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The explanation of Einstein’s special theory of relativity in his original 1905 paper is examined. His analysis is confusing, as terms x, y, z, t, etc., have different meanings at various points, and he presents equations based on different and inconsistent assumptions. Adding subscripts clarifies these issues but exposes errors in his reasoning. To calculate his transformation equations, he selects a combination of equations which gives results matching the Lorentz transformation but he ignores other possible valid solutions. Also his calculations contain serious errors. Therefore, he fails to prove that his theory leads to the Lorentz equations as a unique solution. Einstein’s analysis includes “moving” clocks which show “stationary” time t, so the idea that a moving clock should run slower than a stationary clock is incompatible with his theory. Also, his calculation of time dilation contains serious errors. As a result, he fails to provide a theoretical justification for his famous “clocks paradox.” [ABSTRACT FROM AUTHOR]

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Reproducibility of results is a cornerstone of the scientific method. Scientific computing encounters two challenges when aiming for this goal. Firstly, reproducibility should not depend on details of the runtime environment, such as the compiler version or computing environment, so results are verifiable by third-parties. Secondly, different versions of software code executed in the same runtime environment should produce consistent numerical results for physical quantities. In this manuscript, we test the feasibility of reproducing scientific results obtained using the IllinoisGRMHD code that is part of an open-source community software for simulation in relativistic astrophysics, the Einstein Toolkit. We verify that numerical results of simulating a single isolated neutron star with IllinoisGRMHD can be reproduced, and compare them to results reported by the code authors in 2015. We use two different supercomputers: Expanse at SDSC, and Stampede2 at TACC. By compiling the source code archived along with the paper on both Expanse and Stampede2, we find that IllinoisGRMHD reproduces results published in its announcement paper up to errors comparable to round-off level changes in initial data parameters. We also verify that a current version of IllinoisGRMHD reproduces these results once we account for bug fixes which have occurred since the original publication. [ABSTRACT FROM AUTHOR]

Copyright of Physics Essays is the property of Physics Essays Publication and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In his groundbreaking 1905 paper on special relativity, Einstein distinguished between local and global time in inertial systems, introducing his famous definition of distant simultaneity to give physical content to the notion of global time. Over the following decade, Einstein attempted to generalize this analysis of relativistic time to include accelerated frames of reference, which, according to the principle of equivalence, should also account for time in the presence of gravity. Characteristically, Einstein's methodology during this period focused on simple, intuitively accessible physical situations, exhibiting a high degree of symmetry. However, in the final general theory of relativity, the a priori existence of such global symmetries cannot be assumed. Despite this, Einstein repeated some of his early reasoning patterns even in his 1916 review paper on general relativity and in later writings. Modern commentators have criticized these arguments as confused, invalid, and inconsistent. Here, we defend Einstein in the specific context of his use of global time and his derivations of the gravitational redshift formula. We argue that a detailed examination of Einstein's early work clarifies his later reasoning and demonstrates its consistency and validity. [ABSTRACT FROM AUTHOR]

Gravitational waves are being shown to derive directly from Newtonian dynamics for a continuous mass distribution, e.g. compressible fluids or equivalent. It is shown that the equations governing a continuous mass distribution, i.e. the inviscid Navier–Stokes equations for a general variable gravitational field g(t,x) , are equivalent to a form identical to the Maxwell equations from electromagnetism, subject to a specified condition. The consequence of this equivalence is the creation of gravity waves that propagate at a finite speed. The latter implies that Newtonian gravitation as presented in this paper is not 'spooky action at a distance' but rather is similar to electromagnetic waves propagating at finite speed, despite the apparent form appearing in the integrated field formula. In addition, this proves that, in analogy to the Maxwell equations, the Newtonian gravitation equations are Lorentz invariant for waves propagating at the speed of light. Since gravitational waves were so far derived only from Einstein's general relativity theory, it becomes appealing to check if there is a connection between the Newtonian waves presented in this paper and the general relativity type of waves at least in a certain limit of overlapping validity, i.e. as a flat-space approximation. The latter is left for follow-up research. [ABSTRACT FROM AUTHOR]

At first glance, thermodynamic properties of gravity with asymptotically AdS conditions and those with box boundary conditions, where the spatial section of the boundary is a sphere of finite radius, appear similar. Both exhibit a similar phase structure and Hawking-Page phase transition. However, when we introduce a U(1) gauge field to the system, discrepancies in thermodynamic properties between the two cases has been reported in [7] (JHEP 11 (2016) 041). In this paper, by accepting the assumption that all Euclidean saddles contribute to the partition function, I found that these discrepancies are resolved due to the contribution from the "bag of gold (BG)," which is the class of Euclidean geometries whose area of bolt is bigger than that of the boundary. As a result, the Hawking-Page phase structure is restored, with the unexpected properties that the upper bound of thermodynamic entropy is always larger than the boundary area divided by 4G when the chemical potential is non-zero, and that such high entropy states are realized at sufficiently high temperature. [ABSTRACT FROM AUTHOR]

This paper is the fourth in a series dedicated to the mathematically rigorous asymptotic analysis of gravitational radiation under astrophysically realistic set-ups. It provides an overview of the physical ideas involved in setting up the mathematical problem, the mathematical challenges that need to be overcome once the problem is posed, as well as the main new results we will obtain in upcoming work. From the physical perspective, this includes a discussion of how post-Newtonian theory provides a prediction on the gravitational radiation emitted by N infalling masses from the infinite past in the intermediate zone, i.e. up to some finite advanced time. From the mathematical perspective, we then take this prediction, together with the condition that there be no incoming radiation from I− , as a starting point to set up a scattering problem for the linearized Einstein vacuum equations around Schwarzschild and near spacelike infinity, and we outline how to solve this scattering problem and obtain the asymptotic properties of the scattering solution near i0 and I+. The full mathematical details will be presented in the sequel to this paper. This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'. [ABSTRACT FROM AUTHOR]

Recently proposed duality relates the critical level limit of WZW models to a classical three-dimensional Einstein gravity on a sphere. In this paper, we propose a dimensional reduced version of this duality. The gravity side is reduced to a Jackiw-Teitelboim (JT) gravity on S2 with a non-standard boundary term, or a BF theory with SU(2) gauge symmetry. At least in low temperature limit, these two-dimensional gravity theories completely capture the original three-dimensional gravity effect. The CFT side is reduced to a certain complex Liouville quantum mechanics (LQM) with SU(2) gauge symmetry. Our proposal gives an interesting example of a holography without boundary. We also discuss a higher-spin generalization with SU(N) gauge symmetry. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of Riemannian warped-twisted product submersions and examine their fundamental properties, including total geodesicity, total umbilicity and minimality. Additionally, we investigate the Ricci tensor of Riemannian warped-twisted product submersions, specifically about the horizontal and vertical distributions. Finally, we obtain Einstein condition for base manifold if the horizontal and vertical distributions of the ambient manifold is Einstein. [ABSTRACT FROM AUTHOR]

The main object of the present paper is to discuss about the quarter symmetric metric connection on α-Sasakian Manifold with respect to Ricci Soliton. In this paper, firstly, we discuss the quarter symmetric metric connection on α-Sasakian manifold. Secondly, we elaborate the results of quarter symmetric metric connection on α-Sasakian manifold which admits Ricci Soliton and also flourish a non-trivial example of α-sasakian manifold and validate some of our results. Thirdly, we classify certain curvature properties of Ricci α-Sasakian manifold in regard to Quarter symmetric metric connection. Finally, we show Ricci Soliton on submanifold of α-Sasakian manifold in term of Levi-Civita and quarter symmetric metric connection. [ABSTRACT FROM AUTHOR]

This research paper explores the properties of quasi-Einstein manifolds with a unit concircular generator vector field within doubly warped product structures. The paper begins by investigating the characteristics of quasi-Einstein manifolds that possess a unit concircular generator vector field. Subsequently, it analyzes the behavior of the Hessian, Riemann, and Ricci vector fields in the context of a doubly warped product. Moreover, the impact of the quasi-Einstein condition on both the doubly warped product and its factor manifolds is studied. Finally, conditions are derived to determine whether a doubly warped product satisfying the quasi-Einstein condition can be classified as a warped or a direct product. By presenting these findings, this study contributes to the comprehension of quasi-Einstein manifolds and their interactions within doubly warped product structures. [ABSTRACT FROM AUTHOR]

In this paper, we aim to characterize the sequential warped product κ -almost gradient conformal Ricci–Bourguignon soliton. We derive applications of some vector fields like conformal vector field, torse-forming vector field, torqued vector field on κ -almost conformal Ricci–Bourguignon soliton. The inheritance properties of the Einstein-like sequential warped product κ -almost gradient conformal Ricci–Bourguignon solitons of class types ℙ , , are investigated in this paper. Later we show that if M ̄ = (M 1 × f I M 2 ) × f ̄ I M 3 is a sequential warped product of a complete connected (n − 2) -dimensional Riemannian manifold M 1 and one-dimensional Riemannian manifolds I M 2 and I M 3 admitting κ -almost conformal Ricci–Bourguignon soliton, then (M 1 , g 1) becomes a (n − 2) -dimensional sphere of radius ρ = n − 2 r 1 + (μ − 1 2 (p + 2 n) + ρ R) (4 − n) . We have discovered that for a κ -almost gradient conformal Ricci–Bourguignon soliton sequential warped product, the warping functions are constants under certain conditions. [ABSTRACT FROM AUTHOR]

In this study, we characterize LP-Kenmotsu manifolds admitting *-Ricci-Yamabe solitons (*-RYSs) and gradient *-Ricci-Yamabe solitons (gradient *-RYSs). It is shown that an LP-Kenmotsu manifold of dimension n admitting a *-Ricci-Yamabe soliton obeys Poisson's equation. We also determine the necessary and sufficient conditions under which the Laplace equation is satisfied by LP-Kenmotsu manifolds. Finally, by using a non-trivial example of an LP-Kenmotsu manifold, we verify some results of our paper. [ABSTRACT FROM AUTHOR]

In the present paper, we investigate perfect fluid spacetimes and perfect fluid generalized Roberston-Walker spacetimes that contain a torse-forming vector field satisfying almost hyperbolic Ricci solitons. We show that the perfect fluid spacetimes that contain a torse-forming vector field satisfy an almost hyperbolic Ricci soliton, and we prove that a perfect fluid generalized Roberston-Walker spacetime satisfying an almost hyperbolic Ricci soliton (g, ζ, ..., µ) is an Einstein manifold. Also, we study an almost hyperbolic Ricci soliton (g, V, ..., µ) on these spacetimes when V is a conformal vector field, a torse-forming vector field, or a Ricci bi-conformal vector field. [ABSTRACT FROM AUTHOR]

Is it possible for today's man to return to the historical past several centuries or millennia and find himself among his ancestors as shown in various science fiction films such as the cult British series "Outlander" when the main heroine enters the hollow of the tree and returns in the middle ages. Is it possible to travel into the future several centuries or millennia into the future as shown by Herbert George Wells in the science fiction novel Time machine or the French film "Les Visiteurs" when the heroes of the Middle Ages travel to the future. Are there parallel worlds or multiverses in which one day future generations will travel only with advanced technologies at the speed of light like in the cult TV series Wars or Dr.No? For now, these impossible feats are possible only on movies, but scientists like Albert Einstein, Nikola Tesla, and especially Everett Hughes, Stephen Hawking, theoretically explained the probability of such hypotheses. The concepts of time travel and parallel worlds are phenomena that are mutually related and interdependent both in literature and cinema, and in other scientific cultural-artistic or entertainment works. They complement and enhance each other because the phenomenon of time travel cannot be effected if there is no other world, even assuming that it is simply a return to the past or travel to the future. In this review, we will only focus on the phenomenon of time travel. This paper is part of the research dedicated to the project Time Travel and Parallel Worlds in Cinema integrated in my doctoral thesis with the same title. [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]

In this paper, we study quintessence compact stars in the paradigm of pure Lovelock gravity. We derive the field equations using a spherically symmetric space–time. Specifically, we discuss the equivalence of Einstein's Lovelock gravity in four-dimensional space–time, Gauss–Bonnet term equivalent Lovelock gravity in seven-dimensional space–time and sixteen-dimensional Lovelock gravity by exploring the impact of the quintessence field parameter on features of compact stars in anisotropic matter fields. For matter inside the star, we use Tolman–Kuchowiz space–time. We discuss the density of the compact star and the density related to the quintessence matter field. We also explore the pressure profiles, anisotropy, speeds of sound for stability, EoS state parameters, mass-to-radius profile, compactification, gravitational and gradients for different values of N, which change the dimensions ( d = 3 N + 1 ) of pure Lovelock gravity. [ABSTRACT FROM AUTHOR]

This paper explains how the so-called Einstein locality is to be understood in the Schrödinger picture of quantum mechanics. This notion is fully compatible with the Bell non-locality exhibited by entangled states. Contrary to the belief that quantum mechanics is incomplete, it is, As a matter of fact, its overcompleteness, as exemplified by the different pictures of quantum physics, that points to the same underlying reality. [ABSTRACT FROM AUTHOR]

The modern textbook analysis of the thermal state of photons inside a three-dimensional reflective cavity is based on the three quantum numbers that characterize photon's energy eigenvalues coming out when the boundary conditions are imposed. The crucial passage from the quantum numbers to the continuous frequency is operated by introducing a three-dimensional continuous version of the three discrete quantum numbers, which leads to the energy spectral density and to the entropy spectral density. This standard analysis obscures the role of the multiplicity of energy eigenvalues associated to the same eigenfrequency. In this paper we review the past derivations of Bose's entropy spectral density and present a new analysis of energy spectral density and entropy spectral density based on the multiplicity of energy eigenvalues. Our analysis explicitly defines the eigenfrequency distribution of energy and entropy and uses it as a starting point for the passage from the discrete eigenfrequencies to the continuous frequency. [ABSTRACT FROM AUTHOR]

We present JWST and Atacama Large Millimeter/submillimeter Array (ALMA) imaging for the lensing system SPT0418−47, which includes a strongly lensed, dusty, star-forming galaxy at redshift z = 4.225 and an associated multiply imaged companion. The JWST NIRCam and MIRI imaging observations presented in this paper were acquired as part of the Early Release Science program Targeting Extremely Magnified Panchromatic Lensed Arcs and Their Extended Star formation (TEMPLATES). This data set provides robust mutiwavelength detections of stellar light in both the main (SPT0418A) and companion (SPT0418B) galaxies, while the ALMA detection of [C ii ] emission confirms that SPT0418B lies at the same redshift as SPT0418A. We infer that the projected physical separation of the two galaxies is 4.42 ± 0.05 kpc. We derive total magnifications of μ = 29 ± 1 and μ = 4.1 ± 0.7 for SPT0418A and SPT0418B, respectively. We use both prospector and cigale to derive stellar masses. We find that SPT0418A has a stellar mass of M * = 3.4 − 0.6 + 1.1 × 10 10 M ⊙ from prospector or M * = 1.5 ± 0.3 × 1010 M ⊙ from cigale. The stellar mass ratio of SPT0418A and SPT0418B is roughly between 4 and 7 ( 4.2 − 1.6 + 1.9 for prospector and 7.5 ± 3.7 for cigale). We see evidence of extended structure associated with SPT0418A that is suggestive of a tidal feature. These features, along with the close projected proximity, imply that the system is interacting. Interestingly, the star formation rates and stellar masses of both galaxies are consistent with the main sequence of star-forming galaxies at this epoch, indicating that this ongoing interaction has not noticeably elevated the star formation levels. [ABSTRACT FROM AUTHOR]

The neuroscience of creativity is built on a tacit and near universal assumption that is false. Paradoxically, this is not contentious; once made explicit, the assumption is readily conceded as false. Psychology regards creativity as made up of many complex, multifaceted, and varied cognitive and emotional processes deployed across many different domains. But we instead think of, and treat, creativity as if it were a single, separate, cohesive, and discrete thing--as in, Einstein had it. In a straightforward extension of this fallacy, cognitive neuroscientists have looked for uniquely creative cognition that (1) is distinct from all other kinds of cognition and (2) has a proprietary neural substrate. In other words, a standalone and monolithic creativity faculty in the brain that manages only creativity and all creativity. First, this paper brings into sharp focus the nature and ubiquity of this fallacy. It then outlines the alternative theoretical position that is (1) based on fundamental neural principles and (2) predicated on taking seriously the concept of creativity as complex and diverse. Like morality or secretiveness, it holds that creativity does not exist as its own, specialized entity in the brain. Instead, its neurocognitive mechanisms are distributed, embedded, and varied; that is, creativity is everywhere and multiply realizable. [ABSTRACT FROM AUTHOR]

In my paper I consider the movement of objects in „space", taking into account the idea of preserving and accumulation of change with time. I compare this view with Newton, Leibniz and Einstein's ideas of movement, space and time. To illustrate this, I represent the movement of two objects along a straight line, as well as some dependences connected to it. I also pose questions as "Why and how the things exist?" in relation to characteristics like discernibility, equality, and change. I also address faith as an integral part of science. [ABSTRACT FROM AUTHOR]

In this paper, we study the Minkowski-type inequality for asymptotically flat static manifolds (M^{n},g) with boundary and with dimension n<8 that was established by McCormick [Proc. Amer. Math. Soc. 146 (2018), pp. 4039–4046]. First, we show that any asymptotically flat static (M^{n},g) which achieves the equality and has CMC or equipotential boundary is isometric to a rotationally symmetric region of the Schwarzschild manifold. Then, we apply conformal techniques to derive a new Minkowski-type inequality for the level sets of bounded static potentials. Taken together, these provide a robust approach to detecting rotational symmetry of asymptotically flat static systems. As an application, we prove global uniqueness of static metric extensions for the Bartnik data induced by both Schwarzschild coordinate spheres and Euclidean coordinate spheres in dimension n < 8 under the natural condition of Schwarzschild stability. This generalizes an earlier result of Miao [Classical Quantum Gravity 22 (2005), pp. L53–L59]. We also establish uniqueness for equipotential photon surfaces with small Einstein-Hilbert energy. This is interesting to compare with other recent uniqueness results for static photon surfaces and black holes, e.g. see V. Agostiniani and L. Mazzieri [Comm. Math. Phys. 355 (2017), pp. 261–301], C. Cederbaum and G. J. Galloway [J. Math. Phys. 62 (2021), p. 22], and S. Raulot [Classical Quantum Gravity 38 (2021), p. 22]. [ABSTRACT FROM AUTHOR]

Einsteinian cubic gravity (ECG) is the most general theory up to cubic order in curvature, which has the same graviton spectrum as the Einstein theory. In this paper, we investigate the geodesic motions of timelike particles around the four dimensional asymptotically flat black holes in ECG, and discuss their potential applications when connecting them with recent observational results. We first explore the effects of the cubic couplings on the marginally bound orbits (MBO), innermost stable circular orbits (ISCO) and on the periodic orbits around the Einsteinian cubic black hole. We find that comparing to Schwarzschild black hole in general relativity, the cubic coupling enhances the energy as well as the angular momentum for all the bound orbits of the particles. Then, we derive the relativistic periastron precessions of the particles and give a preliminary bound on the cubic coupling employing the observational result of the S2 star's pericenter precession in SgrA*. Finally, after calculating the periodic orbits' configurations, we preliminarily evaluate the gravitational waveform radiated from several periodic orbits in one complete period of a test object which orbits a supermassive Einsteinian cubic black hole. Our studies could be helpful for us to better understand the gravitational structure of the theory with high curvatures. [ABSTRACT FROM AUTHOR]

Considering that Einstein's relation between the diffusion coefficient and the drift mobility of free randomly moving charge carriers in homogeneous materials including metals is always valid, it is shown that the effective electric force acting on free electrons in metal depends on the ratio between the kinetic free electron energy at the Fermi surface to the classical particle energy 3 kT/2. The electrical resistivity of elemental metals dependence on very low temperatures has the quadratic term, which has been explained by electron–electron scattering. In this paper, it is shown that the quadratic term of the electrical resistivity at low temperatures is caused by scattering of the free randomly moving electrons by electronic defects due to linear effective free electron scattering cross-section dependence on temperature, but not by electron–electron scattering. [ABSTRACT FROM AUTHOR]

In this paper, we study the gravitational waves of holographic QCD phase transition with hyperscaling violation. We consider an Einstein–Maxwell Dilaton background and discuss the confinement–deconfinement phase transition between thermally charged AdS and AdS black holes. We find that hyperscaling violation reduces the phase transition temperature. In a further study, we discuss the effect of hyperscaling violation on the GW spectrum. We found that the hyperscaling violation exponent suppresses the peak frequency of the total GW spectrum. Moreover, the results of the GW spectrum may be detected by IPTA, SKA, BBO, and NANOGrav. We also find that the hyperscaling violation exponent suppresses the peak frequency of the bubble-collision spectrum h 2 Ω e n v . Hyperscaling violation enhances the energy densities of the sound wave spectrum h 2 Ω s w and the MHD turbulence spectrum h 2 Ω t u r b . The total GW spectrum is dominated by the contribution of the bubble collision in runaway bubbles case. [ABSTRACT FROM AUTHOR]

In this paper, in the classical framework, the lower bounds for the sensitivities of the generalized Lemaitre Tolman Bondi metric are evaluated. The calculated lower bounds via the linear dynamical systems L∂∂θ$L_{\frac{\partial }{\partial \theta }}$, L∂∂r$L_{\frac{\partial }{\partial r}}$, and L∂∂ϕ$L_{\frac{\partial }{\partial \phi }}$ are −ln2+ln|(ṘB)2−(R′)2|−2ln|B|$-\ln 2+\ln|{(\dot{R}B)}^{2}-{(R^{\prime })}^{2}|-2\ln|B|$, 2ln|Ḃ|−ln2$2\ln|\dot{B}|-\ln 2$ and −ln2−2ln|B|+ln|(Ṙ2B2−R′2)sin2θ−B2cos2θ|$-\ln 2-2\ln|B|+ \ln |(\dot{R}^{2}B^{2}-R^{\prime 2})\sin ^{2}\theta -B^{2}\cos ^{2}\theta|$ respectively. The sensitivities and the lower sensitivities via L∂∂t$L_{\frac{\partial }{\partial t}}$ are zero are also shown. In the quantum framework, the properties of the Einstein‐Vaz shells which are the final result of the quantum gravitational collapse arising from the Lemaitre Tolman Bondi discussed by Vaz in 2014 are analyzed. In fact, Vaz showed that continued collapse to a singularity can only be obtained if one combines two independent and entire solutions of the Wheeler‐DeWitt equation. Forbidding such a combination leads naturally to matter condensing on the Schwarzschild surface during quantum collapse. In that way, an entirely new framework for black holes (BHs) has emerged. The approach of Vaz was also consistent with Einstein's idea in 1939 of the localization of the collapsing particles within a thin spherical shell. Here, following an approach of oned of us (CC), we derive the BH mass and energy spectra via a Schrodinger‐like approach, by further supporting Vaz's conclusions that instead of a spacetime singularity covered by an event horizon, the final result of the gravitational collapse is an essentially quantum object, an extremely compact "dark star". This "gravitational atom" is held up not by any degeneracy pressure but by quantum gravity in the same way that ordinary atoms are sustained by quantum mechanics. Finally, the time evolution of the Einstein‐Vaz shells is discussed. In this paper, in the classical framework, the lower bounds for the sensitivities of the generalized Lemaitre Tolman Bondi metric are evaluated. In the quantum framework, the properties of the Einstein‐Vaz shells which are the final result of the quantum gravitational collapse arising from the Lemaitre Tolman Bondi discussed by Vaz in 2014 are analyzed. In fact, Vaz showed that continued collapse to a singularity can only be obtained if one combines two independent and entire solutions of the Wheeler‐DeWitt equation. Forbidding such a combination leads naturally to matter condensing on the Schwarzschild surface during quantum collapse. In that way, an entirely new framework for black holes (BHs) has emerged. The approach of Vaz was also consistent with Einstein's idea in 1939 of the localization of the collapsing particles within a thin spherical shell. Here, following an approach of oned of us (CC), we derive the BH mass and energy spectra via a Schrodinger‐like approach, by further supporting Vaz's conclusions that instead of a spacetime singularity covered by an event horizon, the final result of the gravitational collapse is an essentially quantum object, an extremely compact "dark star". This "gravitational atom" is held up not by any degeneracy pressure but by quantum gravity in the same way that ordinary atoms are sustained by quantum mechanics. Finally, the time evolution of the Einstein‐Vaz shells is discussed. [ABSTRACT FROM AUTHOR]

In this paper we introduce the curvature tensors of (k,µ)-paracontact manifold satisfying the conditions R · W 0 = 0, P · W 0 = 0, e Z · W*0 = 0, e C · W 0 = 0 and W 0 · W 0 = 0. According these cases, (k, µ)-paracontact manifolds have been characterized such as -Einstein. [ABSTRACT FROM AUTHOR]

A hot NUT–Kerr–Newman black hole is a general stationary axisymmetric black hole. In this black hole spacetime, the dynamical equations of fermions at the horizon are modified by considering Lorentz breaking. The corrections to the Hawking temperature and Bekenstein–Hawking entropy at the horizon of the black hole are studied in depth. Based on the semiclassical theory correction, the Bekenstein–Hawking entropy of this black hole is quantum-corrected by considering the perturbation effect of the Planck constant ℏ. The latter part of this paper presents a detailed discussion of the obtained results and their physical implications. [ABSTRACT FROM AUTHOR]

The main purpose of the current paper is to study certain curvature conditions in Lorentzian para-Kenmotsu n-manifolds (briefly, (LPK)n) admitting ρ-Einstein solitons (ρ-ES). [ABSTRACT FROM AUTHOR]

In this paper, it has been proven that locally the inertial frames and gauge states of the electromagnetic field are equivalent. This proof is valid for Einstein–Maxwell theories in four-dimensional Lorentzian spacetimes. Theorems proved in a previous paper will be used. These theorems state that locally the group of electromagnetic gauge transformations is isomorphic to the local group of Lorentz transformations of a special set of tetrad vectors. The tetrad that locally and covariantly diagonalizes any non-null electromagnetic stress–energy tensor. There are in total two isomorphisms, one for each orthogonal plane of stress–energy eigenvectors. We discuss the opposite problem in this paper. What happens with local electromagnetic gauge when the test object under study is boosted by any mechanical means? We will prove that boosting matter is indistinguishable from introducing an appropriate local electromagnetic gauge transformation. [ABSTRACT FROM AUTHOR]

Between October 2021 and January 2022 an ambitious combined art and science exhibition presented a unique object-rich cosmological story at the University Library of Leuven, Belgium, as part of the Kunst Leuven KNAL! City Festival 2021 (English: BANG! Big Bang City Festival). To the Edge of Time was a transdisciplinary introduction for general audiences to one of the most famous and complex developments in science, the Big Bang theory. The exhibition presented artworks and science objects as equal partners that through curatorial placement and interpretation could fluidly convey key theoretical moments, materials, philosophical perspectives and ideas. The scientific story focused on how the groundbreaking work of the Belgian priest-astronomer Georges Lemaître bridged the insights of two of the twentieth century's other leading European scientists, German physicist Albert Einstein and the British cosmologist Stephen Hawking. Objects from their lives and archives revealed their specific ideas and processes of thinking and discovery. Artworks from leading international artists brought new material, critical and conceptual dimensions and multisensory encounters. The exhibition was the result of a curatorial collaboration between the author, British contemporary art and transdisciplinary curator Hannah Redler-Hawes, and Belgian cosmologist and former collaborator of Stephen Hawking, Professor Thomas Hertog, of KU Leuven. As guest curators, they worked with Annelies Vogels, Exhibition Coordinator of the university and Wouter Daenen of KU Leuven Libraries, and others to form a closely collaborating curatorial team. To the Edge of Time was not only the first exhibition worldwide to explore Lemaître's work through a transdisciplinary narrative, but also to place Stephen Hawking's work in a broader historical context. In the trans- and interdisciplinary exhibition field, where new commissions and collaborations between living artists and scientists have been increasing, it was somewhat unusual for a cosmology exhibition in its reliance on material culture, concentration on historical art and science objects and its combining of these with presentations of recent contemporary art and advanced theoretical physics concepts. These combinations helped to convey parallel movements of thought where neither the art nor the science were presented as derivative to each other, a key curatorial ambition. This practice-based paper, offering Redler-Hawes's personal reflections, discusses how the narrative evolved to define a shared language between the contributors. It considers, through a narrated walk-through of key objectartwork 'constellations', how the presentation generated new insights into different methods of enquiry, knowledge acquisition and making sense of our place in the cosmos, by bringing major themes in twentieth century science into dialogue with international artists working independently and in collaboration with science during the twentieth and early twenty-first centuries. [ABSTRACT FROM AUTHOR]

In his article in Science, Nicolas Gisin claimed that quantum correlations emerge from outside space–time. We explainthat they are due to space-time symmetries. This paper is a critical review of metaphysical conclusions found in many recent articles. It advocates the importance of contextuality, Einstein -causality and global symmetries. Bell tests allow only rejecting probabilistic coupling provided by a local hidden variable model, but they do not justify metaphysical speculations about quantum nonlocality and objects which know about each other's state, even when separated by large distances. The violation of Bell inequalities in physics and in cognitive science can be explained using the notion of Bohr- contextuality. If contextual variables, describing varying experimental contexts, are correctly incorporated into a probabilistic model, then the Bell–CHSH inequalities cannot be proven and nonlocal correlations may be explained in an intuitive way. We also elucidate the meaning of statistical independence assumption incorrectly called free choice, measurement independence or no- conspiracy. Since correlation does not imply causation, the violation of statistical independence should be called contextuality; it does not restrict the experimenter's freedom of choice. Therefore, contrary to what is believed, closing the freedom-of choice loophole does not close the contextuality loophole. [ABSTRACT FROM AUTHOR]

In this paper, we compute holographic Euclidean thermal correlators of the stress tensor and U(1) current from the AdS planar black hole. To this end, we set up perturbative boundary value problems for Einstein's gravity and Maxwell theory in the spirit of Gubser-Klebanov-Polyakov-Witten, with appropriate gauge fixing and regularity boundary conditions at the horizon of the black hole. The linearized Einstein equation and Maxwell equation in the black hole background are related to the Heun equation of degenerate local monodromy. Leveraging the connection relation of local solutions of the Heun equation, we partly solve the boundary value problem and obtain exact two-point thermal correlators for U(1) current and stress tensor in the scalar and shear channels. [ABSTRACT FROM AUTHOR]

The Scalar Field Dark Matter model has been known in various ways throughout its history; Fuzzy, BEC, Wave, Ultralight, Axion-like Dark Matter, etc. All of them consist in proposing that dark matter of the universe is a spinless field Φthat follows the Klein-Gordon (KG) equation of motion □Φ-dV/dΦ=0, for a given scalar field potential V. The difference between different models is sometimes the choice of the scalar field potential V. In the literature we find that people usually work in the non-relativistic, weak-field limit of the Klein- Gordon equation, where it transforms into the Schrödinger equation and the Einstein equations into the Poisson equation, reducing the KG-Einstein system, to the Schrödinger-Poisson system. In this paper, we review some of the most interesting achievements of this model from the historical point of view and its comparison with observations, showing that this model could be the last answer to the question about the nature of dark matter in the universe. [ABSTRACT FROM AUTHOR]

Recently, a "no inner (Cauchy) horizon theorem" for static black holes with non-trivial scalar hairs has been proved in Einstein–Maxwell–scalar theories and also in Einstein–Maxwell–Horndeski theories with the non-minimal coupling of a charged (complex) scalar field to Einstein tensor. In this paper, we study an extension of the theorem to the static black holes in Einstein–Maxwell–Gauss–Bonnet-scalar theories, or simply, charged Gauss–Bonnet (GB) black holes. We find that no inner horizon with charged scalar hairs is allowed for the planar ( k = 0 ) black holes, as in the case without GB term. On the other hand, for the non-planar ( k = ± 1 ) black holes, we find that the haired inner horizon can not be excluded due to GB effect generally, though we can not find a simple condition for its existence. As some explicit examples of the theorem, we study numerical GB black hole solutions with charged scalar hairs and Cauchy horizons in asymptotically anti-de Sitter space, and find good agreements with the theorem. Additionally, in an Appendix, we prove a "no-go theorem" for charged de Sitter black holes (with or without GB terms) with charged scalar hairs in arbitrary dimensions. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to investigate curvature restricted geometric properties of a warped product metric with 1-dimensional base and 3-dimensional fibre and found that such a metric is pseudosymmetric and possesses various type of pseudosymmetric structures such as, Ricci generalized pseudosymmetry, Ricci generalized projective pseudosymmetry, Ricci generalized concircular pseudosymmetry (W ⋅ R = fRQ(S,R)), pseudosymmetry due to conharmonic curvature tensor (K #8901; R = fRQ(g,R)), semisymmetry due to conharmonic curvature tensor (R #8901; K = 0) etc. Later, it is also found that the warped product metric is an Einstein manifold of degree 2 and Ricci tensor has quasi-Einstein nature. Finally, the novelty of the work is that the energy momentum tensor of the metric has also pseudosymmetric nature. [ABSTRACT FROM AUTHOR]

The object of the present paper is to characterize two classes of almost Kenmotsu manifolds admitting almost η-Ricci solitons. In this context we have shown that in a (k, μ) and (k, μ)′-almost Kenmotsu manifold admitting an almost η-Ricci soliton the curvature conditions (i) the manifold is Einstein, (ii) the manifold is Ricci symmetric (∇S = 0), (iii) the manifold is Ricci semisymmetric (R · S = 0) and (iv) the manifold is projective Ricci semisymmetric (P · S = 0) are equivalent. Also we have shown that the curvature condition Q · P = 0 in a (k, μ)-almost Kenmotsu manifold admitting an almost η-Ricci soliton holds if and only if the manifold is locally isometric to the hyperbolic space H2n+1(-1) and if a (k, μ)′-almost Kenmotsu manifold admitting an almost η-Ricci soliton satisfies the curvature condition Q · R = 0, then it is locally isometric to the Riemannian product Hn+1(-4) × Rn. [ABSTRACT FROM AUTHOR]

This paper investigates charged black holes within the framework of quintic quasi-topological gravity, focusing on their thermodynamics, conserved quantities, and stability. We construct numerical solutions and explore their thermodynamic properties, supplemented by the study of analytically solvable special cases. By verifying the first law of thermodynamics, we validate our approach and compare our findings to those of Einstein gravity. The physical properties of the solutions are examined across anti-de Sitter, de Sitter, and flat spacetime backgrounds. Our analysis reveals that anti-de Sitter solutions demonstrate thermal stability, while de Sitter and flat solutions lack this property. Finally, we discuss the implications of our results and propose potential avenues for future research in this field. [ABSTRACT FROM AUTHOR]

We show that Einstein's conformal gravity can explain, simply, and on the geometric ground, galactic rotation curves, without the need to introduce any modification in both the gravitational as well as in the matter sector of the theory. The geometry of each galaxy is described by a metric obtained, making a singular rescaling of Schwarzschild's spacetime. The new exact solution, asymptotically anti-de Sitter, manifests an unattainable singularity at infinity that cannot be reached in finite proper time; namely, the spacetime is geodetically complete. It deserves to be noticed that, in this paper, we have a different opinion from the usual one. Indeed, instead of making the metric singularity-free, we make it apparently but harmlessly even more singular than Schwarzschild's. Finally, it is crucial to point out that Weyl's conformal symmetry is spontaneously broken into the new singular vacuum rather than the asymptotically flat Schwarzschild's one. The metric is unique according to the null energy condition, the zero acceleration for photons in the Newtonian regime, and the homogeneity of the Universe at large scales. Once the matter is conformally coupled to gravity, the orbital velocity for a probe star in the galaxy turns out to be asymptotically constant consistent with the observations and the Tully–Fisher relation. Therefore, we compare our model with a sample of 175 galaxies and show that our velocity profile very well interpolates the galactic rotation curves after a proper choice of the only free parameter in the metric. The mass-to-luminosity ratios of galaxies turn out to be close to 1, consistent with the absence of dark matter. [ABSTRACT FROM AUTHOR]

In this paper, an optimal lower bound is given for the Submanifold Dirac operator in terms of the trace of an Energy−Momentum tensor, scalar curvature and mean curvature. In the equality case, it is proven that the submanifold is Einstein if the normal bundle is flat. [ABSTRACT FROM AUTHOR]

The goal of this paper is to investigate complete noncompact warped product gradient Ricci solitons. Nonexistence results, estimates for the warping function and for its gradient are proven. When the soliton is steady or expanding these nonexistence results generalize to a broader context certain estimates and rigidity obtained when studying warped product Einstein manifolds. When the soliton is shrinking, it is presented as a nonexistence theorem with no counterpart in the Einstein case, which is proved using properties of the first eigenvalue of a weighted Laplacian. [ABSTRACT FROM AUTHOR]

In this paper, we explore a set of geometric properties of Mixed Super Quasi-Einstein (MSQE) manifolds and provide examples of both Riemannian and Lorentzian MSQE manifolds to demonstrate their existence. Furthermore, we examine MSQE spacetimes in the context of the space-matter tensor, discussing several related properties. Finally, we establish the existence of an MSQE spacetime through a nontrivial example. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a Lichnerowicz-type formula for J -Witten deformation and give the proof of the Kastler–Kalau–Walze-type theorems associated with J -Witten deformation on four-dimensional and six-dimensional almost product Riemannian manifold with (respectively, without) boundary. We give an explanation of the Einstein–Hilbert action for J -Witten deformation on four-dimensional manifold with boundary. [ABSTRACT FROM AUTHOR]

In this paper, we will discuss an alternative theory for the origin of dark matter and dark energy based on the new concept of tetrad gauge states of spacetime. The new tetrads already introduced new physics since it has been proved that local electromagnetic gauge transformations can boost the local tetrad fields in a four-dimensional curved Lorentz spacetime. It is within this context that we will present a different qualitative explanation for the so-called dark matter and dark energy and new possible topological solutions of a galactic nature for Einstein–Maxwell spacetimes in its relation to dark matter and new possible topological solutions of a cosmological nature for Einstein–Maxwell spacetimes in its relation to dark energy. [ABSTRACT FROM AUTHOR]

Dabrowski et al. [Spectral metric and Einstein functionals for Hodge–Dirac operator, preprint (2023), arXiv:2307.14877] gave spectral Einstein bilinear functionals of differential forms for the Hodge–Dirac operator d + δ on an oriented even-dimensional Riemannian manifold. In this paper, we generalize the results of Dabrowski et al. to the cases of 4-dimensional oriented Riemannian manifolds with boundary. Furthermore, we give the proof of Dabrowski–Sitarz–Zalecki-type theorems associated with the Hodge–Dirac operator for manifolds with boundary. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel curvature tensor called the 풦-curvature tensor, which is formed by combining the Weyl tensor and the 풲2-curvature tensor. It is proved that a semi-Riemannian manifold with traceless 풦-curvature tensor is Einstein, while a 풦-curvature flat semi-Riemannian manifold exhibits constant sectional curvature. We show that a space-time with traceless 풦-curvature tensor or 풦-curvature flat represents dark energy era. A semi-Riemannian manifold with divergence-free 풦-curvature tensor is Weyl harmonic. In a space-time where the 풦-curvature tensor is of divergence-free, both the isotropic pressure and energy density are constants. Under certain conditions, it is shown that a pseudo-풦-symmetric semi-Riemannian manifold reduces to a pseudo-Riemannian manifold. It is demonstrated that pseudo-풦-symmetric space-times can be regarded as generalized Robertson–Walker (GRW) space-times. Finally, a concrete example of pseudo-풦-symmetric semi-Riemannian manifolds is presented. [ABSTRACT FROM AUTHOR]

In this paper, we develop an extended space-time geometry that includes an internal space built with division octonions with realization via Pauli matrices and Zorn (vectorial) matrices. Here, we extend a former field theory that used split octonion algebra to a division octonion algebra on a non-Riemannian manifold. The octonionic algebra is the last possible algebra allowed by the Hurwitz theorem. The interpretation of the “octonionic field” in this division octonionic algebra is not straightforward, however it behaves in a similar way to the quaternionic Yang–Mills fields. Former work suggests that this Yang–Mills-like octonionic field is associated with the field governing quarks within nucleons. In this work, we discover that the inclusion of octonionic fields in the geometry of an internal space necessarily excludes the quaternionic (Yang–Mills) fields in an extended non-Riemannian geometry. This is not what is expected from the standpoint of a “unified” field theory, which leads us to propose a different approach to Einstein’s unified field theory. [ABSTRACT FROM AUTHOR]

The complete title of this paper should be “The geometry of the constant gravitational field or how to switch from the mechanical Lagrangian to a geometric Lagrangian” and in this abstract we sketch why. To begin with, let us say that Einstein managed to integrate the constant gravitational field in the special theory of relativity, obtaining a metric whose geodesics are locally parabolas. The existence of a similar metric deduced from the considerations of Newtonian mechanics is somehow obstructed by the Lagrangian involved in the description of the constant gravitational field. Therefore, we need to explain how the mechanical Lagrangian above which is not suitable for a metric description of the constant gravitational field can be switched into a geometrical Lagrangian having the same geodesics and suitable for the metric description of the constant gravitational field. The geometric method found by us is related to a parabolic type of transformations. A consequence of the previous method can be applied for the study of bending of light rays in a constant gravitational field. [ABSTRACT FROM AUTHOR]