Symmetric Spacetimes Research Articles

Classification of Static Plane Symmetric Spacetime According to their Self Similar Vector Fields

Abstract This article discusses the use of self-similar symmetry to analyze static plane symmetric spacetime. A computer algorithm is employed to convert the symmetry equations, resulting in a tree structure known as a Riff tree, which is utilized for analyzing the aforementioned symmetry within the specified spacetime. The tree comprises several pivots and branches, with the pivots being subject to specific differential conditions on the metric functions. Furthermore, explicit formulas for the metrics and their corresponding self-similar vector fields are derived by solving the set of equations using these constraints. Additionally, this work investigates the bounds for certain energy conditions as well as the kinematic variables.

Spherically symmetric perfect fluid filled universe within the 4 dimensional Einstein–Gauss–Bonnet gravity formalism with vanishing conformal curvature

Conformally flat spacetime geometry is of immense physical importance. In this conext we obtain the most general solutions for 4 dimensional Einstein-Gauss–Bonnet (4D EGB) static spherically symmetric spacetimes. The standard Schwarzschild incompressible fluid sphere is one possible solution, however, new branches of solutions emerge that have cosmological significance. It is intriguing that the geometry of the new model is given by an exactly known spatially directed potential while the remaining potential is given as an integral. It is not necessary to know the explicit form of the temporally directed potential to analyse the physics of the model. However, at least two explicit exact solutions for both potentials are exhibited. Graphical plots are constructed to show that barring a short interval from the centre of the distribution which may be excised and replaced with a well-behaved fluid, all the elementary physical tests are successful. The model considered does not admit a finite radius hence is not applicable to astrophysical compact objects however the pleasing physical characteristics of the fluid suggests applicability to a perfect fluid filled universe. The model satisfies the causality requirement preventing the sound speed from becoming superluminal as well as the Chandrasekar stability criterion demanded of adiabatic fluids. Moreover all the energy conditions are complied with. The analysis effectively rules out the existence of conformally flat stars in 4D EGB gravity aside from the interior Schwarzschild spacetime.

General geometry realized by four-scalar model and application to [formula omitted] gravity

In this paper, we propose a model including four scalar fields coupled with general gravity theories, which is a generalization of the two-scalar model proposed in Phys. Rev. D 103 (2021) no.4, 044055, where it has been shown that any given spherically symmetric static/time-dependent spacetime can be realized by using the two-scalar model. We show that by using the four-scalar model, we can construct a model that realizes any given spacetime as a solution even if the spacetime does not have a spherical symmetry or any other symmetry. We also show that by imposing constraints on the scalar fields by using the Lagrange multiplier fields, the scalar fields become non-dynamical and they do not propagate. This tells that there does not appear any sound which is usually generated by the density fluctuation of the fluid. In this sense, the model with the constraints is a most general extension of the mimetic theory in JHEP 11 (2013), 135, where there appears an effective dark matter. The dark matter is non-dynamical and it does not collapse even under gravitational force. Our model can be regarded as a general extension of any kind of fluid besides dark matter. We may consider the case that the potential of the scalar fields vanishes and the model becomes a non-linear σ model. Then our formulation gives a mapping from the geometry of the spacetime to the geometry of the target space of the non-linear σ model via gravity theory although the physical meaning has not been clear. We also consider the application of the model to f(Q) gravity theory, which is based on a non-metricity tensor and Q is a scalar quantity constructed from the non-metricity tensor. When we consider the f(Q) gravity in the coincident gauge where the total affine connections vanish, when f(Q) is not a linear function of Q, spherically symmetric spacetime cannot be realized except in the case that Q is a constant. The situation does not change if we use the two-scalar model, as we show. If we use the four-scalar model in this paper, however, spherically symmetric spacetime can be realized in the framework of f(Q) gravity with the coincident gauge.

Cosmic Censorship in Sgr A* and M87*: Observationally Excluding Naked Singularities

The imaging of Sagittarius A* (Sgr A*) and the supermassive black hole at the center of Messier 87 (M87*) by the Event Horizon Telescope constrains the location and nature of emission from these objects. Coupled with flux limits from the near-infrared through the ultraviolet, the attendant size constraints provide strong evidence for the absence of an accretion-powered photosphere, and therefore for the existence of an event horizon about an astrophysical black hole. Here, we demonstrate that a broad class of naked singularities exhibit inner turning points for time-like geodesics, and therefore may generically be excluded, regardless of the nature and unknown physical impact of the singularity itself, subject to the single weak assumption that its nongravitational impact is localized to its immediate vicinity. While we restrict our attention to static, spherically symmetric spacetimes, we are nevertheless able to exclude or constrain a large number of commonly invoked naked singularity spacetimes in this way.

Study of light deflection and shadow in the Rindler-like Schwarzschild solution

In this paper, we calculate the deflection angle in the non-plasma medium by expanding the Keeton–Petters approach. We use analysis to determine how non-magnetic plasma affects the shadow of a Schwarzschild–Rindler black hole. We only consider the spherically symmetric case in which the shadow is circular. It is assumed that the plasma is independent of pressure and magnetization. From a specified spherically symmetric spacetime, we compute the results for a spherically symmetric plasma density. Our main purpose is to derive analytically a formula for the orbital radius of the shadow. Due to the diffusive nature of plasma, the shadow’s radius is influenced by the frequency of the photons. The impacts of the non-magnetic plasma are important in radio establishment. We determine that the non-magnetic plasma incorporates a decreasing impact on the shadow size for a distant observer from the Schwarzschild–Rindler black hole. Moreover, we graphically analyze the impacts of different parameters on the shadow of the corresponding black hole.

Gauge invariant perturbations of static spatially compact LRS II spacetimes

Abstract We present a framework to describe completely general first-order perturbations of static, spatially compact, and locally rotationally symmetric class II spacetimes within the theory of general relativity. The perturbation variables are by construction covariant and identification gauge invariant and encompass the geometry and the thermodynamics of the fluid sources. The new equations are then applied to the study of isotropic, adiabatic perturbations. We discuss how the choice of frame in which perturbations are described can significantly simplify the mathematical analysis of the problem and show that it is possible to change frames directly from the linear level equations. We find explicitly that the case of isotropic, adiabatic perturbations can be reduced to a singular Sturm–Liouville eigenvalue problem, and lower bounds for the values of the eigenfrequencies can be derived. These results lay the theoretical groundwork to analytically describe linear, isotropic, and adiabatic perturbations of static, spherically symmetric spacetimes.

Event Horizon Telescope observations exclude compact objects in baseline mimetic gravity

Mimetic gravity has gained significant appeal in cosmological contexts, but static spherically symmetric space-times within the baseline theory are highly non-trivial: the two natural solutions are a naked singularity and a black hole space-time obtained through an appropriate gluing procedure. We study the shadow properties of these two objects, finding both to be pathological. In particular, the naked singularity does not cast a shadow, whereas the black hole casts a shadow which is too small. We argue that the Event Horizon Telescope images of M87\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\star }$$\\end{document} and Sgr A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{\\star }$$\\end{document} rule out the baseline version of mimetic gravity, preventing the theory from successfully accounting for the dark sector on cosmological scales. Our results highlight an interesting complementarity between black hole imaging observations and modified gravity theories of cosmological interest.

Observational signatures of strong gravitational lensing in GUP-modified Schwarzschild black holes

We investigate gravitational lensing in strong-field limit by a static spherically symmetric GUP-modified Schwarzschild black holes having additional parameter ϵ . We found that influences of negative and positive values of ϵ parameter differ from Schwarzschild black hole. We expand the deflection angle of the photon in the neighborhood of complete capture, defining a strong field limit in opposition to the standard weak field limit. This expansion is performed for a generic spherically symmetric spacetime without referencing the field equations and assuming that the light ray follows the geodesics equation. We prove that the deflection angle always diverges logarithmically when the minimum impact parameter is reached. We apply this general formalism to Schwarzschild GUP black holes. We then compare the coefficients characterizing these metrics and find that different strong field limits characterize different collapsed objects. The strong field limits coefficients, such as the relativistic images’ position and magnification, are directly connected to the observables. As a concrete example, we consider the black hole at the center of our galaxy and estimate the optical resolution needed to investigate its strong field behavior through its relativistic images.

Probing the solar system for dark matter using the Sagnac effect

This study investigates the potential of the Sagnac Effect for detecting dark matter in the Solar System, particularly within the Sun. Originating from the relative delay and interference of light beams traveling in opposite directions on rotating platforms, the effect can account for how varying gravitational conditions affect its manifestation. We analyze the Sagnac time in two static, spherically symmetric spacetimes: Schwarzschild and one incorporating dark matter, in the form of a perfect fluid. Comparing the relative deviations in Sagnac time calculated for these metrics in the reference frame of satellites orbiting our star, which serve as a rotating circular platform and emit laser beams in opposite directions, with the precision of onboard atomic clocks (about 10−11), allows us to evaluate the potential for detecting dark matter’s gravitational influence through this effect.

General relativistic gravitational induction and causal temperatures

Abstract In this paper, we describe the process of general relativistic gravitational induction in spherically symmetric spacetimes by defining an energy momentum tensor for the induction process, which is divergence-free and hence conserved. The aforementioned tensor explicitly describes how the matter-free gravity, as measured by the geometrical Weyl curvature, interacts with the matter. This tensor is clearly different from the energy momentum tensor of the standard matter and we transparently show that in spherical symmetry, the Bianchi identities reduce to the conservation laws for these two such energy momentum tensors. Working with a semitetrad covariant formalism in spherically symmetric spacetimes, we then demonstrate the process of constructing a consistent causal thermodynamical picture for the free gravity and matter interaction via the general non-truncated Israel-Stewart heat transport equation. As an illustrative example, we consider the Lemaitre-Tolman-Bondi spacetime to highlight the relationship between the shear and the Weyl curvature in determining the inductive heat flux.

Generalized Schwarzschild Spacetimes with a Linear Term and a Cosmological Constant

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

Unstable Regions of Anisotropic Relativistic Spheres in Higher-Dimensions

Abstract In this work, we consider the collapse of a $\mathbb{D}$-dimensional sphere in the framework of a higher dimensional spherically symmetric space-time in which the gravitational action chosen is claimed to be somehow linked to the $\mathbb{D}$-dimensional modified term.
This work investigates the criteria for dynamical instability of
anisotropic relativistic sphere systems with
$\mathbb{D}$-dimensional modified gravity. The certain conditions are
applied that lead to the collapse equation and their effects on
adiabatic index $\Gamma$ in both Newtonian (N) and Post-Newtonian
(PN) regimes by using a perturbation scheme. The study explores that
the $\Gamma$ plays a crucial role in determining the degree of
dynamical instability. This index characterizes the fluid's
stiffness and has a significant i7mpact on defining the ranges of
instability. This systematic investigation demonstrates the
influence of various material properties such as anisotropic
pressure, kinematic quantities, mass function, $\mathbb{D}$-dimensional modified gravity parameters, and the radial profile of energy density on the
instability of considered structures during their evolution. This
work also displays the dynamical behavior of spherically symmetric
fluid configuration via graphical approaches.

Notes on pseudo symmetric and pseudo Ricci symmetric generalized Robertson–Walker space-times

We establish two key results regarding pseudo symmetric and pseudo Ricci symmetric space-times. Firstly, we demonstrate that in pseudo symmetric generalized Robertson-Walker space-times either the scalar curvature remains constant or the associated vector field Bi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{i}$$\\end{document} is irrotational. Secondly, in pseudo Ricci symmetric generalized Robertson-Walker space-times, we establish that either the scalar curvature is zero or the associated vector field Ai\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_{i}$$\\end{document} is irrotational. We identify the conditions to ensure both Bi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_{i}$$\\end{document} and Ai\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_{i}$$\\end{document} of these manifolds are acceleration-free and vorticity-free. We provide evidence that a pseudo symmetric and pseudo Ricci symmetric GRW space-time can be described as a perfect fluid. In a pseudo symmetric space-time, the state equation is given by p=4-n2n-2μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p=\\frac{4-n}{ 2n-2}\\mu $$\\end{document}, whereas in a pseudo Ricci symmetric space-time, the state equation takes the form p=3-nn-1μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p=\\frac{3-n}{n-1}\\mu $$\\end{document}, where p and μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu $$\\end{document} are the isotropic pressure and the energy density. It is noteworthy that if n=4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=4$$\\end{document} , a pseudo symmetric space-time corresponds to the dust matter era, while a pseudo Ricci symmetric space-time corresponds to the phantom era.

The common solution space of general relativity

We review the solution space for the field equations of Einstein's General Relativity for various static, spherically symmetric spacetimes. We consider the vacuum case, represented by the Schwarzschild black hole; the de Sitter-Schwarzschild geometry, which includes a cosmological constant; the Reissner-Nordström geometry, which accounts for the presence of charge. Additionally we consider the homogenenous and anisotropic locally rotational Bianchi II spacetime in the vacuum. Our analysis reveals that the field equations for these scenarios share a common three-dimensional group of point transformations, with the generators being the elements of the D⊗sT2 Lie algebra, known as the semidirect product of dilations and translations in the plane. Due to this algebraic property the field equations for the aforementioned gravitational models can be expressed in the equivalent form of the null geodesic equations for conformally flat geometries. Consequently, the solution space for the field equations is common, and it is the solution space for the free particle in a flat space. This approach open new directions on the construction of analytic solutions in gravitational physics and cosmology.

Similarity solutions of inhomogeneous spherically symmetric spacetime with dust fluid and dark energy

Similarity solutions of inhomogeneous spherically symmetric spacetime with dust fluid and dark energy

Comprehensive discussion of Krori–Barua Bardeen compact stars on modified f(R) theories of gravity with scalar potential

The objective of this paper is to deal with physical features of charged anisotropic compact objects in the framework of [Formula: see text] modified theory of gravity. To accomplish the desired objective, we consider a spherically symmetric spacetime with charged anisotropic fluid distribution. In addition, we utilize the Krori–Barua metric, i.e. [Formula: see text] and [Formula: see text] for exploring the field equations. Moreover, we compare the interior boundary to the bardeen model as an exterior geometry to calculate the unknown constrains. Further, to check the existence of bardeen stellar structure, we discuss the behavior of physical properties such as energy density, pressure components, anisotropy, equation of state parameters, stability analysis, energy bounds, equilibrium condition, adiabatic index, compactness factor and surface redshift. Conclusively, all the obtained results show that the system under consideration is physically stable, free from singularity and viable.

Semi-Riemannian structures for symmetric Galilean spacetimes

We introduce semi-Riemannian structures well-adapted to certain fields of observers in a Galilean spacetime. The Levi-Civita connection of such a semi-Riemannian metric will allow us to obtain variational characterizations of the Galilean geodesics as well as global results on the topological and differentiable structure of the spacetime. Moreover, these new semi-Riemannian metrics provide a new way to compare the studied Newton–Cartan models with their relativistic counterparts.

Physical characteristics of anisotropic solutions in f(Q,T) gravity under the vanishing complexity, embedding class one, conformally flat and conformally Killing conditions

The foundation of this paper is to present a comparative study of the properties of anisotropic solutions for compact stars in the framework of modified f(Q,T) gravity for the first time under the schemes of vanishing complexity, embedding class one, conformally flat and conformally Killing, where Q is the nonmetricity scalar and T is the trace of the energy-momentum tensor. The model f(Q,T)=ϕQ+αQn+1−γ(1−e−Q/γ)+βT is chosen in order to compare the results of the various forms f(Q,T) and f(Q) gravity theories. The f(Q,T) and f(Q) gravities in this model are then further simplified to depend on parameters ϕ,α,γ&β. Then, we discussed several approaches to determining the spherically symmetric spacetime components. Schwarzschild geometry represents the exterior spacetime, while a Tolman-Kuchowiz spacetime is used to examine the spherically symmetric spacetime inside the interior geometry. Many properties of compact stars are investigated, like energy density, energy conditions, pressure profiles, sound speeds, gradients, adiabatic index, TOV equation, mass function, compactness, and redshift function are all carefully examined in order to complete the analysis. We have compiled results for both stable and unstable scenarios, derived from gravity theories categorized into various cases, with solutions considered under different frameworks such as Tolman-Kuchowiz spacetime, embedding class 1 spacetime, the vanishing complexity condition, the conformally flat condition, and the conformal Killing vector condition.

Static, cylindrically symmetric spacetime in the coincident f(Q) gravity

In this paper we consider a static, cylindrically symmetric spacetime with coincident f(Q) gravity. Since the field equation of this spacetime in symmetric teleparallel gravity is suitable for choosing the function of f(Q) in the form of power series and exponential forms which are in coherent with cosmological observations, anisotropic perfect fluid solutions of these forms are discussed for this spacetime. Energy densities, directional pressures and energy conditions are plotted and analysed for a few different metric potentials. Although corresponding cosmic strings violate all energy conditions in both f(Q) functions, the corresponding Levi-Civita solution violates all energy conditions in the power law function of f(Q), but for exponential f(Q) gravity they are satisfied in small regions.

Gradient conformal stationarity and the CMC condition in LRS spacetimes

Abstract We study the existence of gradient conformal Killing vectors (CKVs) in the class of locally rotationally symmetric (LRS) spacetimes which generalizes spherically symmetric spacetimes, and investigate some implications for the evolutionary character of marginally outer trapped surfaces. We first study existence of gradient CKVs via the obtention of a relationship between the Ricci curvature and the gradient of the divergence of the CKV. This provides an alternative set of equations, for which the integrability condition is obtained, to analyze the existence of gradient CKVs. A uniqueness result is obtained in the case of perfect fluids, where it is demonstrated that the Robertson-Walker solution is the unique perfect fluid solution with a nonvanishing pressure, admitting a timelike gradient CKV. The constant mean curvature condition for LRS spacetimes is also obtained, characterized by three distinct conditions which are specified by a set of three scalars. Linear combinations of these scalars, whose vanishing define the constant mean curvature condition, turn out to be related to the evolutions of null expansions of 2-spheres along their null normal directions. As such, some implications for the existence of black holes and the character of the associated horizons are obtained. It is further shown that dynamical black holes of increasing area, with a non-vanishing heat flux across the horizon, will be in equilibrium, with respect to the frame of the conformal observers.