radial position r 2 . [ABSTRACT FROM AUTHOR]

In a recent series of papers new exact analytical interior spacetimes sourced by stationary rigidly rotating cylinders of fluids have been displayed. A fluid with an axially directed pressure has been first considered, then a perfect fluid, followed by a fluid with an azimuthally directed pressure, and, finally, by a fluid where the pressure is radially oriented. The perfect fluid configuration has subsequently been extended to the case of differential rotation. In the present paper, three different cases of anisotropic pressure analogous to those studied for rigidly rotating motion are considered in turn for differentially rotating fluids. General methods for generating mathematical solutions to the field equations and physically well-behaved examples are displayed for the axial and azimuthal pressure cases. As regards radial pressure fluids, four classes of solutions naturally emerge from the corresponding Einstein's equations, among which one class, after being fully integrated, exhibits physically well-behaved solutions. [ABSTRACT FROM AUTHOR]

Monitoring the time-variable geopotential identifies the mass redistribution across the Earth and reveals, e.g., climate change and availability of water resources. The features of interest are characterized by spatial and temporal scales accessible only through space missions. Among the most important gravity missions are GRACE (2002–2017), its successor GRACE-FO (since 2018), and GOCE (2009–2013), which all sense the Earth’s gravity field via the geopotential derivatives. We investigate the geopotential estimation through frequency comparisons between orbiting clocks by means of the Doppler-canceling technique, describing the clocks’ behavior in the Earth’s gravitational field via Einstein’s general relativity. The novelty of this approach lies in measuring gravity by sensing the geopotential itself. The proof of principle for the measurement is achieved through an innovative mission scenario: for the first time, the observations are collected by a probing clock in LEO. We show gravity solutions obtained by simulating an estimation problem via our proposed architecture. The results suggest that we can conceivably retrieve the geopotential coefficients with accuracy comparable to the GRACE measurement concept by employing clocks with stabilities of order 10 - 18 . Presently, terrestrial clocks can routinely attain fractional frequency stabilities of 10 - 18 , whereas spaceborne clocks are still at the 10 - 15 level. While our findings are promising, further analysis is needed to obtain more realistic indications on the feasibility of an actual mission, whose realization will be possible when clock technology reaches the required performance. The goal is for the technique investigated in this study to become a future staple for gravity field estimation. [ABSTRACT FROM AUTHOR]