Symmetric Spacetimes Research Articles

Overturning and cracking of stellar objects in modified f(R,φ) gravity

This study extends the concept of cracking to self-gravitating, spherically symmetric compact objects in modified f(R,φ) theory of gravity, where R represents the Ricci scalar, and φ is the scalar potential. In this regard, we consider spherically symmetric spacetime characterized with an anisotropic matter to detect the instabilities of self-gravitating compact objects via cracking and overturning. Further, we construct the general framework to observe the cracking and overturning points by applying the local density perturbation technique to the configuration governed by barotropic equation of state. The effectiveness of this approach is assessed by analyzing its results on the data of Her X-1, SAX J1808.4-3658, and 4U 1820-30 respectively. It is concluded that cracking points appear in the different interior regions of these three stars. Significantly, this study illustrates the effectiveness of the cracking approach by highlighting the regions sensitive to localized density disruptions, offering valuable insights into the structural behavior of compact stars within a modified gravity framework.

Correspondence between two gravitational lens equations in a static and spherically symmetric spacetime

Correspondence between two gravitational lens equations in a static and spherically symmetric spacetime

The energy quantization in hydrogen atom and proton–electron mass ratio in light of symmetrical special relativity

In this paper, we show the existence of an invariant minimum speed in space–time by forming the basis of a deformed special relativity so-called symmetrical special relativity (SSR). Such observer-independent minimum speed emerges from Dirac’s large number hypothesis (LNH), which leads us to build SSR-theory. This allows us to understand that the hydrogen atom represents the most stable bound state in the universe as being a fundamental structure of the symmetrical space–time with two limits of speed, namely the speed of light c and a minimum speed V. Such minimum speed is associated with a background reference frame for representing the vacuum energy related to the cosmological constant. So the symmetry in space–time given by the invariant minimum speed, which has origin in the electrical and gravitational bound states in hydrogen atom is able to provide a deeper understanding of the proton-electron mass ratio, i.e. [Formula: see text] given in terms of the universal minimum speed V. Furthermore, we investigate how the minimum speed in space–time plays a fundamental role in the quantization of energy in hydrogen atom.

Gravity-induced birefringence in spherically symmetric spacetimes

Gravity-induced birefringence in spherically symmetric spacetimes

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.

Higher dimensional heat conducting models with vanishing shear

A shear-free relativistic fluid with nonzero heat flux is studied by examining the higher dimensional spherically symmetric shear-free interior spacetime. The model is a heat conducting fluid undergoing dissipation. The Einstein field equations are generated in arbitrary dimensions for such a fluid and the assumption of isotropic fluid pressure realises a coupled partial differential equation in the gravitational potentials. We generate exact solutions to the isotropic pressure condition equation which represents a generalisation of the known four dimensional solutions. We also illustrate that the matter variables are physically well behaved and that the energy conditions are satisfied which is essential for constructing a complete and physically viable model in the context of radiating stars with vanishing shear.

Kasner-Like Description of Spacelike Singularities in Spherically Symmetric Spacetimes with Scalar Matter

Kasner-Like Description of Spacelike Singularities in Spherically Symmetric Spacetimes with Scalar Matter

Analytical solutions for Maxwell-scalar system on radially symmetric spacetimes

We investigate Maxwell-scalar models on radially symmetric spacetimes in which the gauge and scalar fields are coupled via the electric permittivity. We find the conditions that allow for the presence of minimum energy configurations. In this formalism, the charge density must be written exclusively in terms of the components of the metric tensor and the scalar field is governed by first-order equations. We also find a manner to map the aforementioned equation into the corresponding one associated to kinks in (1, 1) spacetime dimensions, so we get analytical solutions for three specific spacetimes. We then calculate the energy density and show that the energy is finite. The stability of the solutions against contractions and dilations, following Derrick’s argument, and around small fluctuations in the fields is also investigated. In this direction, we show that the solutions obeying the first-order framework are stable.

Removing naked singularities in static axially symmetric spacetimes by patching with flat spacetimes

Removing naked singularities in static axially symmetric spacetimes by patching with flat spacetimes

Non-singular anisotropic solutions for strange star model in f(R,T,RζγTζγ) gravity theory

This article focuses on different anisotropic models within the framework of a specific modified f(R,T,RζγTζγ) gravity theory. The study adopts a static spherically symmetric spacetime to determine the field equations for two different modified models: (i) f(R,T,RζγTζγ)=R+ηRζγTζγ, and (ii) f(R,T,RζγTζγ)=R(1+ηRζγTζγ), where η is a constant parameter. To address the additional degrees of freedom in the field equations and obtain their corresponding unique solution, the Durgapal-Fuloria spacetime geometry and MIT bag model are utilized. Matching conditions are applied to determine unknown constants within the chosen spacetime geometry. We adopt a certain range of model parameters to analyze the physical characteristics of the developed models in the interior distribution of a particular compact star candidate 4U 1820-30. Energy conditions and some other tests are also implemented to ensure their viability and stability. Additionally, the disappearing radial pressure constraint is employed to find the values of the model parameter, aligning with the observed information of an array of stars. The study concludes that both of our models are well-behaved and satisfy all necessary conditions, and thus we observe them suitable for the modeling of astrophysical objects.

The Chini integrability condition in second order Lovelock gravity

We analyse neutral and charged matter distributions in second order Lovelock gravity, also known as Einstein–Gauss–Bonnet gravity, in arbitrary dimensions for a static, spherically symmetric spacetime. We first transform the charged condition of pressure isotropy, an Abel differential equation of the second kind, into canonical form. We then determine a systematic approach to integrate the condition of pressure isotropy by showing that the canonical form is a Chini differential equation. The Chini invariant, which allows the master differential equation to be separable, is identified. This enables us to find three new general solutions, in implicit form, to the condition of pressure isotropy. We also show that previously obtained exact specific solutions arise as special cases in our general class of models. The Chini invariant does not arise in general relativity; it is a distinguishing feature of Einstein–Gauss–Bonnet gravity.

Killing Motion of Static Cylindrically Symmetric Spacetimes in the f(R) Gravity

In this study we have studied "Killing Motion of Static Cylindrically Symmetric Spacetimes in f(R) Gravity" by using algebraic and direct integration techniques. This study investigates the Killing motions of static cylindrically symmetric spacetimes with in framework of f(R) gravity, a generalization of Einstein’s General Relativity. We explore the existence of Killing vector fields to understand the symmetries and conserved quantities in such spacetimes. By analysing the modified field equations, we determine the constraints imposed by f(R) gravity on the geometry and dynamics of cylindrically symmetric spacetimes. These contribute to understanding the interplay between symmetry properties and gravitational theories beyond General Relativity. The results have implications for astrophysical and cosmological models influenced by alternative gravity theories. We discussed four cases and found that the dimension of Killing vector fields is either three, four or ten.

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 (SSVFs) 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.

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.