Spacetime Metric Research Articles

Anisotropic stellar model in F(T,𝒯 ) gravity under the Karmarkar condition

In this study, we have explored an anisotropic stellar configuration by applying the Karmarkar condition in the framework of [Formula: see text] [where [Formula: see text] and [Formula: see text] stand for torsion and trace of energy–momentum tensor (EMT)] gravity. We have developed field equations of [Formula: see text] gravity for a spherically symmetric line element and considered a viable [Formula: see text] model, i.e. [Formula: see text] (where [Formula: see text] and [Formula: see text] are arbitrary constants) for meaningful results. Following [S. K. Maurya, B. S. Ratanpal and M. Govender, Ann. Phys. 382 (2017) 36], a spherically symmetric solution of embedding class I has been explored which resulted into a generalized compact stellar model. For the evaluation of unknown parameters, we use the matching conditions at the boundary by taking spherical space-time metric as interior and Schwarzschild space-time solution as exterior space-time metric. The viability of our proposed model is checked by exploring the nature of thermodynamical variables ([Formula: see text], [Formula: see text], [Formula: see text]), anisotropy, energy condition, Tolman–Oppenheimer–Volkov (TOV) forces, Abreu condition, equation of state parameters and adiabatic index taking the observational data of different compact stars like PSR J1416-2230, 4U 1608-52, Cen X-3, EXO 1785-248 and SMC X-1. Our stellar model is found.

Non-commutativity and non-inertial effects on a scalar field in a cosmic string space-time: I. Klein–Gordon oscillator

We analyse the Klein–Gordon oscillator in a cosmic string space-time and study the effects stemming from the rotating frame and non-commutativity in momentum space. We show that the latter mimics a constant magnetic field, imparting physical interpretation to the setup. The field equation for the scalar field is solved via separations of variables, and we obtain quantization of energy and angular momentum. The space-time metric is non-degenerate as long as the particle is confined within a hard-wall, whose position depends on the rotation frame velocity and the string mass parameter. We investigate the energy quantization both for a finite hard-wall (numerical evaluation) and in the limit of an infinite hard-wall (analytical treatment). We stress the effect of non-commutativity upon the energy quantization in each case.

Accurate Determination of Hubble Attenuation and Amplification in Expanding and Contracting Cold-Atom Universes.

In the expanding universe, relativistic scalar fields are thought to be attenuated by "Hubble friction," which results from the dilation of the underlying spacetime metric. By contrast, in a contracting universe this pseudofriction would lead to amplification. Here, we experimentally measure, with fivefold better accuracy, both Hubble attenuation and amplification in expanding and contracting toroidally shaped Bose-Einstein condensates, in which phonons are analogous to cosmological scalar fields. We find that the observed attenuation or amplification depends on the temporal phase of the phonon field, which is only possible for nonadiabatic dynamics. The measured strength of the Hubble friction disagrees with recent theory [Gomez Llorente etal., Phys. Rev. A 100, 043613 (2019)PLRAAN2469-992610.1103/PhysRevA.100.043613 and Eckel etal., SciPost Phys. 10, 64 (2021)SPCHCW2542-465310.21468/SciPostPhys.10.3.064].

Higher-dimensional black holes with multiple equal rotations

We study a limit of the Kerr-(A)dS spacetime in a general dimension where an arbitrary number of its rotational parameters is set equal. The resulting metric after the limit formally splits into two parts - the first part has the form of the Kerr-NUT-(A)dS metric analogous to the metric of the entire spacetime, but only for the directions not subject to the limit, and the second part can be interpreted as the K\"{a}hler metrics. However, this separation is not integrable, thus it does not lead to a product of independent manifolds. We also reconstruct the original number of explicit and hidden symmetries associated with Killing vectors and Killing tensors. Therefore, the resulting spacetime represents a special subcase of the generalized Kerr-NUT-(A)dS metric that retains the full Killing tower of symmetries. In $D=6$, we present evidence of an enhanced symmetry structure after the limit. Namely, we find additional Killing vectors and show that one of the Killing tensors becomes reducible as it can be decomposed into Killing vectors.

Black Hole Surface Gravity in Doubly Special Relativity Geometries

In a quantum gravity theory, spacetime at mesoscopic scales can acquire a novel structure very different from the classical concept of general relativity. A way to effectively characterize the quantum nature of spacetime is through a momentum dependent space-time metric. There is a vast literature showing that this geometry is related to relativistic deformed kinematics, which is precisely a way to capture residual effects of a quantum gravity theory. In this work, we study the notion of surface gravity in a momentum dependent Schwarzschild black hole geometry. We show that using the two main notions of surface gravity in general relativity we obtain a momentum independent result. However, there are several definitions of surface gravity, all of them equivalent in general relativity when there is a Killing horizon. We show that in our scheme, despite the persistence of a Killing horizon, these alternative notions only agree in a very particular momentum basis, obtained in a previous work, so further supporting its physical relevance.

Classification of Kerr–de Sitter-like spacetimes with conformally flat I in all dimensions

Using asymptotic characterization results of spacetimes at conformal infinity, we prove that Kerr-Schild-de Sitter spacetimes are in one-to-one correspondence with spacetimes in the Kerr-de Sitter-like class with conformally flat $\mathscr{I}$. Kerr-Schild-de Sitter are spacetimes of Kerr-Schild form with de Sitter background that solve the $(\Lambda>0)$-vacuum Einstein equations and admit a smooth conformal compactification sharing $\mathscr{I}$ with the background metric. Kerr-de Sitter-like metrics with conformally flat $\mathscr{I}$ are a generalization of the Kerr-de Sitter metrics, defined originally in four spacetime dimensions and extended here to all dimensions in terms of their initial data at null infinity. We explicitly construct all metrics in this class as limits or analytic extensions of Kerr-de Sitter. The structure of limits is inferred from corresponding limits of the asymptotic data, which appear to be hard to guess from the spacetime metrics.

The constraints of post-quantum classical gravity

We study a class of theories in which space-time is treated classically, while interacting with quantum fields. These circumvent various no-go theorems and the pathologies of semi-classical gravity, by being linear in the density matrix and phase-space density. The theory can either be considered fundamental or as an effective theory where the classical limit is taken of space-time. The theories have the dynamics of general relativity as their classical limit and provide a way to study the back-action of quantum fields on the space-time metric. The theory is invariant under spatial diffeomorphisms, and here, we provide a methodology to derive the constraint equations of such a theory by imposing invariance of the dynamics under time-reparametrization invariance. This leads to generalisations of the Hamiltonian and momentum constraints. We compute the constraint algebra for a wide class of realisations of the theory (the “discrete class”) in the case of a quantum scalar field interacting with gravity. We find that the algebra doesn’t close without additional constraints, although these do not necessarily reduce the number of local degrees of freedom.

Nonlinear electromagnetic fields in strictly stationary spacetimes

We prove two theorems which imply that any stationary nonlinear electromagnetic field obeying a dominant energy condition in a strictly stationary, everywhere regular, asymptotically flat spacetime must be either trivial or a stealth field. The first theorem holds in static spacetimes and is independent of the gravitational part of the action, as long as the coupling of the electromagnetic field to the gravitational field is minimal. The second theorem assumes Einstein--Hilbert gravitational action and relies on the positive energy theorem, but does not assume that the spacetime metric is static. In addition, we discuss possible generalizations of these results, to theories with charged matter, as well as higher-dimensional nonlinear electromagnetic fields.

Relativistic extended uncertainty principle from spacetime curvature

The investigations presented in this study are directed at relativistic modifications of the uncertainty relation derived from the curvature of the background spacetime. These findings generalize previous work that is recovered in the nonrelativistic limit. Applying the $3+1$ splitting in accordance with the ADM formalism, we find the relativistic physical momentum operator and compute its standard deviation for wave functions confined to a geodesic ball on a spacelike hypersurface. Its radius can then be understood as a measure of position uncertainty. Under the assumption of small position uncertainties in comparison to background curvature length scales, we obtain the corresponding corrections to the uncertainty relation in flat space. Those depend on the Ricci scalar of the effective spatial metric, the particle is moving on, and, if there are nonvanishing time-space components of the spacetime metric, there are gradients of the shift vector and the lapse function. Interestingly, this result is applicable not only to massive but also to massless particles. Over all, this is not a covariant, yet a consistently general relativistic approach. We further speculate on a possible covariant extension.

The Progenitor of the Big Bang and Its Connection to the Flatness and Acceleration of the Universe

It was argued that old and massive neutron stars end up as black objects that are made of purely incompressible superconducting gluon-quark superfluid matter (henceforth SuSu-objects). Based on theoretical investigations and numerical solving of the field equations with time-dependent spacetime topologies, I argue that a dense cluster of SuSu-objects at the background of flat spacetime that merged smoothly is a reliable candidate for the progenitor of the big bang. Here, we present and use a new time-dependent spacetime metric, which unifies the metrics of Minkowski, Schwarzschild, and Friedmann as well as a modified TOV-equation for modeling dynamical contractions of relativistic objects. Had the progenitor undergone an abrupt decay, a hadronizing front forms at its surface and starts propagating from outside-to-inside, thereby hadronizing its entire content and changing the topology of the embedding spacetime from a flat into a dynamically expanding curved one. For an observer located at the center of the progenitor, H0, the universe would be seen as isotropic and homogeneous, implying therefore that the last big bang event must have occurred in our neighborhood. For the curved spacetime re-converges into a flat one, whereas the outward-propagation topological front, which separates the enclosed curved spacetime from the exterior flat one, would appear spatially and temporally accelerating outwards. The here-presented scenario suggests possible solutions to the flatness problem, the origin of acceleration of the universe and the pronounced activities of high redshift QSOs. We anticipate that future observations by the James-Webb-Telescope to support our scenario when active QSOs with z >12 would be detected.

Resilience Assessment and Improvement for Cyber-Physical Power Systems Under Typhoon Disasters

The cyber-physical deep coupling makes power systems face more risks under small-probability and high-risk typhoon disasters. Resilience describes the ability of cyber-physical power system (CPPS) withstanding extreme disasters and resuming normal operation. To improve the resilience assessment and analysis method of CPPS, first, a CPPS resilience assessment framework that considers the space-time metrics of disasters and the interactions of information systems and power grids is proposed, including fault scenarios extraction, response and recovery analysis, quantitative assessment of resilience. Second, from the perspective of the geographical coupling between OPGW and transmission lines and the control coupling between automatic generation control system (AGC), substation automation system (SAS) and power system, the interaction of information flow and energy flow during the failure period is analyzed. The network flow theory is used to establish an information network traffic model to describe the operating status of the information system at each stage. On this basis, a mixed integer linear programming model for DC optimal power flow considering the information network constraints and a multi-stage bi-level model for cyber-physical collaborative recovery are established. Finally, we take the IEEERTS-79 system as an example to show that the proposed method can improve the quantization accuracy comparing with the assessment method of the conventional power system, and evaluate the enhancement of typical measures at different stages.

Tunneling effect of <inline-formula><tex-math id="M2">\begin{document}$ \mathbf{S}\mathbf{L}\left(\mathit{n}, \mathit{R}\right) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221415_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20221415_M2.png"/></alternatives></inline-formula> Toda black hole

The SL(<i>n</i>,<i>R</i>) Toda black hole is an ideal field for us to study black hole physics because of its excellent mathematical structure and high symmetry. This work is mainly to study the Hawking radiation of SL(<i>n</i>,<i>R</i>) Toda black hole and and the problem about its related black hole information loss . For simplicity, we only consider the Hawking radiation by calculating the tunneling effect of particles with zero rest mass near the event horizon under the four-dimensional static spherical symmetric SL(<i>n</i>,<i>R</i>) Toda black hole. In the process of particle tunneling through the event horizon of the black hole, due to the conservation of energy, the mass of black hole will be changed, which will cause the event horizon to shrink. Therefore, the reaction of tunneling particles to the background space-time leads to the dynamic change of spacetime metric, that is, the self-gravitational action of the particles generates the tunneling barrier. The tunneling probability of the particle passing through the event horizon depends on the change of the black hole entropy before and after the particle exits. Under certain conditions, our results are consistent with those of RN black holes and Schwartz black holes, and the calculation results once again support the tunneling model proposed by Parikh and Wilczek. This semi-classical image shows that the new black hole radiation spectrum is not a pure heat spectrum, but there is a small deviation from the pure thermal spectrum. From the knowledge of probability theory, it can be proved that there is a correlation process between non-thermal spectra. According to the Shannon entropy definition, the black hole entropy is analogous to Shannon information entropy. We calculate the SL(<i>n</i>,<i>R</i>) Toda black hole information paradox, and find that the correlation between the particles emitted from black hole can carry information and keep the information of black hole unchanged. The specific source of this correlation, as well as the generation mechanism, remains to be further studied. The research on the problem about black hole information loss reveals that information conservation remains true when gravitational correlations among Hawking radiations are properly taken into account. Information conservation principle thus states that the Hawking radiation is unitary, which shows that the dynamics of a black hole obeys the laws of quantum mechanics. Since a black hole is a result of general relativity, the unitarity of a black hole definitely indicates the possibility of a unified gravity and quantum mechanics.

Circuit realization of a tilted Dirac cone: Platform for fabrication of curved spacetime geometry on a chip

We present an $LC$ circuit model that supports a tilted ``Dirac cone'' in its spectrum. The tilt of the Dirac cone is specified by the parameters of the model consisting of mutual inductance between the neighboring sites and a capacitance ${C}_{0}$ at every lattice site. These parameters can be completely measured by impedance spectroscopy. Given that a tilted Dirac cone can be described by a background spacetime metric, the impedance spectroscopy can perfectly provide (local) information about the metric of the spacetime. Nonuniform spatial dependence of the mutual inductance or capacitance induces a nontrivial geometrical structure on the emergent spacetime. Our work extends the range of usefulness of circuit models to emulate nontrivial spacetime structures.

Blázquez-Salcedo–Knoll–Radu wormholes are not solutions to the Einstein-Dirac-Maxwell equations

Recently, Bl\'azquez-Salcedo, Knoll, and Radu (BSKR) have given a class of static, spherically symmetric, traversable wormhole spacetimes with Dirac and Maxwell fields. The BSKR wormholes are obtained by joining a classical solution to the Einstein-Dirac-Maxwell (EDM) equations on the "up" side of the wormhole ($r \geq 0$) to a corresponding solution on the "down" side of the wormhole ($r \leq 0$). However, it can be seen that the BSKR metric fails to be $C^3$ on the wormhole throat at $r=0$. We prove that if the matching were done in such a way that the resulting spacetime metric, Dirac field, and Maxwell field composed a solution to the EDM equations in a neighborhood of $r=0$, then all of the fields would be smooth at $r=0$ in a suitable gauge. Thus, the BSKR wormholes cannot be solutions to the EDM equations. The failure of the BSKR wormholes to solve the EDM equations arises both from the failure of the Maxwell field to satisfy the required matching conditions (which implies the presence of an additional shell of charged matter at $r=0$) and, more significantly, from the failure of the Dirac field to satisfy required matching conditions (which implies the presence of a spurious source term for the Dirac field at $r=0$.

Schwarzschild-like black hole with a topological defect in bumblebee gravity

In this paper, we derive an exact black hole spacetime metric in the Einstein–Hilbert–Bumblebee (EHB) gravity around global monopole field. We study the horizon, temperature, and the photon sphere of the black hole. Using the null geodesics equation, we obtain the shadow cast by the Schwarzschild-like black hole with a topological defect in bumblebee gravity. Interestingly, the radius of shadow of the black hole increases with increase in the global monopole parameter. We also visualize the shadows and energy emission rates for different values of parameters. Moreover, using the Gauss–Bonnet theorem, we calculate the deflection angle in weak field limits and we discuss the possibility of testing the effect of global monopole field and bumblebee field, on a weak deflection angle. We find that the global monopole parameter and also Lorentz symmetry breaking parameter has an increasing effect on the deflection angle.

The Relation between General Relativity’s Metrics and Special Relativity’s Gravitational Scalar Generalized Potentials and Case Studies on the Schwarzschild Metric, Teleparallel Gravity, and Newtonian Potential

This paper shows that gravitational results of general relativity (GR) can be reached by using special relativity (SR) via a SR Lagrangian that derives from the corresponding GR time dilation and vice versa. It also presents a new SR gravitational central scalar generalized potential V=V(r,r.,ϕ.), where r is the distance from the center of gravity and r.,ϕ. are the radial and angular velocity, respectively. This is associated with the Schwarzschild GR time dilation from where a SR scalar generalized potential is obtained, which is exactly equivalent to the Schwarzschild metric. Thus, the Precession of Mercury’s Perihelion, the Gravitational Deflection of Light, the Shapiro time delay, the Gravitational Red Shift, etc., are explained with the use of SR only. The techniques used in this paper can be applied to any GR spacetime metric, Teleparallel Gravity, etc., in order to obtain the corresponding SR gravitational scalar generalized potential and vice versa. Thus, the case study of Newtonian Gravitational Potential according to SR leads to the corresponding non-Riemannian metric of GR. Finally, it is shown that the mainstream consideration of the Gravitational Red Shift contains two approximations, which are valid in weak gravitational fields only.

Static Perfect Fluid Space-Time on Almost Kenmotsu Manifolds

In this work, we intend to investigate the characteristics of static perfect fluid space-time metrics on almost Kenmotsu manifolds. At first we prove that if a Kenmotsu manifold $M$ is the spatial factor of static perfect fluid space-time then it is $\eta$-Einstein. Moreover, if the Reeb vector field $\xi$ leaves the scalar curvature invariant, then $M$ is Einstein. Next we consider static perfect fluid space-time on almost Kenmotsu $(\kappa,\mu)'$-manifolds and give some characteristics under certain conditions.

Absence of covariant singularities in pure gravity

The assumptions of the Hawking–Penrose singularity theorem are not covariant under field redefinitions. Following the works on the covariant formulation of quantum field theory initiated by Vilkovisky and DeWitt in the 80s, we propose to study singularities in field space, where the spacetime metric is treated as a coordinate along with the other fields in the theory. From this viewpoint, a spacetime singularity might be just a singularity in the field-space coordinates, analogously to the standard coordinate singularities in General Relativity. Objects invariant under field-space coordinate transformations can then reveal whether certain spacetime singularity is indeed singular. We recall that observables in quantum field theory are scalar functionals in field space. Therefore, in principle, spacetime singularities corresponding to regular field-space curvature invariants would not affect physical observables. In this paper, we show that the field-space Kretschmann scalar for a certain choice of the DeWitt field-space metric is everywhere finite. This fact could be interpreted as an indication that no singularities actually exist in pure gravity for any gravitational action. In particular, all vacuum singularities of General Relativity result from an unhappy choice of field variables. The extension to the case in which matter fields are present, as required by singularity theorems, is left for future development.

Spacetime expansion in the presence of a background velocity field

In this article, we introduce a new metric assuming an additional velocity-based term in a spacetime metric. Although the inclusion of this additional phrase can indicate that the Lorentz symmetry has broken, the results of null geodesics demonstrate that the amount of variation in the speed of light is considerably smaller than what can be observed. This article delves into the primary use of this additional phrase in the expansion development of Minkowski and de Sitter spacetimes. The findings indicate that multiple versions of the velocity function may explain the universe's initial explosion and expansion behavior even before the inflation epoch, the inflation itself, and the universe's positive acceleration in late time cosmology without dark matter or dark energy. These models can also rebuild primordial black holes in the early universe as an alternative to dark matter.

Wave packet treatment of neutrino flavor oscillations in various spacetimes

We study the effect of gravity on neutrino flavor oscillations when each mass eigenstate is described by a wave packet instead of a plane wave. Two different approaches for implementing the wave packet formalism in the study of neutrino flavor oscillations in curved spacetime are examined. We work with a general static and spherically symmetric spacetime before applying our results to a few spacetime metrics of interest. We first focus on general relativity by examining the effect of the exterior and interior Schwarzschild solutions, as well as the de Sitter-Schwarzschild metric, and then we examine selected metrics from modified gravity models.