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In physics literature, there is a crucial link of timelike ruled surfaces in which null curves lying with some subjects of general relativity such as the world lines of photon surfaces. Based upon this motivation, we try to see the mutual relations of null asymptotic lines and null lines of curvature in timelike ruled surfaces in dual Lorentzian 3-space D13. We suggest a system of differential equations featuring the relative characterizations of these geometric objects. Regarding to the solutions of the system, we contributed to the area by some geometric results linked to both null asymptotic lines and timelike ruled surfaces, and null lines of curvature and timelike ruled surfaces in the aforementioned space. For example, one of these results is to express the curve–surface pair in terms of Blaschke vectors. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

In this paper I raise a worry about the most extended resolutions of the problem of time of canonical quantizations of general relativity. The reason for this is that these resolutions are based on analogies with deparametrizable models for which the problem can be solved, while I argue in this paper that there are good reasons for doubting about these resolutions when the theory is not deparametrizable, which is the case of general relativity. I introduce an example of a non-deparametrizable model, a double harmonic oscillator system expressed by its Jacobi action, and argue that the problem of time for this model is not solvable, in the sense that its canonical quantization doesn't lead to the quantum theory of two harmonic oscillators and the standard resolutions of the problem of time don't work for this case. I argue that as general relativity is strongly analogous to this model, one should take seriously the view that the canonical quantization of general relativity doesn't lead to a meaningful quantum theory. Finally, I comment that this has an impact on the foundations of different approaches to quantum gravity., Comment: To be published in General Relativity and Gravitation

Super-substantivalism (of the type we’ll consider) roughly comprises two core tenets: (1) the physical properties which we attribute to matter (e.g. charge or mass) can be attributed to spacetimedirectly, with no need for matter as an extraneous carrier “on top of” spacetime; (2) spacetime is more fundamental than (ontologically prior to) matter. In the present paper, we revisit a recent argument in favour of super-substantivalism, based on General Relativity. A critique is offered that highlights the difference between (various accounts of) fundamentality and (various forms of) ontological dependence. This affords a metaphysically more perspicuous view of what super-substantivalism’s tenetsactuallyassert, and how it may be defended. We tentatively propose a re-formulation of the original argument that not only seems to apply to all classical physics, but also chimes with a standard interpretation of spacetime theories in the philosophy of physics.

A Planck-scale model for the microscopic degrees of freedom of space and gravity, based on a fundamental principle that involves fluctuating one-dimensional strands, is tested. Classical and quantum properties of space and gravitation, from the field equations of general relativity to gravitons, are deduced. Predictions include the lack of any change to general relativity at all sub-galactic scales, the validity of black hole thermodynamics, the lack of singularities and the lack of unknown observable quantum gravity effects. So far, all predictions agree with observations, including the validity of the maximum luminosity or power value $$c^5/4G$$ for all processes in nature, from microscopic to astronomical. Finally, it is shown that the strand conjecture implies a model for elementary particles that allows deducing ab-initio upper and lower limits for their mass values.

Traversable wormhole spacetimes are constructed in Palatini version of modified f(R) gravity theory. We impose that the matter supporting these spacetimes satisfies the null energy condition (NEC) and the weak energy condition (WEC). The gravitational field equations in Palatini approach are totally different to those field equations obtained in general relativity and f(R) metric approach. In this framework, by considering $$f(R)= R - \beta R^n$$ which is a given f(R) model that has consistent results with observations, the field equations have been simplified. To explicitly examine the NEC and the WEC, we take three different shape functions $$b(r)=r_0^2/r$$ , $$b(r)=\sqrt{r_0r}$$ , and $$b(r)=r_0^3/r^2$$ . Then, the existence of traversable wormholes in Palatini f(R) gravity is investigated in the absence of exotic matter. It is clearly demonstrated that the matter stress-energy tensor satisfies the NEC and the WEC.

Within the framework of the general theory of relativity, a cosmological model with expansion and rotation with a Bianchi type-IX metric is constructed for the scenario in which the gravitation sources are an anisotropic fluid, a pure radiation field, and a scalar field. The Wheeler–De Witt equation is derived, and the possibility of minisuperspace quantization is investigated.

Within the framework of general relativity, possible effects of the gravitational interactions in the Dirac spinor field are considered. It is shown that these interactions manifest locally as contact spin-spin interaction of the gravitational and spinor fields. This interaction leads to the classical rotation of particles with spin ħ/2. As a result, this leads to the appearance of local internal space-time with specific geometric properties for each particle. New effect of an increase of the mass of spinor particles due to this interaction is found. Also, an explanation of existence of a magnetic moment in the Dirac spinor particles as a result of a local electro-spin-spin interaction has been proposed.

Cosmological evolution is examined in a model with a conformally-coupled scalar field and with a cosmological constant. Models of this type arise in two types of gravitational theory: in the general theory of relativity and in scalar-tensor theories with a cosmological function. Exact solutions are found in the absence of nongravitational matter and a qualitative analysis is made of the corresponding dynamical system. It is shown that in later stages of evolution the expansion is accelerated, with a de Sitter solution as a future attractor for the general solution. There is also a special solution with exponential expansion, for which the energy density of the scalar field equals zero. In the early stages, the general solution describes a decelerated expansion similar to the radiation-dominated expansion in the general theory of relativity.

Some terms identify enigmata of today’s cosmology: “Inflation” is expected to explain the homogeneity and isotropy of the cosmic background. The repulsive force of a “dark energy” shall prevent a re-collapse of the cosmos. The additional gravitational effect of a “dark matter” was originally supposed to explain the deviations of the rotation curves of the galaxies from Kepler’s laws. Adopting a theory founded on the core notion of absolute quantum information–Protyposis–being a cosmological concept from the outset, the observed phenomena can be explained without postulating further unknown specific “particles” or “fields”. Moreover, this theory allows for a rationalization of the fact that huge black holes with their enormous jet structures, acting as “seeds” of the galaxies, are detected ever closer to the big bang. The problem of the rotation curves in the galaxies can be addressed outside of General Relativity within a Newtonian approximation: by an attenuation of the gravitational acceleration as in the modified Newtonian dynamics, or by the effect of additional invisible “particles of dark matter”, yet unknown and not yet established in natural sciences. Within the Protyposis theory, these problems are solved without having to invent a lot of parameters. The cosmology of the Protyposis causes the change of the gravitational acceleration in the vicinity of large (black hole) masses and, at the same time, avoids a recollapse of the cosmos for which a cosmological constant or “dark energy” was invented.

The National Aeronautics and Space Administration's Deep Space Quantum Link mission concept enables a unique set of science experiments by establishing robust quantum optical links across extremely long baselines. Potential mission configurations include establishing a quantum link between the Lunar Gateway moon-orbiting space station and nodes on or near the Earth. In this publication, we summarize the principal experimental goals of the Deep Space Quantum Link mission. These include long-range teleportation, tests of gravitational coupling to quantum states, and advanced tests of quantum nonlocality., Comment: 74 pages, 24 figures

Journal of high energy physics 08(8), 167 (2022). doi:10.1007/JHEP08(2022)167, We compare the path integral for transition functions in unimodular gravity and in general relativity. In unimodular gravity the cosmological constant is a property of states that are specified at the boundaries whereas in general relativity the cosmological constant is a parameter of the action. Unimodular gravity with a nondynamical background spacetime volume element has a time variable that is canonically conjugate to the cosmological constant. Wave functions depend on time and satisfy a Schrödinger equation. On the contrary, in the covariant version of unimodular gravity with a 3-form gauge field, proposed by Henneaux and Teitelboim, wave functions are time independent and satisfy a Wheeler-DeWitt equation, as in general relativity. The 3-form gauge field integrated over spacelike hypersurfaces becomes a “cosmic time” only in the semiclassical approximation. In unimodular gravity the smallness of the observed cosmological constant has to be explained as a property of the initial state., Published by SISSA, [Trieste]

The idea of a negative-pressure dark energy component in the Universe which causes an accelerated expansion in the late Universe has deep implications in models of field theory and general relativity. In this article, we survey the evidence for dark energy from cosmological observations which started from the compilation of distance-luminosity plots of Type Ia supernovae. This turned out to be consistent with the dark energy inferred from the CMB observations and large scale surveys and gave rise to the concordance $\Lambda$CDM model of cosmology. In this article, we discuss the observational evidence for dark energy from Type Ia supernovae, CMB, galaxy surveys, observations of the Sunyaev-Zeldovich effect from clusters, and lensing by clusters. We also discuss the observational discrepancy in the values of $H_0$ and $\sigma_8$ between CMB and large scale structures and discuss if varying dark energy models are able to resolve these tensions between different observations., Comment: A mini review to apear in EPJST (18 pages, 4 figures)

In the late 1990's, observations of 93 Type Ia supernovae were analysed in the framework of the FLRW cosmology assuming these to be `standard(isable) candles'. It was thus inferred that the Hubble expansion rate is accelerating as if driven by a positive Cosmological Constant $\Lambda$. This is still the only direct evidence for the `dark energy' that is the dominant component of the standard $\Lambda$CDM cosmological model. Other data such as BAO, CMB anisotropies, stellar ages, the rate of structure growth, etc are all `concordant' with this model but do not provide independent evidence for accelerated expansion. Analysis of a larger sample of 740 SNe Ia shows that these are not quite standard candles, and highlights the "corrections" applied to analyse the data in the FLRW framework. The latter holds in the reference frame in which the CMB is isotropic, whereas observations are made in our heliocentric frame in which the CMB has a large dipole anisotropy. This is assumed to be of kinematic origin i.e. due to our non-Hubble motion driven by local inhomogeneity in the matter distribution. The $\Lambda$CDM model predicts how this peculiar velocity should fall off as the averaging scale is raised and the universe becomes sensibly homogeneous. However observations of the local `bulk flow' are inconsistent with this expectation and convergence to the CMB frame is not seen. Moreover the kinematic interpretation implies a corresponding dipole in the sky distribution of high redshift quasars, which is rejected by observations at 4.9$\sigma$. The acceleration of the Hubble expansion rate is also anisotropic at 3.9$\sigma$ and aligned with the bulk flow. Thus dark energy may be an artefact of analysing data assuming that we are idealised observers in an FLRW universe, when in fact the real universe is inhomogeneous and anisotropic out to distances large enough to impact on cosmological analyses., Comment: 14 pages, 4 figures, 4 tables

Stationary configuration of a rotating electrically charged ideal fluid with self-gravitation is considered within the framework of general relativity. Barotropic equation of state of the liquid is p = we (w = const). A combination of a longitudinal magnetic field and a vortex gravitational field is considered. The boundaries of the interval of the barotropic coefficient w in which the material system under study can exist are found. It has been shown that for w > 0, the formation of wormholes is possible. Corresponding solutions describing the space-time wormhole geometry are found.

With the help of certain inequalities which we have established for multiplication in Sobolev–Slobodeckij spaces, we will give a simple proof of a version of elliptic estimate for elliptic operators that belong to a certain general class of operators denoted by $$D^{e,q}_m$$ . This version of elliptic estimate is not restricted to second order operators and the coefficients are not assumed to be smooth. Our proof is tailored to accommodate fractional Sobolev spaces and our methods are elementary in nature in the sense that they do not directly appeal to the theory of pseudo-differential operators or Littlewood–Paley theory. The elliptic estimate whose proof is presented in this paper has applications in the existence theory of several important PDEs that appear in the study of Einstein constraint equations in general relativity.

Among the known particles, the neutron is special because it provides experimental access to all of the four fundamental forces and a wide range of hypothetical interactions. Despite being unstable, free neutrons live long enough to be used as test particles in interferometric, spectroscopic and scattering experiments probing low-energy scales. Recognized already in the 1970s, fundamental concepts of quantum mechanics can be tested in neutron interferometry using silicon perfect single crystals. Besides enabling tests of uncertainty relations or Bell inequalities, neutrons offer the opportunity to observe the effects of gravity and hypothetical dark forces acting on extended matter wavefunctions. Such tests gained importance in the light of recent discoveries of inconsistencies in the understanding of cosmology and the incompatibility between quantum mechanics and general relativity. Experiments with low-energy neutrons are, thus, indispensable tools for probing fundamental physics and represent a complementary approach to particle colliders. In this Review, we discuss the history and experimental methods used at this low-energy frontier of physics and overview the current bounds and limits on quantum mechanical relations and dark energy interactions. Low-energy neutrons are key for understanding fundamental concepts of quantum mechanics and physics beyond the standard model. This Review addresses topics such as matter-wave interferometry, quantum mechanical relations and hypothetical dark sector models and interactions.

The manuscript deals with the study of the FLRW universe together with domain walls and quark matter in f(R, T) gravity where R is the Ricci scalar and T is the trace of the energy momentum tensor. We choose $$f(R,T)=R+\alpha R^2+\lambda T$$ . Exact solutions are obtained under the assumptions: (1) a constant and variable deceleration parameter of the form $$q=m-1$$ and $$q=-\frac{\alpha _3}{t^2}+\beta -1$$ , $$\alpha _3\ne 0$$ and (2) an equation of the state of the form $$p_m=(\gamma -1)\rho _m$$ and $$p_m=\frac{1}{3}(\rho _m-4B_c)$$ . The physical quantities involved in the cosmological models are obtained and analysed graphically. The solutions obtained here are most general which reduce to the solutions in general relativity, f(R, T) theory and higher derivative theory with suitable choices of the parameters.

A common physical theory connecting both quantum and classical phenomena has been developed. A particle like electron can be visualized to possess an extended structure having separate center of charge and center of mass. Using Lagrangian approach, a generalized Newton’s equation has been derived in the complex vector space. At the quantum level, it yields a generalized Schrodinger equation containing higher order relativistic terms and in the limiting case quantum Hamilton–Jacobi equation. In the classical case, neglecting spin terms, it reduces to Newtonian equation with a modified potential term. When an electron in hydrogen atom oscillates at its internal frequency, the modified potential gives the Darwin term. When the cut-off frequency is set equal to de Broglie frequency, it yields the Lamb shift in the purview of stochastic electrodynamics. At macro level, with modified central potential, the advance of perihelion has been estimated and found to be equal to the one obtained in general relativity.

In this paper, we propose a new semi-classical mechanism for the gravitational lensing of emitted light in order to investigate the evidence claiming that the general relativistic curvature interpretation of gravity is a mathematical tool to predict the physical phenomena correctly, rather than a physical phenomenon itself. Although it seems impossible for a mass-less object such as light to undergo the gravitational interaction, Einstein proposed that the effect is governed by a space–time curvature mechanism in which the mass-less light follows this curved path as its trajectory. Here, we propose a semi-classical mass induction mechanism on the light due to a gravitational field, say a black hole, in order to explain the gravitational interaction of mass-less light. Then, we derive the gravitational lensing equation due to this black hole, in the framework of semi-classical perspective. Results are surprisingly in accordance with the predictions of Einstein’s general theory of relativity for the weak field limit. This implies a novel understanding of the gravitational interaction of light.

One of the three consequences of Einstein’s theory of general relativity was the curvature of light passing near a massive body. In 1911, he published a first value of the angle of deflection of light, then a second value in 1915, equal twice the first. In the early 1920s, when he received the Nobel Prize in Physics, a violent controversy broke out over this result. It was then disclosed that the first value he had obtained in 1911 had been calculated more than a century before by a German astronomer named Johann von Soldner. The aim of this article is therefore to compare the methods used by Soldner and then by Einstein leading to this first value and to explain the importance of the doubling of this value in the framework of Einstein’s theory of general relativity. Such a consequence of this theory lies at the intersection of several scientific fields such as Mathematics, Physics, Astronomy and Philosophy.

The purpose of this article is to use an algorithm to obtain a non-static solution to the Einstein–Euler equations of a spherically symmetric matter distribution of a perfect fluid. The equations obtained make up a nonlinear system of partial derivative equations (PDE), which in the vast majority of cases is quite difficult to solve, either analytically or numerically. In this context, the spherical symmetry of space-time is very useful since it allows to establish the self-similarity of the solutions. This assumption reduces the PDEs to a set of ordinary differential equations (ODE). Therefore, the self-similarity hypothesis is very powerful in the search for non-static analytical or numerical solutions. The ODEs thus established allow defining a set of variables adjusted to the boundary conditions of the spherical distribution of matter, together with an equation of state (EOS). In this work, Tolman’s V solution has been selected as EOS. Once the numerical integration has been carried out, the variables established in the ODE and some other physical variables determined in the algorithm (density, pressure, radiation, etc.) can present damped oscillations (rebounds), depending on the initial values. This behavior is similar to that found near phase transitions in condensed matter physics, but now the mass distribution plays the role of an order parameter. This result has been obtained in other simulations of numerical relativity, where the PDE obtained from the gravitational field equations are integrated and the expression of an ultrarelativistic fluid $$\left( P=\kappa \,\rho \right) $$ . It is important to note that there is the possibility of carrying out simulations with other EOS (with electrical charge, anisotropy, etc.) with this algorithm. Many of the calculations to obtain the field equations, such as the conservation equations, were performed using the GRTensorIII computational algebra package, running on Maple 2017; as well as some Maple routines that have been used for these types of problems.

Einstein’s genius and penetrating physical intuition led to the general theory of relativity, which incorporates gravity into the geometry of spacetime. However, the theory of general relativity leads to perspectives which go far beyond the vision of its creator. Many of these insights came to light only after Einstein’s death in 1955. These developments were due to a new breed of relativists, like Penrose, Hawking and Geroch, who approached the subject with a higher degree of mathematical sophistication than earlier workers. Some of these insights were made possible because of work by Amal Kumar Raychaudhuri (AKR) who derived an equation which turned out to be a key ingredient in the singularity theorems of general relativity. This article explains AKR’s work in elementary terms.

The Nobel Prize in Physics 2020 has been divided, one half awarded to Roger Penrose for the discovery that black hole formation is a robust prediction of the general theory of relativity, and the other half jointly to Reinhard Genzel and Andrea Ghez for the discovery of a supermassive compact object at the centre of our galaxy. Here, we describe their work and put it in historical context and discuss specific advances that have been rewarded.

The equations of motion for the parametrized post-Newtonian (PPN) formalism for several S-stars close to the relativistic compact object Sgr A* at the center of the galaxy are examined. The effect of the difference in the periods of Newtonian and post-Newtonian orbits is taken into account. The period of the best approximation to the PN-orbit of the star S2 exceeds the period of the Newtonian orbit by 16 days. The PPN parameters βPPN and γPPN are measured. Bayesian methods are used for fitting the trajectories of the PPN motion. Posterior estimates of βPPN and γPPN $$ {0.97}_{-0.65}^{+0.42} $$ and $$ {0.81}_{-0.60}^{+0.46} $$ are obtained, respectively. This result confirms the prediction of the general theory of relativity for the post-Newtonian equations of motion under conditions close to Sgr A*.

Doubly warped product of Finsler manifolds is useful in theoretical physics, particularly in general relativity. In this paper, we study doubly warped product of Finsler manifolds with isotropic mean Berwald curvature or weak isotropic S-curvature.

In this paper, we present a new class of exact solutions satisfying Einstein’s field and modified TOV-equations. The thermodynamic quantities of stellar matter like anisotropic pressures, baryon density, red-shift and velocity of sound have been investigated using the embedding class I methodology with the Karmarkar condition. The solutions satisfy the static stability criterion, energy conditions, stability factor, adiabatic index and causality condition. In addition to it, we perform complete graphical analysis of neutron stars in Vela $$X-1$$ and Her $$X-1$$ in the setting of the Karmarkar space-time.

In this article, we present and analyze cosmological models with an anisotropic variable parameter. We have set up the field equations with the space time in the form of Bianchi I metric with an f(R, T) gravity. The functional form for the f(R, T) gravity has been assumed to be $$f(R,T)=R+2f(T)$$ , where R and T are, respectively, the Ricci scalar and trace of the energy–momentum tensor. Two different models are constructed with respect to the scale factors, such as power law scale factor and hybrid scale factor. Moreover, the anisotropic parameter taken here in the form of hyperbolic function further gives clarity on the behavior of equation of state parameter. It is to note that when the values of the coefficient constant vanish, the model yields the isotropic universe. For both the cases, the deceleration parameter, state finder diagnostic pair and energy conditions have been obtained and analyzed which provide physical plausibility of the models.

Within the framework of the general theory of relativity, an anisotropic cosmological model with expansion and rotation with a Bianchi type IX metric is constructed. The first stage of inflation of a Universe filled with a scalar field and an anisotropic liquid is considered. The Wheeler–De Witt equation is obtained, and the possibility of minisuperspace quantization is investigated.

Properties of an ideal self-gravitating fluid with a barotropic equation of state in the equilibrium configurations and its vortex physical fields have been studied within the framework of general theory of relativity. In this case, the gravitational field of the liquid always contains a vortex component. It has been shown that with a proper choice of the system parameters, the solution of the Einstein equations describes the space-time geometry with wormholes resulting from the action of the vortex field. The wormholes in this case have plane asymptotes.

One typically disturbs a system from equilibrium and studies its behavior to understand its stability. This procedure gives insight into the dynamics at play. It is one of the few techniques used in all areas of physics, be it Newtonian mechanics, quantum mechanics, or general relativity. We have continued this effort by disturbing black holes. We will see that a black hole chimes like a bell when it is disturbed. We will study this chiming mathematically in Schwarzschild black holes.

In this paper, we study the minimizers of curvature functionals (Willmore functional and extrinsic energy functional) subject to an area constraint in asymptotically flat manifolds. Under some certain conditions, we prove that such minimizers exist. Besides the surface theory related to the Willmore functional, the proofs also rely on the inverse mean curvature flow developed by Huisken and Ilmanen, on the positive mass theorem due to Schoen–Yau, and on the positive mass theorem for asymptotically flat manifolds with corners due to Miao and Shi–Tam. Our results may be of some interest in the General Relativity.

In this paper, we study the hyper-generalized quasi-Einstein (HGQE) warped product spaces with non-positive scalar curvature. This note deals with investigating of some geometric and physical properties of $$(HGQE)_{n}$$ manifolds. Next, we study the general relativistic viscous fluid $$(HGQE)_{4}$$ spacetimes with some physical applications. Lastly, we show the existence of $$(HGQE)_{4}$$ spacetimes by constructing a non-trivial example.

The Einstein–Klein–Gordon equations have been solved exactly for the case of a minimally coupled, plane-symmetric static massless scalar field with cosmological constant. Here, using the Riccati equation, we find additional, overlooked solutions, as well as anisotropic cosmologies derived by analytic continuation. Setting an integration constant equal to zero, the latter solutions become equivalent to known homogeneous, isotropic cosmologies featuring stiff matter. The interplay between the scalar field stress energy and cosmological constant allows several outcomes for universal evolution, including a singularity-free bounce cosmology. The Riccati equation appears to be particularly well suited for finding certain exact solutions in general relativity.

A covariant equation of motion and energy of a body with variable rest mass with dark energy taken into account in the general theory of relativity is considered on the basis of the equivalence principle.

The uncertainty on measurements, given by the Heisenberg principle, is a quantum concept usually not taken into account in General Relativity. From a cosmological point of view, several authors wonder how such a principle can be reconciled with the Big Bang singularity, but, generally, not whether it may affect the reliability of cosmological measurements. In this letter, we express the {Compton mass} as a function of the cosmological redshift. The cosmological application of the indetermination principle unveils the differences of the Hubble-Lema\^{i}tre constant value, $H_0$, as measured from the Cepheids estimates and from the Cosmic Microwave Background radiation constraints. In conclusion, the $H_0$ tension could be related to the effect of indetermination derived in comparing a kinematic with a dynamic measurement., Comment: 7 pages, 1 figure, accepted for publication in Foundations of Physics

Continuing recent efforts in extending the classical singularity theorems of General Relativity to low regularity metrics, we give a complete proof of both the Hawking and the Penrose singularity theorem for $C^1$-Lorentzian metrics - a regularity where one still has existence but not uniqueness for solutions of the geodesic equation. The proofs make use of careful estimates of the curvature of approximating smooth metrics and certain stability properties of long existence times for causal geodesics. On the way we also prove that for globally hyperbolic spacetimes with a $C^1$-metric causal geodesic completeness is $C^1$-fine stable. This improves a similar older stability result of Beem and Ehrlich where they also used the $C^1$-fine topology to measure closeness but still required smoothness of all metrics. Lastly, we include a brief appendix where we use some of the same techniques in the Riemannian case to give a proof of the classical Myers Theorem for $C^1$-metrics., Comment: 40 pages; v3: reviewer corrections, added some remarks, corrected typos; To appear in CMP

We offer to extend structural realism into the field of mind and brain studies. The naturalised metaphysics of structural realism has been defined in terms of unification of sciences. The unification program has been carried out nicely in fields of Quantum Mechanics and General Relativity. But for the structural realist metaphysics to receive a recommendation, the unification program needs to be extended to the fields of especial sciences. Our aim in the paper is twofold. On the one hand, we present a structural realist theory of the brain that is well-supported by the best theories of computational neurosciences. On the other hand, and at the same time, we provide further reason for being optimistic about the structural realism metaphysical claim which is based on the idea of unification in sciences.

In this note we survey a selection of classical results and recent advances concerning our understanding of spaces of positive scalar metrics on closed manifolds, and describe how the basic questions can be transplanted to compact manifolds with boundary, a setting that naturally connects to the study of data sets in general relativity. Special emphasis is devoted to highlighting links with nearby fields and discussing some promising future directions.

In prior work, we have argued that spacetime functionalism provides tools for clarifying the conceptual difficulties specifically linked to the emergence of spacetime in certain approaches to quantum gravity. We argue in this article that spacetime functionalism in quantum gravity is radically different from other functionalist approaches that have been suggested in quantum mechanics and general relativity: in contrast to these latter cases, it does not compete with purely interpretative alternatives, but is rather intertwined with the physical theorizing itself at the level of quantum gravity. Spacetime functionalism allows one to articulate a coherent realist perspective in the context of quantum gravity, and to relate it to a straightforward realist understanding of general relativity.

The exact solutions of the relativistic hyperbolic heat equation on a flat Friedman spacetime metric are obtained. These solutions are obtained in three cases of flat Friedman model which correspond to radiation, matter and dark energy-dominated universe models. In particular, in the dark energy-dominated universe case, a closed form solution is obtained for which, using appropriate boundary conditions, an interesting exact solution is derived. This solution suggests that the temperature of the universe drops as it expands by a scale of an exponential function.

A clock at a higher altitude ticks faster than one at a lower altitude, in accordance with Einstein’s theory of general relativity. The outstanding stability and accuracy of optical clocks, at 10−18 levels1–5, allows height differences6 of a centimetre to be measured. However, such state-of-the-art clocks have been demonstrated only in well-conditioned laboratories. Here, we demonstrate an 18-digit-precision frequency comparison in a broadcasting tower, Tokyo Skytree, by developing transportable optical lattice clocks. The tower provides the clocks with adverse conditions to test the robustness and a 450 m height difference to test the gravitational redshift at (1.4 ± 9.1) × 10−5. The result improves ground-based clock comparisons7–9 by an order of magnitude and is comparable with space experiments10,11. Our demonstration shows that optical clocks resolving centimetres are technically ready for field applications, such as monitoring spatiotemporal changes of geopotentials caused by active volcanoes or crustal deformation12 and for defining the geoid13,14, which will have an immense impact on future society. A pair of transportable optical lattice clocks with 10−18 uncertainty is developed. The relativistic redshift predicted by the theory of general relativity has been tested at the 10–5 level by the two optical clocks with a height difference of 450 m on the ground.

In 1919, the observation during a solar eclipse of the deflection of light rays from stars near the Sun decreed the validity of Einstein’s general relativity. One hundred years later, the image of the black hole M87* by the Event Horizon Telescope collaboration proved the existence of these fascinating objects on the one hand, and on the other, the validity of general relativistic magnetohydrodynamics (GRMHD) in the strong gravity regime. Numerical simulations have been used to model the accreting plasma around the black hole, whose emission is at the base of the synthetic images compared with data. Here, we briefly discuss the methods and the initialization employed for these simulations, and we briefly report the results of GRMHD axisymmetric simulations where a dynamo mechanism operates inside the disk, enhancing the magnetic field from its initial seed values up to those needed to explain the observed plasma emission.

In Beig and Simon (Commun Math Phys 144:373–390, 1992) the authors prove a uniqueness theorem for static solutions of the Einstein–Euler system which applies to fluid models whose equation of state fulfills certain conditions. In this article it is shown that the result of Beig and Simon (1992) can be applied to isotropic Vlasov matter if the gravitational potential well is shallow. To this end we first show how isotropic Vlasov matter can be described as a perfect fluid giving rise to a barotropic equation of state. This Vlasov equation of state is investigated, and it is shown analytically that the requirements of the uniqueness theorem are met for shallow potential wells. Finally the regime of shallow gravitational potential is investigated by numerical means. An example for a unique static solution is constructed, and it is compared to astrophysical objects like globular clusters. Finally we find numerical indications that solutions with deep potential wells are not unique.

Two interesting “no hole” spacetime properties (being epistemically hole free (g), not being future nakedly singular) are unstable in the fine topology.

This paper describes general relativity at the gravito-electromagnetic precision level as a constrained field theory. In this novel formulation, the gravity field comprises two auxiliary fields, a static matter field and a moving matter field. Equations of motion, continuity equation, energy conservation, field tensor, energy-momentum tensor, constraints and Lagrangian formulation are presented as a simple and unified formulation that can be useful for future research., Comment: accept by Braz. J. Phys

We analyze the role of the Mathisson–Papapetrou equations in establishing the regularities of spingravitational interaction under the conditions of ultrarelativistic motions of spinning particles in the fields of black holes and neutron stars. In recent years, these equations are extensively used in the investigation of spin-gravitational effects. At the same time, it is necessary to perform the detailed analysis of the specific features of ultrarelativistic motions of spinning particles. This is done in the present paper. We apply the representation of the Mathisson–Papapetrou equations in terms of comoving tetrads, which enables us to reveal physical foundations of the specific features of spingravitational effects for spinning particles. We also make conclusions that follow from the obtained new solutions of the Mathisson–Papapetrou equations.

In this paper, we discuss the global aspect of the geometric dynamics of volumetric expansion and its applications to the problem of the existence in the space-time of compact and complete spacelike hypersurfaces and to the global geometry of generalized Robertson–Walker space-times.

On the basis of the general theory of relativity, a solution of the spherically symmetric field with a dark energy model taken into account is proposed; both the external problem and the internal problem are considered. For a particle in the field of a collapsar on the basis of the obtained solution and also of the solution of the limiting Kerr field, the radius of circular orbits is found also with the dark energy model taken into account.

This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/., Analogue gravity systems offer many insights into gravitational phenomena, both at the classical and at the semiclassical level. The existence of an underlying Minkowskian structure (or Galilean in the non-relativistic limit) in the laboratory has been argued to directly forbid the simulation of geometries with Closed Timelike Curves (CTCs) within analogue systems. We will show that this is not strictly the case. In principle, it is possible to simulate spacetimes with CTCs whenever this does not entail the presence of a chronological horizon separating regions with CTCs from regions that do not have CTCs. We find an Analogue-gravity Chronology protection mechanism very similar in spirit to Hawking’s Chronology Protection hypothesis. We identify the universal behaviour of analogue systems near the formation of such horizons and discuss the further implications that this analysis has from an emergent gravity perspective. Furthermore, we build explicit geometries containing CTCs, for instance spacetimes constructed from two warp-drive configurations, that might be useful for future analysis, both from a theoretical and an experimental point of view. © The Author(s) 2022., Financial support was provided by the Spanish Government through the projects PID2020-118159GB-C43 and PID2020-118159GB-C44, and by the Junta de Andalucía through the project FQM219. C.B. and G.G.M. acknowledge financial support from the State Agency for Research of the Spanish MCIU through the “Center of Excellence Severo Ochoa” award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709). GGM is funded by the Spanish Government fellowship FPU20/01684.

In Hamiltonian GR, change has seemed to be missing, defined only asymptotically, or otherwise obscured at best. By construing change as essential time dependence, can one find change locally in Hamiltonian GR with spinors? This paper is motivated by tendencies in space-time philosophy to slight fermionic/spinorial matter, in Hamiltonian GR to misplace changes of time coordinate, and in treatments of the Einstein-Dirac equation to include a gratuitous local Lorentz gauge symmetry. Spatial dependence is dropped in most of the paper. To include all and only the coordinate freedom, the Einstein-Dirac equation is investigated using the Schwinger time gauge and Kibble-Deser symmetric triad condition as a $3+1$ version of the DeWitt-Ogievetsky-Polubarinov nonlinear group realization formalism that dispenses with a tetrad and local Lorentz gauge freedom. Change is the lack of a time-like stronger-than-Killing field for which the Lie derivative of the metric-spinor complex vanishes. An appropriate $3+1$-friendly form of the Rosenfeld-Anderson-Bergmann-Castellani gauge generator $G$, a tuned sum of first class-constraints, changes the canonical Lagrangian by a total derivative and implements changes of time coordinate for solutions., Forthcoming in Foundations of Physics