On Black Hole Solutions in a Model With Anisotropic Fluid (original) (raw)

On black hole solutions in model with anisotropic fluid

2002

A family of spherically symmetric solutions in the model with 1-component anisotropic fluid is considered. The metric of the solution depends on a parameter q > 0 relating radial pressure and the density and contains n -1 parameters corresponding to Ricci-flat ``internal space'' metrics. For q = 1 and certain equations of state the metric coincides with the metric of black brane solutions in the model with antisymmetric form. A family of black hole solutions corresponding to natural numbers q = 1,2, ... is singled out. Certain examples of solutions (e.g. containing for q =1 Reissner-Nordstr\"{o}m, M2 and M5 black brane metrics) are considered. The post-Newtonian parameters beta and gamma corresponding to the 4-dimensional section of the metric are calculated.

Black hole in closed spacetime with an anisotropic fluid

Physical Review D, 2017

We study spherically symmetric geometries made of anisotropic perfect fluid based on general relativity. The purpose of the work is to find and classify black hole solutions in closed spacetime. In a general setting, we find that a static and closed space exists only when the radial pressure is negative but its size is smaller than the density. The Einstein equation is eventually casted into a first order autonomous equation on two-dimensional plane of scale-invariant variables, which are equivalent to the Tolman-Oppenheimer-Volkoff (TOV) equation in general relativity. Then, we display various solution curves numerically. An exact solution describing a black hole solution in a closed spacetime was known in Ref. [1], which solution bears a naked singularity and negative energy era. We find that the two deficits can be remedied when ρ + 3p1 > 0 and ρ + p1 + 2p2 < 0, where the second violates the strong energy condition.

On spherically symmetric solutions with horizon in model with multicomponent anisotropic fluid

Journal of Mathematical Physics, 2004

A family of spherically symmetric solutions in the model with mcomponent multicomponent anisotropic fluid is considered. The metric of the solution depends on parameters q s > 0, s = 1, . . . , m, relating radial pressures and the densities and contains (n − 1)m parameters corresponding to Ricci-flat "internal space" metrics and obeying certain m(m − 1)/2 ("orthogonality") relations. For q s = 1 (for all s) and certain equations of state (p s i = ±ρ s ) the metric coincides with the metric of intersecting black brane solution in the model with antisymmetric forms. A family of solutions with (regular) horizon corresponding to natural numbers q s = 1, 2, . . . is singled out. Certain examples of "generalized simulation" of intersecting M -branes in D = 11 supergravity are considered. The post-Newtonian parameters β and γ corresponding to the 4-dimensional section of the metric are calculated.

Anholonomic Triads and New Classes of (2+1)Dimensional Black Hole solutions

2001

We apply the method of moving anholonomic frames in order to construct new classes of solutions of the Einstein equations on (2+1)-dimensional pseudo-Riemannian spaces. There are investigated black holes with deformed horizons and renormalized locally anisotropic constants. We speculate on properties of such anisotropic black holes with characteristics defined by anholonomic frames and anisotropic interactions of matter and gravity. The thermodynamics of locally anisotropic black holes is discussed in connection with a possible statistical mechanics background based on locally anisotropic variants of Chern-Simons theories.

Black hole at Lovelock gravity with anisotropic fluid

arXiv: General Relativity and Quantum Cosmology, 2016

In this work a new family of black hole solutions in Lovelock gravity is discussed. These solutions describe anisotropic fluids which extend to the spatial infinity. Though far from the horizon their geometries approach some previously known black holes solutions the location of the horizons differ. Furthemore, although the masses of these solutions match the masses of those previously known black holes, their temperatures and entropies differ.

Anisotropic black holes in Einstein and brane gravity

Arxiv preprint hep-th/0108065, 2001

We consider exact solutions of Einstein equations defining static black holes parametrized by off-diagonal metrics which by anholonomic mappings can be equivalently transformed into some diagonal metrics with coefficients being very similar to those from the Schwarzschild and/or Reissner-Nördstrom solutions with anisotropic renormalizations of constants. We emphasize that such classes of solutions, for instance, with ellipsoidal symmetry of horizons, can be constructed even in general relativity theory if off-diagonal metrics and anholonomic frames are introduced into considerations. Such solutions do not violate the Israel's uniqueness theorems on static black hole configurations [1] because at long radial distances one holds the usual Schwarzschild limit. We show that anisotropic deformations of the Reissner-Nördstrom metric can be an exact solution on the brane, re-interpreted as a black hole with an effective electromagnetic like charge anisotropically induced and polarized by higher dimension gravitational interactions.

Post-Newtonian parameters for general black hole and spherically symmetric p-brane solutions

Gravitation and Cosmology, 2001

Black hole p-brane solutions for a wide class of intersection rules are considered. The solutions are defined on a manifold which contains a product of n-1 Ricci-flat "internal'' spaces. The post-Newtonian parameters "beta" and "gamma" corresponding to a 4-dimensional section of the metric for general intersection rules are studied. It is shown that "beta" does not depend but "gamma" depends on brane intersections. For "block-orthogonal" intersection rules spherically symmetric solutions are considered, and explicit relations for post-Newtonian parameters are obtained. The bounds on parameters of solutions following from observational restrictions in the Solar system are presented.

Black holes and other spherical solutions in quadratic gravity with a cosmological constant

Physical Review D, 2021

We study static spherically symmetric solutions to the vacuum field equations of quadratic gravity in the presence of a cosmological constant Λ. Motivated by the trace no-hair theorem, we assume the Ricci scalar to be constant throughout a spacetime. Furthermore, we employ the conformalto-Kundt metric ansatz that is valid for all static spherically symmetric spacetimes and leads to a considerable simplification of the field equations. We arrive at a set of two ordinary differential equations and study its solutions using the Frobenius-like approach of (infinite) power series expansions. While the indicial equations considerably restrict the set of possible leading powers, careful analysis of higher-order terms is necessary to establish the existence of the corresponding classes of solutions. We thus obtain various non-Einstein generalizations of the Schwarzschild, (anti-)de Sitter [or (A)dS for short], Nariai, and Plebański-Hacyan spacetimes. Interestingly, some classes of solutions allow for an arbitrary value of Λ, while other classes admit only discrete values of Λ. For most of these classes, we give recurrent formulas for all series coefficients. We determine which classes contain the Schwarzschild-(A)dS black hole as a special case and briefly discuss the physical interpretation of the spacetimes. In the discussion of physical properties, we naturally focus on the generalization of the Schwarzschild-(A)dS black hole, namely the Schwarzschild-Bach-(A)dS black hole, which possesses one additional Bach parameter. We also study its basic thermodynamical properties and observable effects on test particles caused by the presence of the Bach tensor. This work is a considerable extension of our letter [

Late-time tails, entropy aspects, and stability of black holes with anisotropic fluids

The European Physical Journal C

In this work we consider black holes surrounded by anisotropic fluids in four dimensions. We first study the causal structure of these solutions showing some similarities and differences with Reissner–Nordström–de Sitter black holes. In addition, we consider scalar perturbations on this background geometry and compute the corresponding quasinormal modes. Moreover, we discuss the late-time behavior of the perturbations finding an interesting new feature, i.e., the presence of a subdominant power-law tail term. Likewise, we compute the Bekenstein entropy bound and the first semiclassical correction to the black hole entropy using the brick wall method, showing their universality. Finally, we also discuss the thermodynamical stability of the model.

Radiating black hole solutions in arbitrary dimensions

General Relativity and Gravitation, 2007

We prove a theorem that characterizes a large family of non-static solutions to Einstein equations in N-dimensional space-time, representing, in general, spherically symmetric Type II fluid. It is shown that the best known Vaidya-based (radiating) black hole solutions to Einstein equations, in both four dimensions (4D) and higher dimensions (HD), are particular cases from this family. The spherically symmetric static black hole solutions for Type I fluid can also be retrieved. A brief discussion on the energy conditions, singularities and horizons is provided.