Symmetric Spacetimes Research Articles

A note on almost pseudo symmetric spacetimes with certain application to f(R), gravity

A note on almost pseudo symmetric spacetimes with certain application to f(R), gravity

The non-minimally coupled symmetric teleparallel gravity with electromagnetic field

We construct a symmetric teleparallel gravity model which is non-minimally coupled with electromagnetic field in four dimensions inspired by its Riemannian equivalent. We derive the field equations by taking the variation of this model, which is written here for the first time. Then, we find some classes of spherically symmetric static solutions by the coincident gauge of symmetric teleparallel spacetime.

Generalized approach for the perturbative dynamical braneworld in D dimensions

In this paper, we propose an approach to derive the brane cosmology in the D-dimensional braneworld model. We generalize the “bulk-based” approach by treating the 4-brane as a small perturbation to the D-dimensional spherically symmetric spacetime. The linear corrections from a static 4-brane to the metric are derived from the linearized perturbation equations, while the nonlinear corrections are found by a parameterization of the perturbed metric solution. We use a time-dependent generalization to give the nonlinearly perturbed metric solution for the dynamical braneworld model, and analyze the stability of the model under the motion of the 4-brane. Through the fine tuning, we can recover the Friedmann equations for the universe with and without an effective cosmological constant. More importantly, the de Sitter expansion of the universe can be reproduced.

Approximating photon trajectories in spherically symmetric spacetimes

In this paper we use the Homotopy analysis method to obtain an analytic approximation for the entire photon trajectory in the Schwarzschild spacetime. This is usually expressed exactly in terms of an elliptic integral. We compare our approximation with other formulae found in the literature, which were specifically obtained for the Schwarzschild solution. Unlike some of these formulae, our approximation can be applied and maintains a good accuracy for emission point close to the event horizon and also for emission angles close to and greater than π/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi /2$$\\end{document}. We show that our method can easily be applied to other spherically symmetric solutions such as the Reissner-Nordström solution. Such an approximation would be useful when accurate determination of the light trajectories around compact objects is required without the need to revert to time consuming numerical integration of elliptic integrals.

On pseudo-𝒦-symmetric semi-Riemannian manifolds and relativistic applications

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

Liouville gravity at the end of the world:deformed defects in AdS/BCFT

We study shape deformations of two-dimensional end-of-the-world (ETW) branes, such as those in bottom-up models of two-dimensional holographic boundary conformal field theories (BCFT), and derive an action for the theory of brane deformations in any bulk three-dimensional maximally symmetric spacetime. In the case of a bulk anti-de Sitter (AdS) spacetime, at leading order in the ultraviolet cutoff, the induced theory on the brane controlling its shape is Liouville gravity coupled to quantum matter. We show in certain limits the theory reduces to semi-classical AdS, dS or flat Jackiw-Teitelboim (JT) gravity, thus providing the first doubly-holographic derivation of two-dimensional models of dilaton gravity minimally coupled to a large number of conformal fields. Specializing to the AdS JT gravity limit, we discuss the dual BCFT interpretation and provide evidence that changing the boundary conditions of JT gravity on the brane is equivalent to a deformation of the dual BCFT with the displacement operator. This establishes a doubly-holographic triality between (i) brane deformations in the bulk, (ii) JT gravity in the brane description, and (iii) irrelevant deformations of the CFT boundary. Lastly, in the presence of a non-trivial dilaton profile, we prove that the Ryu-Takayanagi formula for holographic BCFTs receives a contact term whenever the minimal surface ends on the brane.

Nonlinear dynamics driving the conversion of gravitational and electromagnetic waves in cylindrically symmetric spacetime

Nonlinear dynamics driving the conversion of gravitational and electromagnetic waves in cylindrically symmetric spacetime

Static and spherically symmetric vacuum spacetimes with non-expanding principal null directions in f(R) gravity

In this work we characterize all the static and spherically symmetric vacuum solutions in f(R) gravity when the principal null directions of the Weyl tensor are non-expanding. In contrast to General Relativity, we show that the Nariai spacetime is not the only solution of this type when general f(R) theories are considered. In particular, we find four different solutions for the non-constant Ricci scalar case, all of them corresponding to the same theory, given by f(R)=r0-1R-3/r021/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(R) = r_0^{-1}\\left|R-3/r_0^2\\right|^{1/2}$$\\end{document}, where r0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_0$$\\end{document} is a non-null constant. Finally, we briefly present some geometric properties of these solutions.

Spherically symmetric electrovac spacetimes in conformal Killing gravity

Recently Harada proposed a third-order gravitational theory for the derivatives of the metric. Mantica and Molinari showed that Harada’s theory may be recast into the form of Einstein’s field equations (EFEs) with an additional source term which is a second-order conformal Killing tensor. Accordingly they named the theory conformal Killing gravity. However, they overlooked the fact that all solutions of the new theory (except those satisfying EFEs) admit a non-trivial second-order Killing tensor. Harada derived an analog of the Schwarzschild solution. Recently Tarciso et al obtained a generalization of Harada’s vacuum solution analogous to the Reissner–Nordström solution. However, like Harada they assumed a restricted form for a static spherically symmetric metric. In this study the most general spherically symmetric static vacuum solution of Harada’s theory and its generalization with a Maxwell electromagnetic field as source were obtained. The validity of Birkhoff’s theorem for static spherically symmetric electrovac fields in conformal Killing gravity is investigated.

Spacetime symmetries and geometric diffusion

We examine relativistic diffusion through the frame and observer bundles associated with a Lorentzian manifold (M, g). Our focus is on spacetimes with a non-trivial isometry group, and we detail the conditions required to find symmetric solutions of the relativistic diffusion equation. Additionally, we analyze the conservation laws associated with the presence of Killing vector fields on (M, g) and their implications for the expressions of the geodesic spray and the vertical Laplacian on both the frame and the observer bundles. Finally, we present several relevant examples of symmetric spacetimes.

Perturbations of bimetric gravity on most general spherically symmetric spacetimes

Perturbations of bimetric gravity on most general spherically symmetric spacetimes

Kodama-like vector fields in axisymmetric spacetimes

We extend the concept of the Kodama symmetry, a quasi-local time translation symmetry for dynamical spherically symmetric spacetimes, to a specific class of dynamical axisymmetric spacetimes, namely the families of Kerr–Vaidya and Kerr–Vaidya–de Sitter spacetimes. We study some geometrical properties of the asymptotically flat Kerr–Vaidya metric, such as the Brown–York mass and the Einstein tensor. Furthermore, we propose a generalization of the Kerr–Vaidya metric to an asymptotic de Sitter background. We show that for these classes of dynamical axisymmetric black hole spacetimes, there exists a timelike vector field that exhibits similar properties to the Kodama vector field in spherical symmetry. This includes the construction of a covariantly conserved current and a corresponding locally conserved charge, which in the Kerr–Vaidya case converges to the Brown–York mass in the asymptotically flat region.

A generalization of photon sphere based on escape/capture cone

In general asymptotically flat spacetimes, bearing the null geodesics reaching the future null infinity in mind, we propose new concepts, the “dark horizons” (outer dark horizon and inner dark horizon) as generalizations of the photon sphere. They are defined in terms of the structure of escape/capture cones of photons with respect to a unit timelike vector field to capture the motion of light sources. More specifically, considering a two-sphere that represents a set of emission directions of photons, the dark horizons are located at positions where a hemisphere is marginally included in the capture and escape cones, respectively. In addition, our definition succeeds in incorporating relativistic beaming effect. We show that the dark horizon is absent in the Minkowski spacetime, while they exist in spacetimes with black hole(s) under a certain condition. We derive the general properties of the dark horizons in spherically symmetric spacetimes and explicitly calculate the locations of the dark horizons in the Vaidya spacetime and the Kerr spacetime. In particular, in the Kerr spacetime, the outer dark horizon coincides with the shadow observed from infinity on the rotation axis.

Energy bounds in f(R,T) gravity with anisotropic backgrounds

This research work discusses the energy bounds in [Formula: see text] gravity with an anisotropic background, where [Formula: see text] is the Ricci scalar and [Formula: see text] is the trace of the energy–momentum tensor. For our study, we consider the locally rotationally symmetric Bianchi Type-I space-time. Moreover, we calculate the field equations and find exact solutions by considering different [Formula: see text] gravity models. We investigate the graphical behavior of energy density and pressure components by considering these distinct gravity models. We further use Hubble, deceleration, jerk, and snap parameters to evaluate the viability of our models. We also perform the graphical analysis to observe the behavior of energy conditions especially null energy conditions, weak energy conditions, strong energy conditions, and dominant energy conditions. It can be noticed that all considered [Formula: see text] gravity models support the idea of the presence of exotic matter, which justifies the phenomenon of expansion of the universe.

Accurate analytical modeling of light rays in spherically symmetric spacetimes: Applications in the study of black hole accretion disks and polarimetry

Accurate analytical modeling of light rays in spherically symmetric spacetimes: Applications in the study of black hole accretion disks and polarimetry

Barrow’s holographic dark energy model in axially symmetric spacetime

The Barrow’s Holographic Dark Energy (BHDE) Model is proposed in an axially symmetric anisotropic spacetime which is employing Hubble horizon as an infrared cutoff (IR cutoff). The transition of the universe from a matter dominated era to a dark energy dominated era is investigated in this model. Furthermore, the Equation of State (EoS) parameter explains how the universe evolves with non-extensive term or Barrow parameter [Formula: see text] for both phase (i) phantom era ([Formula: see text]) and (ii) quintessence era ([Formula: see text]). In order to reconcile the dark energy, the reconstruction of scalar field potential is considered. Some of the physical properties of the model are also described.

Euler–Heisenberg black hole surrounded by perfect fluid dark matter

A generation method of new metric in the case of static spherically symmetric space-time is derived. Using this approach, we construct a metric which describes Euler–Heisenberg black hole surrounded by perfect fluid dark matter and investigate its optical and thermodynamic properties. We found that radius of shadow will increase with the increase of dark matter effect, and more strong dark matter will diminish the light intensity of accretion disk generally. Moreover, in thermodynamics, when quantum electrodynamic parameter is positive, there will be a critical value of dark matter parameter, which determine the number of black hole’s critical points.

Tetrad formalism in the solution of spherically symmetric spacetime in general relativity

Abstract Spherically symmetric solutions in general relativity are the most fundamental solutions to the Einstein field equation. The first exact solution of the Einstein field equation is the spherically symmetric solution given by the Schwarzschild metric, as easily found in any standard textbook on general relativity. The FLRW (Friedmann-Lemaitre-Robertson-Walkers) metric is another spherically symmetric solution of Einstein’s equation describing the standard model in Cosmology. The standard approach to solving Einstein’s equations is by considering the metric. However, we can also adopt a tetrad-based method or tetrad formalism. We review these two solutions by the tetrad formalism as an alternative approach. In addition, we give some more cases, including the cosmological constant and the Taub-NUT metric.

Impact of Tolman–Kuchowicz potentials on Gauss–Bonnet gravity and isotropic stellar structures

In this manuscript, we study the behavior of charged isotropic compact stellar objects within the framework of modified f(G) theory of gravity by considering the Tolman–Kuchowicz spacetime. We use some matching condition of spherically symmetric space–time with Bardeen’s model as an exterior geometry and examine the physical behavior of stellar structures. In the current analysis, we discuss the energy conditions to check the viability of our model. Many physical aspects have been examined, such as energy density, pressure evolution, equation of state parameter, and causality condition. Furthermore, an equilibrium condition can be visualized through the modified Tolman–Oppenheimer–Volkov equation. Further, we study mass–radius function, compactness and redshift function, which are some essential features of charged compact star model. It is worthwhile to mention here for the current study that our stellar structure in the background of Bardeen’s model is more viable and stable.

Hotspots and photon rings in spherically symmetric space–times

ABSTRACT Future black hole (BH) imaging observations are expected to resolve finer features corresponding to higher order images of hotspots and of the horizon-scale accretion flow. In spherical space–times, the image order is determined by the number of half-loops executed by the photons that form it. Consecutive-order images arrive approximately after a delay time of ≈π times the BH shadow radius. The fractional diameters, widths, and flux-densities of consecutive-order images are exponentially demagnified by the lensing Lyapunov exponent, a characteristic of the space–time. The appearance of a simple point-sized hotspot when located at fixed spatial locations or in motion on circular orbits is investigated. The exact time delay between the appearance of its zeroth and first-order images agrees with our analytic estimate, which accounts for the observer inclination, with $\lesssim 20~{{\ \rm per\ cent}}$ error for hotspots located about ≲ 5M from a Schwarzschild BH of mass M. Since M87⋆ and Sgr A⋆ host geometrically thick accretion flows, we also explore the variation in the diameters and widths of their first-order images with disc scale-height. Using a simple ‘conical torus’ model, for realistic morphologies, we estimate the first-order image diameter to deviate from that of the shadow by $\lesssim 30~{{\ \rm per\ cent}}$ and its width to be ≲ 1.3M. Finally, the error in recovering the Schwarzschild lensing exponent (π), when using the diameters or the widths of the first and second-order images is estimated to be $\lesssim 20~{{\ \rm per\ cent}}$. It will soon become possible to robustly learn more about the space–time geometry of astrophysical BHs from such measurements.