The existence of black holes is one of the key predictions of general relativity (GR) and therefore a basic consistency test for modified theories of gravity. In the case of spherical symmetry in GR the existence of an apparent horizon and its regularity is consistent with only two distinct classes of physical black holes. Here we derive constraints that any self-consistent modified theory of gravity must satisfy to be compatible with their existence. We analyze their properties and illustrate characteristic features using the Starobinsky model. Both of the GR solutions can be regarded as zeroth-order terms in perturbative solutions of this model. We also show how to construct nonperturbative solutions without a well-defined GR limit.
It is known that spherically symmetric static spacetimes admit a foliation by °at hypersurfaces. Such foliations have explicitly been constructed for some spacetimes, using different approaches, but none of them have proved or even discussed the uniqueness of these foliations. The issue of uniqueness becomes more important due to suitability of °at foliations for studying black hole physics. Here °at spherically symmetric spacelike hy- persurfaces are obtained by a direct method. It is found that spherically symmetric static spacetimes admit °at spherically symmetric hypersurfaces, and that th…
Regular generalizations of spherically and axially symmetric metrics and their properties are considered. Newton gravity law generalizations are reduced for null geodesic.
Finding spherically symmetric exact solutions in modified gravity is usually a difficult task. In this paper we use the Noether's symmetry approach for a modified Teleparallel theory of gravity labelled as $f(T,B)$ gravity where $T$ is the scalar torsion and $B$ the boundary term. Using the Noether's theorem, we were able to find exact spherically symmetric solutions for different forms of the function $f(T,B)$ coming from the Noether's symmetries.
We study a four-dimensional gauge theory of the Poincaré group with topological action which generalizes some well-known two-dimensional gravity models. We classify the spherically symmetric solutions and discuss the perturbative propagation of excitations around flat spacetime.
The possibility of spherically symmetric solutions in bi-metric theory of gravity is examined. It is shown that two possible black hole type solutions exists in the model. Spherically symmetric solution of general theory of relativity is recovered in the absence of the second metric. The result is compared with other bi-metric models as well as general theory of relativity.
Different versions of consistent canonical realizations of hypersurface deformations of spherically symmetric space-times have been derived in models of loop quantum gravity, modifying the classical dynamics and sometimes also the structure of space-time. Based on a canonical version of effective field theory, this paper provides a unified treatment, showing that modified space-time structures are generic in this setting. The special case of Euclidean gravity demonstrates agreement also with existing operator calculations.
We search for spherically symmetric solutions of f(R) theories of gravity via the Noether Symmetry Approach. A general formalism in the metric framework is developed considering a point-like f(R)-Lagrangian where spherical symmetry is required. Examples of exact solutions are given.
In this paper we analyze spherically symmetric static vacuum solutions with various topologies in mimetic gravity. When the Einstein's tensor is different from zero, a new class of solutions different from the Schwarzschild one emerges from the theory. We analyze the feature of the new solutions and we study the planar motion for the spherical case.
Geometric structure of spherically-symmetric space-time in metric-affine gauge theory of gravity is studied. Restrictions on curvature tensor and Bianchi identities are obtained. By using certain simple gravitational Lagrangian the solution of gravitational equations for vacuum spherically-symmetric gravitational field is obtained.
We determine sufficient and necessary conditions for a spherically symmetric initial data set to satisfy the dynamical horizon conditions in the spacetime development. The constraint equations reduce to a single second order linear master equation, which leads to a systematic construction of all spherically symmetric dynamical horizons (SSDH) satisfying certain boundedness conditions. We also find necessary and sufficient conditions for a given spherically symmetric spacetime to contain a SSDH.
We investigate spherically symmetric continuously self-similar (CSS) solutions in the SU(2) sigma model coupled to gravity. Using mixed numerical and analytical methods, we provide evidence for the existence (for small coupling) of a countable family of regular CSS solutions. This fact is argued to have important implications for the ongoing studies of black hole formation in the model.
It is shown that an effective anisotropic spherically symmetric fluid model with heat flow can absorb the addition to a perfect fluid of pressure anisotropy, heat flow, bulk and shear viscosity, electric field and null fluid.
We investigate the proper projective collineation in non-static spherically symmetric space-times using direct integration and algebraic techniques. Studying projective collineation in the above space-times, it is shown that the space-times which admit proper projective collineations turn out to be very special classes of static spherically symmetric space-times.
We have found some new exact static spherically symmetric interior solutions of metric $f(R)$ gravitational theories describing the equilibrium configuration of a star. Then the solution is matched to the exterior solution and thus gives a complete description of a star in $R^{1-n/2}$ theory.
We investigate non-minimal $R^βF^2$-type couplings of electromagnetic fields to gravity. We derive the field equations by a first order variational principle using the method of Lagrange multipliers. Then we present various static, spherically symmetric solutions describing the exterior fields in the vicinity of electrically charged massive bodies.
The spherically symmetric volume operator is discussed and all its eigenstates and eigenvalues are computed. Even though the operator is more complicated than its homogeneous analog, the spectra are related in the sense that the larger spherically symmetric volume spectrum adds fine structure to the homogeneous spectrum. The formulas of this paper complete the derivation of an explicit calculus for spherically symmetric models which is needed for future physical investigations.
We use the 1+3 frame formalism to write down the evolution equations for spherically symmetric models as a well-posed system of first order PDEs in two variables, suitable for numerical and qualitative analysis.
We derive matter collineations for some static spherically symmetric spacetimes and compare the results with Killing, Ricci and Curvature symmetries. We conclude that matter and Ricci collineations are not, in general, the same.
We have studied the properties of the static, spherically symmetric solution of Jordan, Brans-Dicke theory. An exact interior solution for standard space-time line element in the Schwarzschild form is obtained.
Using an estimate, we prove that if solution of the spherically symmetric Einstein-Vlasov-Maxwell system develops a singularity at all time, then the first one has to appear at the center of symmetry.
The static spherically symmetric solution for (R +- μ^4/R) model of f(R)gravity is investigated. We obtain the metric for space-time in the solar system that reduces to the Schwarzschild metric, when μ tends to zero. For the obtained metric, the deviation from Einstein gravity is very small. This result is different from the other results have been obtained by equivalence between f(R) gravity and scalar tensor theory. Also it is shown that the vacuum solution in the solar system depends on the shape of matter distribution which differ from the Einstein's gravity.
We discuss stability of spherically symmetric static solutions in Newtonian limit of Jordan, Brans-Dicke field equations. The behavior of the stable equilibrium solutions for the spherically symmetric configurations considered here, it emerges that the more compact a model is, the more stable it is. Moreover, linear stability analysis shows the existence of stable configurations for any polytropic index.
We propose a new test of Einstein's theory of gravitation. It concerns the velocity distribution of low-energy particles in a spherically symmetric gravitational field.
We categorize the global structure of spherically symmetric static solutions of Einstein SU(2) Yang Mills equations with positive cosmological constant that are smooth at the center of spherical symmetry.
We investigate solutions of Einstein field equations for the non-static spherically symmetric perfect fluid case using different equations of state. The properties of an exact spherically symmetric perfect fluid solutions are obtained which contain shear. We obtain three different solutions out of these one turns out to be an incoherent dust solution and the other two are stiff matter solutions.
The stability of transparent spherically symmetric thin shells (and wormholes) to linearized spherically symmetric perturbations about static equilibrium is examined. This work generalizes and systematizes previous studies and explores the consequences of including the cosmological constant. The approach shows how the existence (or not) of a domain wall dominates the landscape of possible equilibrium configurations.
We consider spherically symmetric linear perturbations of static spherically symmetric spacetimes where the matter content is ellectrically counterpoised dust. We show that the evolution equation for the fluid perturbation implies that the fluid elements move with constant velocities. Therefore there are neither oscillations nor exponential departure from the background solution. We present an explicit example that shows that the perturbation could lead to the formation of a black hole.
Einstein, Landau-Lifshitz, Papapetrou, Weinberg, and Møller energy-momentum prescriptions in general spherically symmetric space-times are investigated. It is shown that for two special but not unusual classes of general spherically symmetric space-times several energy-momentum prescriptions in Schwarzschild Cartesian coordinates lead to some coincidences in energy distribution. It is also obtained that for a special class of spherically symmetric metrics Møller and Einstein energy-momentum prescriptions give the same result for energy distribution if and only if it has a specific dependence o…
Gravitational theories generated from Lagrangians of the form f(R) are considered. The spherically symmetric solutions to these equations are discussed, paying particular attention to features that differ from the standard Schwarzschild solution. The asymptotic form of solutions is described, as is the lack of validity of Birkhoff's theorem. Exact solutions are presented which illustrate these points and their stability and geodesics are investigated.
The purpose of this article is to obtain the periastron precession of a free particle moving around an extremal spherically symmetric dilaton black hole. To get the formulae for the periastron precession we use the phase-plane analysis of the general relativistic equations of motion.
Using the iterative Scheme we prove the local existence and uniqueness of solutions of the spherically symmetric Einstein-Vlasov-Maxwell system with small initial data. We prove a continuation criterion to global in-time solutions.
In a recent paper Cañate (CQG, {\bf 35}, 025018 (2018)) proved a no hair theorem to static and spherically symmetric or stationary axisymmetric black holes in general $f(R)$ gravity. The theorem applies for isolated asymptotically flat or asymptotically de Sitter black holes and also in the case when vacuum is replaced by a minimally coupled source having a traceless energy momentum tensor. This theorem excludes the case of pure quadratic gravity, $f(R) = R^2$. In this paper we use the scalar tensor representation of general $f(R)$ theory to show that there are no hairy black hole in pure $R^2…
A non-diagonal spherically symmetric tetrad field, involving four unknown functions of radial coordinate $r$, is applied to the equations of motion of f(T) gravity theory. A special exact vacuum solution with one constant of integration is obtained. The scalar torsion related to this special solution vanishes. To understand the physical meaning of the constant of integration we calculate the energy associated with this solution and show how it is related to the gravitational mass of the system.
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and Lorentzian Hamiltonian constraints. The construction fits completely into the general scheme available in loop quantum gravity for the quantization of the full theory as well as symmetric models. This then presents a further consistency check of the whole scheme in inhomogeneous situations, lending further credence to the physical results obtained so far mainly in …
We propose to describe the dynamics of a cosmological term in the spherically symmetric case by an r-dependent second rank symmetric tensor invariant under boosts in the radial direction. This proposal is based on the Petrov classification scheme and Einstein field equations in the spherically symmetric case. The inflationary equation of state p=-ρis satisfied by the radial pressure. The tangential pressure is calculated from the conservation equation (the contracted Bianchi identity).
We consider the dynamical stability of a class of static, spherically-symmetric solutions of the nonsymmetric gravitational theory. We numerically reproduce the Wyman solution and generate new solutions for the case where the theory has a nontrivial fundamental length scale μ^{-1}. By considering spherically symmetric perturbations of these solutions we show that the Wyman solutions are generically unstable.
The Lagrangian derivation of the Equations of Motion for topological static spherically symmetric metrics in $\mathcal F (R,G)$-modified gravity is presented and the related solutions are discussed. In particular, a new topological solution for the model $\mathcal F (R,G)=R+\sqrt{G}$ is found. The black hole solutions and the First Law of thermodynamic are analyzed. Furthermore, the coupling with electromagnetic field is also considered and a Maxwell solution is derived.
There was obtained a numerical external solution for the exact system of the RTG equations with some natural boundary conditions in the static spherically symmetric case. The properties of the solution are discussed.
The hierarchies of both Lovelock gravity and power-Yang-Mills field are combined through gravity in a single theory. In static, spherically symmetric ansatz exact particular integrals are obtained in all higher dimensions. The advantage of such hierarchies is the possibility of choosing coefficients, which are arbitrary otherwise, to cast solutions into tractable forms. To our knowledge the solutions constitute the most general spherically symmetric metrics that incorporate complexities both of Lovelock and Yang-Mills hierarchies within the common context. A large portion of our general class …
In this paper, we discuss gravitational collapse of spherically symmetric spacetimes. We derive a general formalism by taking two arbitrary spherically symmetric spacetimes with $g_{00}=1$. Israel's junction conditions are used to develop this formalism. The formulae for extrinsic curvature tensor are obtained. The general form of the surface energy-momentum tensor depending on extrinsic curvature tensor components is derived. This leads us to the surface energy density and the tangential pressure. The formalism is applied to two known spherically symmetric spacetimes. The results obtained sho…
It is known that spherically symmetric spacetimes admit flat spacelike foliations. We point out a simple method of seeing this result via the Hamiltonian constraints of general relativity. The method yields explicit formulas for the extrinsic curvatures of the slicings.
The spherically symmetric Einstein-Vlasov system in Schwarzschild coordinates (i.e. polar slicing and areal radial coordinate) is considered. An improved continuation criterion for global existence of classical solutions is given. Two other types of criteria which prevent finite time blow-up are also given.
Using ODE techniques we prove the existence of large classes of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system. These include data for which the ratio of total charge to total mass is arbitrarily large.
The energy distribution in the most general nonstatic spherically symmetric space-time is obtained using Møller's energy-momentum complex. This result is compared with the energy expression obtained by using the energy-momentum complex of Einstein. Some examples of energy distributions in different prescriptions are discussed.
Using tunnelling approach, Hawking radiation is derived for a general class of non-static spherically symmetric space time. The standard tunnelling rate formula is obtained using the unified first law of thermodynamics on the trapping horizon and Hawking temperature is measured by an Kodama observer inside the horizon.
This paper investigates the global properties of a class of spherically symmetric spacetimes. The class contains the maximal development of asymptotically flat spherically symmetric initial data for a wide variety of coupled Einstein-matter systems. For this class, it is proven here that the existence of a single trapped surface or marginally trapped surface implies the completeness of future null infinity and the formation of an event horizon whose area radius is bounded by twice the final Bondi mass.
After dimensional reduction the stationary spherically symmetric sector of Einstein's gravity is identified with an SL(2,R)/SO(2) Sigma model coupled to a one dimensional gravitational remnant. The space of classical solutions consists of a one parameter family interpolating between the Schwarzschild and the Taub-NUT solution. A Dirac Quantization of this system is performed and the observables -- the Schwarzschild mass and the Taub-NUT charge operator -- are shown to be self-adjoint operators with a continuous spectrum ranging from $-\infty$ to $\infty$. The Hilbert space is constructed expli…
An analitical approximation of $<ϕ^2>$ for a massive scalar field in a zero temperature vacuum state in static spherically symmetric spacetimes is obtained. The calculations are based on the method for computing vacuum expectations values for scalar fields in general static spherically symmetric spacetimes derived by Anderson, Hiscock and Samuel [Phys. Rev. D {\bf 51}, 4337 (1995)]. The analitical approximation is used to compute $<ϕ^2>$ in Schwarzschild and wormhole spacetimes.
It is proven that any spherically symmetric spacetime that possesses a compact Cauchy surface $Σ$ and that satisfies the dominant-energy and non-negative-pressures conditions must have a finite lifetime in the sense that all timelike curves in such a spacetime must have a length no greater than $10 \max_Σ(2m)$, where $m$ is the mass associated with the spheres of symmetry. This result gives a complete resolution, in the spherically symmetric case, of one version of the closed-universe recollapse conjecture (though it is likely that a slightly better bound can be established). This bound has th…
Conformally flat spherically symmetric cosmological models representing a charged perfect fluid as well as a bulk viscous fluid distribution have been obtained. The cosmological constant Λis found positive and is a decreasing function of time which is consistent with the recent supernovae observations. The physical and geometrical properties of the models are discussed.
We critically examine the Roberts homothetic solution for the spherically symmetric Einstein-scalar field equations in double null coordinates, and show that the Roberts solution indeed solves the field equations only for one non-trivial case. We generalize this solution and discuss its relations with other known exact solutions.
We find the most general spherically symmetric non singular black hole solution in a special class of teleparallel theory of gravitation. If $r$ is large enough, the general solution coincides with the Schwarzschild solution. Whereas, if $r$ is small, the general solution behaves in a manner similar to that of de Sitter solution. Otherwise it describes a spherically symmetric black hole singularity free everywhere. Moreover, the energy associated with the general solution is calculated using the superpotential given by Møller 1978.
We consider the interesting "near-horizon test" reported in (PRD84, 084006(2011), arXiv:1107.5727) for any static, spherically symmetric (SSS) black hole solution admitted in f(R) gravity. Before adopting the necessary conditions for the test, however, revisions are needed as we point out in this Comment.
In this article, a study of the scalar field shells in relativistic spherically symmetric configurations has been performed. We construct the composite solution of Jordan-Brans-Dicke field equation by matching the conformal Brans solutions at each junction surfaces. This approach allows us to associate rigorously with all solutions as a single glued "space", which is a unique differentiable manifold M^4.
We study the quantum theory of the Einstein-Maxwell action with a cosmological term in the spherically symmetric space-time, and explored quantum black hole solutions in Reissner-Nordstrom-de Sitter geometry. We succeeded to obtain analytic solutions to satisfy both the energy and momentum constraints.
