Spherically-symmetric Solutions Research Articles

Spherical symmetric solutions of conformal Killing gravity: black holes, wormholes, and sourceless cosmologies

Spherical symmetric solutions of conformal Killing gravity: black holes, wormholes, and sourceless cosmologies

Spherical and plane symmetric solutions in macroscopic gravity

Spherical and plane symmetric solutions in macroscopic gravity

Replica trick calculation for entanglement entropy of static black hole spacetimes

We calculate the entanglement entropy between two (maximally-extended) spacetime regions of static black hole, separated by horizon. As a first case, we consider the Schwarzschild black hole, and then we extend the calculations to the charged Reissner–Nordström and Schwarzschild–de Sitter black holes with more than one horizon. The case for static and spherically-symmetric solution to the more general [Formula: see text] gravity is also considered. The calculation of the entanglement entropy is performed using the replica trick by obtaining the explicit form of the metric which corresponds to the replica spacetime for each black hole under consideration. The calculation of static and spherically-symmetric black holes results in the entanglement entropy that matches the Bekenstein–Hawking area law entropy.

Scale-invariance at the core of quantum black holes

We study spherically-symmetric solutions to a modified Einstein–Hilbert action with renormalization group (RG) scale-dependent couplings, inspired by Weinberg’s Asymptotic Safety scenario for quantum gravity. The RG scale is identified with the Tolman temperature for an isolated gravitational system in thermal equilibrium with Hawking radiation. As a result, the point of infinite local temperature is shifted from the classical black-hole horizon to the origin and coincides with a timelike curvature singularity. Close to the origin, the spacetime is determined by the scale-dependence of the cosmological constant in the vicinity of the Reuter fixed point: the free components of the metric can be derived analytically and are characterized by a radial power law with exponent . Away from the fixed point, solutions for different masses are studied numerically and smoothly interpolate between the Schwarzschild exterior and the scale-invariant interior. Whereas the exterior of objects with astrophysical mass is described well by vacuum general relativity, deviations become significant at a Planck distance away from the classical horizon and could lead to observational signatures. We further highlight potential caveats in this intriguing result with regard to our choice of scale-identification and identify future avenues to better understand quantum black holes in relation to the key feature of scale-invariance.

SOLITON OF SELF-CONSISTENT SYSTEM OF NONLINEAR SPINOR AND GRAVITATIONAL FIELDS WITH THE ARBI- TRARY FUNCTION DEPENDING ON THE BILINEAR PAULI- FIERZ INVARIANT IS = S2 IN GENERAL RELATIVITY

A self-consistent system of nonlinear spinor and gravitational fields, modeled by static spherical symmetric metric, is considered and studied. Exact spherical symmetric solutions of nonlinear spinor field equations in the Gravitational Theory are obtained. The nonlinearity in the spinor lagrangian is given by an arbitrary function which depends on the invariant generated from the Fierz-Pauli bilinear spinor form IS = S2. It is shown that a soliton-like configuration has a localized energy density and a finite total energy. In addition, The total charge and total spin are also finite. Let us emphasize that the effect of gravitational field on the properties of regular localized solutions significantly depends on the symmetry of the system. The nonlin- ear terms, the gravitational field of elementary particles and the geometrical properties of the metric of the space-time play an important role in the obtaining of analytical solutions having the soliton-like configuration. Let us emphasize that the numerical solutions of the solutions obtained here are presented in graphical form.

Structural stability of transonic shock flows with external force in a divergent 3-D axisymmetric perturbed nozzle

This paper concerns with the structural stability of the transonic shock for steady Euler flows with external force in a divergent 3-D axisymmetric perturbed nozzle. We first establish the existence and uniqueness of spherical symmetric transonic shock solution to steady isentropic Euler system with external force by prescribing suitable exit pressure at the exit of a straight divergent nozzle when the incoming flow at the entrance is spherical symmetric supersonic flow. Then we investigate the stability of this spherical symmetric transonic shock solution to the 3-D axisymmetric steady isentropic Euler system with external force when the incoming supersonic flow and the nozzle boundary and the exit pressure and the external force are suitable perturbed. One of new ideas in the analysis is to use the deformation-curl decomposition provided in [21] to deal with the transonic shock problem.

Stability of black holes with non-minimally coupled scalar hair to the Einstein tensor

General relativity admits a plethora of exact compact object solutions. The augmentation of Einstein’s action with non-minimal coupling terms leads to modified theories with rich structure, which, in turn, provide non-trivial solutions with intriguing phenomenology. Thus, assessing their viability under generic fluctuations is of utmost importance for gravity theories. We consider static and spherically-symmetric solutions of a Horndeski subclass which includes a massless scalar field non-minimally coupled to the Einstein tensor. Such theory possesses second-order field equations and admits an exact black hole solution with scalar hair. Here, we study the stability of such solution under axial gravitational perturbations and find that it is linearly stable. The qualitative features of the ringdown waveform depend solely on the ratio of the two available parameters of spacetime, namely the black hole mass m and the non-minimal coupling strength ell _eta . Finally, we demonstrate the gravitational-wave ringdown transitions between three distinct patterns as the ratio m/ell _eta increases; a state which is dominated by photon-sphere excitations and maintains a typical quasinormal ringdown, an intermediate long-lived state which exhibits gravitational-wave echoes and, finally, a state where the ringdown and echoes are depleted rapidly to turn to an exponential tail.

Soliton-like solutions of nonlinear scalar and electromagnetic field equations in gravitational theory

In this work, exact analytical static spherical symmetric solutions to the nonlinear interacting electromagnetic and massless scalar field equations have been determined taking into account the proper gravitational field of elementary particles. The obtained results prove that all solutions of the Einstein equation and those of the interacting fields are regular with localized energy density. All non-zero components of the 4-vector potential are solutions to the inverted Painlevé-Gambier XI equation. Moreover, the total energy of interacting fields is limited and the total charge of elementary particles is finite. These solutions obtained are soliton-like and can be used as a model to describe the internal structure of elementary particles.

Soliton-Like Spherical Symmetric Solutions to the Electromagnetic and Scalar Nonlinear Induction Field Equations in the General Relativity Theory

In this paper, we have used the static spherical symmetric metric. The parameter of the nonlinearity fields is included in the arbitrary function characterizing the interaction between the electromagnetic and scalar fields. Taking into account the own gravitational field of elementary particles, we have obtained exact static spherical symmetric solutions to the electromagnetic and scalar field equations of nonlinear induction. Considering all forms of the solution of Liouville equation, we proved that the metric functions are regular with localized energy density. Moreover, the total energy of the nonlinear induction fields is bounded and the total charge of the elementary particles has a finite value (soliton-like). In the flat space-time, soliton-like solutions exist.

Physical interpretation of Newman-Janis rotating systems. I. A unique family of Kerr-Schild systems

The Newman-Janis algorithm and its generalizations can be used mathematically to generate rotating solutions from nonrotating spherically-symmetric solutions within general relativity. The energy-momentum tensors of these solutions may or may not represent the same physical system, in the sense of both being a perfect fluid, or an electromagnetic field, or a $\Lambda$-term, and so on. In a series of two papers, we compare the structure of the eigenvalues and eigenvectors of the rotating and nonrotating energy-momentum tensors (their Segre types) and look for the existence of equations of state relating the energy density and the principal pressures. Part I covers Kerr-Schild systems, Part II more general systems. We find that there is a unique family of stationary axisymmetric Kerr-Schild systems that obey the same equation of state in both the rotating and nonrotating configurations. This family includes the Kerr and Kerr-Newman black holes, as well as rotating spacetimes whose mass function in the nonrotating limit contains a constrained superposition of a cloud of strings term, a Reissner-Nordstrom term, a cosmological constant term, and a Schwarzschild term. We describe the common equation of state relating energy density and pressure in this family of spacetimes and discuss some of its properties.

Exact static spherical symmetric soliton-like solutions to the scalar and electromagnetic nonlinear induction field equations in general relativity

In this paper, we have obtained exact static spherical symmetric soliton-like solutions to the electromagnetic and scalar nonlinear induction field equations taking into account the own gravitational field of the elementary. The results show that the metric tensor functions are regular with localized energy density. Moreover, the total energy of the nonlinear induction fields is bounded and the total charge of elementary particles has a finite value. The importance of the own gravitational field of elementary particles and the role of the nonlinearity of fields in the determination of these solutions have been proved.

Exploration of a singular fluid spacetime

We investigate the properties of a special class of singular solutions for a self-gravitating perfect fluid in general relativity: the singular isothermal sphere. For arbitrary constant equation-of-state parameter w=p/rho , there exist static, spherically-symmetric solutions with density profile propto 1/r^2, with the constant of proportionality fixed to be a special function of w. Like black holes, singular isothermal spheres possess a fixed mass-to-radius ratio independent of size, but no horizon cloaking the curvature singularity at r=0. For w=1, these solutions can be constructed from a homogeneous dilaton background, where the metric spontaneously breaks spatial homogeneity. We study the perturbative structure of these solutions, finding the radial modes and tidal Love numbers, and also find interesting properties in the geodesic structure of this geometry. Finally, connections are discussed between these geometries and dark matter profiles, the double copy, and holographic entropy, as well as how the swampland distance conjecture can obscure the naked singularity.

Fuzzy and discrete black hole models* *The first author was partially supported by CONACyT (México).

Using quantum Riemannian geometry, we solve for a Ricci = 0 static spherically-symmetric solution in 4D, with the S 2 at each t, r a noncommutative fuzzy sphere, finding a dimension jump with solutions having the time and radial form of a classical 5D Tangherlini black hole. Thus, even a small amount of angular noncommutativity leads to radically different radial behaviour, modifying the Laplacian and the weak gravity limit. We likewise provide a version of a 3D black hole with the S 1 at each t, r now a discrete circle , with the time and radial form of the inside of a classical 4D Schwarzschild black hole far from the horizon. We study the Laplacian and the classical limit . We also study the 3D FLRW model on with S 2 an expanding fuzzy sphere and find that the Friedmann equation for the expansion is the classical 4D one for a closed Universe.

Spherical Symmetric Solitons of Interacting Spinor, Scalar and Gravitational Fields in General Relativity

The concept of soliton as regular localized stable solutions of nonlinear differential equations is being widely utilized in pure science for various aims. In present analysis, the soliton concept is used as a model in order to describe the configurations of elementary particles in general relativity. To this end, our study deals with the spherical symmetric solitons of interacting Spinor, Scalar and Gravitational Fields in General Relativity. Thus, exact spherical symmetric general solutions to the interaction of spinor, scalar and gravitational field equations have been obtained. The Einstein equations have been transformed into a Liouville equation type and solved. Let us emphasize that these solutions are regular with localized energy density and finite total energy. In addition, the total charge and spin are limited. Moreover, the obtained solutions are soliton-like solutions. These solutions can be used in order to describe the configurations of elementary particles.

Eicheons instead of Black holes

A new spherically-symmetric solution for a gravitational field is found in the conformally-unimodular metric. It is shown, that the surface of the black hole horizon in the standard Schwarzschild metric can be squeezed to a point by converting coordinates to the conformally-unimodular metric. In this new metric, there is no black hole horizon, while the naked singularity corresponds to a point massive particle. The reason for the study of this particular gauge (i.e., conformally-unimodular metric) is its relation to the vacuum energy problem. That aims to relate it to other physical phenomena (including black holes), and one could argue that they should be considered in this particular metric. That means the violation of the gauge invariance of the general theory of relativity. As a result, the nonsingular ‘eicheons’ appear as the non-point compact objects with different masses and structures. They are a final product of the stellar collapse, with the masses exceeding the Tolman-Oppenheimer-Volkoff limit.

Radiating-collapsing models satisfying Karmarkar condition

This paper presents a class of exact spherical symmetric solutions of the Einstein equations admitting heat-conducting anisotropic fluid as a collapsing matter. The exterior spacetime is assumed to be the Vaidya metric. This class of solutions is shown to satisfy all the energy conditions throughout the interior of the star, and the luminosity is time independent, radiating uniformly throughout the collapse.

Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields

The present research work deals with an extension of a previous work [Exact Soliton-like spherical symmetric solutions of the Heisenberg-Ivanenko type nonlinear spinor field equation in gravitational theory, Journal of Applied Mathematics and Physics, 2020, 8, 1236-1254] to Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields. We have obtained exact kink-like static spherical symmetric solutions to the self-consistent system of spinor and gravitational fields equations. The Einstein’s field equation shave been solved by the Liouville method. The principal difference between kink soliton with antikink soliton has been established. The nonlinear terms in the lagrangian are arbitrary functions F(IS) depending on the invariant IS = S2= ( )2. It is shown that the initial set of the Einstein and spinor field equations have regular solutions with a localized energy density of the spinor field only if m = 0 (m is the mass parameter in the spinor field equations). Equations with polynomial nonlinearities are thoroughly scrutinized. Let us emphasize that the spinor field with polynomial nonlinearities has a regular solutions with localized, positive and alternating energy density and finite total energy. In addition, the total charge and the total spin are also finte. We have also obtained exact solutions to the linear spinor field equations. We remarked that in this case soliton-like solutions are absent. Furthermore, we note that the properties of regular localized solutions depend on the symmetry and the nonlinear terms in the lagrangian of the self-consistent system of gravitational and spinor fields.

Analytical Soliton-Like Solutions to Nonlinear Dirac Equation of Spinor Field in Spherical Symmetric Metric

The present research work deals with an extension of a previous work entitled [Exact Soliton-like spherical symmetric solutions of the Heisenberg-Ivanenko type nonlinear spinor field equation in gravitational theory, Journal of Applied Mathematics and Physics, 2020, 8, 1236-1254] to Analytical Soliton-Like Solutions to Nonlinear Dirac Equation of Spinor Field in Spherical Symmetric Metric. The nonlinear terms in the Lagrangian density are functions of the invariant . Equations with power and polynomial nonlinearities are thoroughly scrutinized. It is shown that soliton is responsible for the deformation in the metric and hence in the geometry as well as gravitational field. The role of nonlinearity and the influence of the proper gravitational field of the elementary particles are also examined. The consideration of the nonlinear terms in the spinor Lagrangian, the own gravitational field of elementary particles and the geometrical properties of the metric are necessary and sufficient conditions in order to obtain soliton-like solutions with total charge and total spin in general relativity.

Exact Soliton-Like Spherical Symmetric Solutions of the Heisenberg-Ivanenko Type Nonlinear Spinor Field Equation in Gravitational Theory

In the present research work, we have obtained the exact spherical symmetric solutions of Heisenberg-Ivanenko nonlinear spinor field equations in the Gravitational Theory. The nonlinearity in the spinor Lagrangian is given by an arbitrary function which depends on the invariant generated from the bilinear spinor form Is = S2. We admit the static spherical symmetric metric. It is shown that a soliton-like configuration has a localized energy density and a finite total energy. In addition, The total charge and total spin are also finite. Role of the metric i.e. the proper gravitational field of elementary particles in the formation of the field configurations with limited total energy, spin and charge has been examined by solving the field equations in flat space-time. It has been established that the obtained solutions are soliton-like configuration with bounded energy density and finite total energy. In order to clarify the role of the nonlinearity in this model, we have obtained exact statical symmetric solutions to the above spinor field equations in the linear case corresponding to Dirac’s linear equation. It is proved that soliton-like solutions are absent.

New algorithms to obtain analytical solutions of Einstein\u2019s equations in isotropic coordinates

The main objective of this work, is to show two inequivalent methods to obtain new spherical symmetric solutions of Einstein’s Equations with anisotropy in the pressures in isotropic coordinates. This was done inspired by the MGD method, which is known to be valid for line elements in Schwarzschild coordinates. As example, we obtained four analytical solutions using Gold III as seed solution. Two solutions, out of four, (one for each algorithm), satisfy the physical acceptability conditions.