Spherically Symmetric Spacetimes Research Articles

Integrability of Dirac equations in static spherical space-times

We consider the Dirac equations in static spherically-symmetric space-times, and we present a type of spinor field whose structure allows the separation of elevation angle and radial coordinate in very general situations. We demonstrate that after such a separation of variables the Dirac equations reduce to two equations that can always be integrated, at least in principle. To prove that ours is a fully-working method, we find an explicit exact solution in the special case of the de Sitter universe.

Imprints of cloud of strings and quintessence field on compact stellar configurations

This paper looks into how stellar configurations with quintessence and a cloud of string fields behave in general relativity in spherical symmetric spacetime. The goal is to find a stable, stellar model. We compute the unknown constants in the metric using the masses and radii of PSRJ1614 − 2230 stars. We employ the effective energy-momentum tensor in general relativity to analyze field equations. Additionally, we also demonstrate the anisotropic behavior, energy conditions, energy density, quintessence density, pressure profiles, gradients, anisotropic factor, energy conditions, sound speeds, compactification, mass function, EoS components, redshift, and stability of the compact stars. We demonstrate that according to the theory of general relativity, these compact stars exhibit physically plausible structures in the quintessence field with clouds of string.

Gauge-independent metric reconstruction of perturbations of vacuum spherically-symmetric spacetimes

Gauge-independent metric reconstruction of perturbations of vacuum spherically-symmetric spacetimes

Gravitational lensing by using the 0th order of affine perturbation series of the deflection angle of a ray near a photon sphere

The 0th order of affine perturbation series of the deflection angle of a ray near a photon sphere is more accurate than a deflection angle in a strong deflection limit, which is used often, because the later has hidden error terms. We investigate gravitational lensing by using 0th order affine perturbation series of the deflection angle in a general asymptotically-flat, static, and spherical symmetric spacetime with the photon sphere. We apply our formula to Schwarzschild black hole, Reissner–Nordström black hole, and Ellis–Bronnikov wormhole spacetimes as examples. By comparing observables by using the deflection angles, we show that we can ignore the effect of the hidden error terms in the the deflection angle in the strong deflection limit on the observables in a usual lens configuration with the photon sphere since the hidden error terms are tiny. On the other hand, in a retro lensing configuration, the deflection angle in the strong-deflection-limit analysis have error of several percent and the 0th order of affine perturbation series of the deflection angle has almost half of the error. Thus, in the retro lensing configuration, we should use the 0th order of affine perturbation series of the deflection angle rather than the deflection angle in the strong-deflection-limit analysis. The 0th order of affine perturbation series of the deflection angle can give a brighter magnification by a dozen percent than the one by using the deflection angle in the strong-deflection-limit analysis.

Bilocal geodesic operators in static spherically-symmetric spacetimes

We present a method to compute exact expressions for optical observables for static spherically symmetric spacetimes in the framework of the bilocal geodesic operator formalism. The expressions are obtained by solving the linear geodesic deviation equations for null geodesics, using the spacetime symmetries and the associated conserved quantities. We solve the equations in two different ways: by varying the geodesics with respect to their initial data and by directly integrating the equation for the geodesic deviation. The results are very general and can be applied to a variety of spacetime models and configurations of the emitter and the observer. We illustrate some of the aspects with an example of Schwarzschild spacetime, focusing on the behaviour of the angular diameter distance, the parallax distance, and the distance slip between the observer and the emitter outside the photon sphere.

Electromagnetic effects on dynamics of string fluid and information paradox in rainbow gravity

This work is devoted to studying the effects of electric field intensity on collapsing anisotropic string fluid in Rainbow gravity. The Einstein field equations are modified and solved for the spherical symmetric spacetime. The physical parameters of fluid including energy density, pressure and string tension are obtained. Moreover, the time and radius of formation of the apparent horizon are estimated. All these quantities depend on the fluid’s electric intensity. The graphical analysis of the physical existence of dynamical quantities depending on the energy of the probing particle is presented. It is found that the presence of an electric field decreases the mass density and increases fluid’s pressure. The electric field increases the time and radius of apparent horizon formation resulting in slowing down the collapsing process.

Conformal Symmetries of the Energy–Momentum Tensor of Spherically Symmetric Static Spacetimes

Conformal matter collineations of the energy–momentum tensor of a general spherically symmetric static spacetime are studied. The general form of these collineations is found when the energy–momentum tensor is non-degenerate, and the maximum number of independent conformal matter collineations is 15. In the degenerate case of the energy–momentum tensor, it is found that these collineations have infinite degrees of freedom. In some subcases of degenerate energy–momentum, the Ricci tensor is non-degenerate, that is, there exist non-degenerate Ricci inheritance collineations.

Conformally Flat Charged Static Spherically Symmetric Space-Time for a Spinning Fluid

Conformally Flat Charged Static Spherically Symmetric Space-Time for a Spinning Fluid

Quasinormal modes of Proca fields in a Schwarzschild-AdS spacetime

We present new results concerning the Proca massive vector field in a Schwarzschild-AdS black hole geometry. We provide a first principles analysis of Proca vector fields in this geometry using both the vector spherical harmonic (VSH) separation method and the Frolov-Krtou\v{s}-Kubiz\v{n}\'{a}k-Santos (FKKS) method that separates the relevant equations in spinning geometries. The analysis in the VSH method shows, on one hand, that it is arduous to separate the scalar-type from the vector-type polarizations of the electric sector of the Proca field, and on the other hand, it displays clearly the electric and the magnetic mode sectors. The analysis in the FKKS method is performed by taking the nonrotating limit of the Kerr-AdS spacetime, and shows that the ansatz decouples the polarizations in the electric mode sector even in the nonrotating limit. On the other hand, it captures only two of the three possible polarizations, the magnetic mode sector is missing. The reason for the absence of this polarization is related to the degeneracy of the principal tensor in static spherical symmetric spacetimes. The degrees of freedom and quasinormal modes in both separation methods of the Proca field are found. The frequencies of the quasinormal modes are also computed. For the electric mode sector in the VSH method the frequencies are found through an extension, which substitutes number coefficients by matrix coefficients, of the Horowitz-Hubeny numerical procedure, whereas for the magnetic mode sector in the VSH method and the electric sector of the FKKS method it is shown that a direct use of the procedure can be made. The values of the quasinormal mode frequencies obtained for each method are compared and showed to be in good agreement with each other. This further supports the analytical approaches presented here for the behavior of the Proca field in a Schwarzschild-AdS black hole background.

Phantom energy-supported wormhole model in f(R,T) gravity assuming conformal motion

In this article, we have discussed Morris and Thorne (MT) wormhole solutions in a modified theory of gravity that admits conformal motion. Here, we explore the wormhole solutions in [Formula: see text] gravity, which is a function of the Ricci scalar ([Formula: see text]) and the trace of the stress–energy tensor ([Formula: see text]). To study wormhole geometries, we make assumption of spherical symmetric static spacetime and the existence of conformal Killing symmetry to get more acceptable astrophysical outcomes. To do this, we choose the expression of [Formula: see text] as [Formula: see text]. Here, we employ the phantom energy EoS relating to radial pressure and density given by [Formula: see text] with [Formula: see text] to constrain our model. Following a discussion of wormhole geometry and behavior of shape function, the study moves on to the computation of proper radial distance, active mass function, the nature of total gravitational energy and a discussion on the violation of energy conditions. We have shown that the wormhole solutions exist for positive as well as negative values of the coupling constant [Formula: see text]. From our analysis, we see that no wormhole solution exists for [Formula: see text]. All the physical parameters have been drawn by employing the values of [Formula: see text] as [Formula: see text] and [Formula: see text], where [Formula: see text] corresponds to general relativity (GR) case. It is found that for our proposed model, a realistic wormhole solution satisfying all the properties can be obtained.

Master functions and equations for perturbations of vacuum spherically symmetric spacetimes

Perturbation theory of vacuum spherically-symmetric spacetimes is a crucial tool to understand the dynamics of black hole perturbations. Spherical symmetry allows for an expansion of the perturbations in scalar, vector, and tensor harmonics. The resulting perturbative equations are decoupled for modes with different parity and different harmonic numbers. Moreover, for each harmonic and parity, the equations for the perturbations can be decoupled in terms of (gauge-invariant) master functions that satisfy 1+1 wave equations. By working in a completely general perturbative gauge, in this paper we study what is the most general master function that is linear in the metric perturbations and their first-order derivatives and satisfies a wave equation with a potential. The outcome of the study is that for each parity we have two branches of solutions with similar features. One of the branches includes the known results: In the odd-parity case, the most general master function is an arbitrary linear combination of the Regge-Wheeler and the Cunningham-Price-Moncrief master functions whereas in the even-parity case it is an arbitrary linear combination of the Zerilli master function and another master function that is new to our knowledge. The other branch is very different since it includes an infinite collection of potentials which in turn lead to an independent collection master of functions which depend on the potential. The allowed potentials satisfy a non-linear ordinary differential equation. Finally, all the allowed master functions are gauge invariant and can be written in a fully covariant form.

Embedded interior solutions of V elaX − 1 model in f(τ,T) gravity

This article is based on the extension of Teleparallel Theory named [Formula: see text] gravity, where the notions [Formula: see text] and [Formula: see text] abbreviate the torsion trace term of the energy–momentum tensor. This study aims to explore the anisotropic outcomes of the [Formula: see text] model. We use the field equations drawn by using the spherical symmetry, including the torsion trace term. The major components [Formula: see text] and [Formula: see text], of spherical symmetric space-time are obtained by inducing the Karmarkar condition. We can obtain the values of the involved parameters [Formula: see text],[Formula: see text], [Formula: see text] in this study by matching the interior spherical metric with the exterior Schwarzschild’s solutions of the Einstein field equations. To explore the stability of the stellar objects predicted by our study, we study the properties like metric potentials, energy density, pressures, anisotropy, gradients, EoS, energy conditions, the behavior of forces, sound speeds, adiabatic index, redshift, mass function, and compactification by graphical analysis in the background of [Formula: see text] gravity.

Slowly rotating neutron stars in scalar torsion theory

In this present paper, a slowly rotating stat is investigated in shift symmetric scalar torsion theory framework using a nondiagonal tetrad that gives an axially symmetric spacetime. We present the general equations for a general Lagrangian in a spherical symmetric space time and then in an axially symmetric spacetime. The obtained equations will allow us to study the behaviour of a specific model at the center of the star and at large distance. We find that this particular model affects the behaviour at the center but it is not case for large value of the radial coordinate r. The integration of the equations of motion, for different realistic equations of state (EoS), confirms that the mass, the radius as well as the moment of inertia are effected by varying the parameters of the model. Finally, we examine the universal relation of normalized moment of inertia and the stellar compactness of neutron star in slow rotation approximation. We showed that for all values of parameters present in the model leads to a deviation from GR for all EoS with a relative deviation below 10%.

Anisotropic spheres via embedding approach in R+βR2 gravity with matter coupling

The manifesto of the current article is to investigate the compact anisotropic matter profiles in the context of one of the modified gravitational theories, known as f(R,T) gravity, where R is a Ricci Scalar and T is the trace of the energy–momentum tensor. To achieve the desired goal, we capitalized on the spherical symmetric space–time and utilized the embedding class-1 solution via Karmarkar’s condition in modeling the matter profiles. To calculate the unidentified constraints, Schwarzschild exterior solution along with experimental statistics of three different stars LMC X-4, Cen X-3, and EXO 1785-248 are taken under consideration. For the evaluation of the dynamical equations, a unique model f(R,T)=R+βR2+λT has been considered, with β and λ being the real constants. Different physical aspects have been exploited with the help of modified dynamical equations. Conclusively, all the stars under observations are realistic, stable, and are free from all singularities.

Null Wave Front and Ryu-Takayanagi Surface.

The Ryu–Takayanagi formula provides the entanglement entropy of quantum field theory as an area of the minimal surface (Ryu–Takayanagi surface) in a corresponding gravity theory. There are some attempts to understand the formula as a flow rather than as a surface. In this paper, we consider null rays emitted from the AdS boundary and construct a flow representing the causal holographic information. We present a sufficient and necessary condition that the causal information surface coincides with Ryu–Takayanagi surface. In particular, we show that, in spherical symmetric static spacetimes with a negative cosmological constant, wave fronts of null geodesics from a point on the AdS boundary become extremal surfaces and therefore they can be regarded as the Ryu–Takayanagi surfaces. In addition, from the viewpoint of flow, we propose a wave optical formula to calculate the causal holographic information.

Conformal vector fields of static spherically symmetric perfect fluid space-times in modified teleparallel theory of gravity

In this paper, initially we solve the Einstein field equations (EFEs) for a static spherically (SS) symmetric perfect fluid space-times in the [Formula: see text] gravity with the aid of some algebraic techniques. The extracted solutions are then utilized in order to get conformal vector fields (CVFs). It is important to mention that the adopted techniques enable us to obtain various classes of space-times with viable [Formula: see text] gravity models which already exist in the literature. Excluding all such classes, we find that there exist three cases for which the space-times admit proper CVFs, whereas in rest of the cases, CVFs become KVFs. We have also highlighted some physical implications of our obtained results.

Perturbative deflection angle for signal with finite distance and general velocities

We propose a perturbative method to compute the deflection angle of both null and massive particles for source and detector at finite distance. This method applies universally to the motion of particles with general velocity in the equatorial plane of stationary axisymmetric spacetimes or static spherical symmetric spacetimes that are asymptotically flat. The resultant deflection angle automatically arranges into a quasi-inverse series form of the impact parameter, with coefficients depending on the metric functions, the signal velocity and the source and detector locations through the apparent angles. In the large impact parameter limit, the series coefficients are reduced to rational functions of sine/cosine functions of the zeroth order apparent angle.

Constraining LQG Graph with Light Surfaces: Properties of BH Thermodynamics for Mini-Super-Space, Semi-Classical Polymeric BH.

This work participates in the research for potential areas of observational evidence of quantum effects on geometry in a black hole astrophysical context. We consider properties of a family of loop quantum corrected regular black hole (BHs) solutions and their horizons, focusing on the geometry symmetries. We study here a recently developed model, where the geometry is determined by a metric quantum modification outside the horizon. This is a regular static spherical solution of mini-super-space BH metric with Loop Quantum Gravity (LQG) corrections. The solutions are characterized delineating certain polymeric functions on the basis of the properties of the horizons and the emergence of a singularity in the limiting case of the Schwarzschild geometry. We discuss particular metric solutions on the base of the parameters of the polymeric model related to similar properties of structures, the metric Killing bundles (or metric bundles MBs), related to the BH horizons’ properties. A comparison with the Reissner–Norström geometry and the Kerr geometry with which analogies exist from the point of their respective MBs properties is done. The analysis provides a way to recognize these geometries and detect their main distinctive phenomenological evidence of LQG origin on the basis of the detection of stationary/static observers and the properties of light-like orbits within the analysis of the (conformal invariant) MBs related to the (local) causal structure. This approach could be applied in other quantum corrected BH solutions, constraining the characteristics of the underlining LQG-graph, as the minimal loop area, through the analysis of the null-like orbits and photons detection. The study of light surfaces associated with a diversified and wide range of BH phenomenology and grounding MBs definition provides a channel to search for possible astrophysical evidence. The main BHs thermodynamic characteristics are studied as luminosity, surface gravity, and temperature. Ultimately, the application of this method to this spherically symmetric approximate solution provides us with a way to clarify some formal aspects of MBs, in the presence of static, spherical symmetric spacetimes.

Explicit Lorentz violation in a static and spherically-symmetric spacetime

Lorentz violation is motivated by quantum gravity and it is generically described by nondynamical tensors. In this work a Lorentz violating extension of general relativity is studied where a nondynamical tensor couples to the Weyl tensor. A family of static and spherically symmetric solutions in vacuum is found, confirming that there are consistent solutions with explicit Lorentz violation in dynamical spacetimes. These solutions produce an unconventional dependence of the gravitational redshift, which, in turn, leads to the first bounds on such nondynamical tensor that do not rely on the physics of the early universe. Moreover, the bounds obtained in this work are competitive with respect to limits on similar nondynamical tensors.

Schwarzschild geometry counterpart in semiclassical gravity

We investigate the effects of vacuum polarization on vacuum static spherically-symmetric spacetimes. We start from the Polyakov approximation to the renormalized stress-energy tensor (RSET) of a minimally coupled massless scalar field. This RSET is not regular at $r=0$, so we define a regularized version of the Polyakov RSET. Using this Regularized RSET, and under the previous symmetry assumptions, we find all the solutions to the semiclassical field equations in vacuum. The resulting counterpart to the Schwarzschild classical geometry substitutes the presence of an event horizon by a wormhole throat that connects an external asymptotically flat region with an internal asymptotic region possessing a naked singularity: there are no semiclassical vacuum solutions with well-defined Cauchy surfaces. We also show that the Regularized Polyakov RSET allows for wormhole geometries of arbitrarily small throat radius. This analysis paves the way to future investigations of proper stellar configurations with an internal non-vacuum region.