Black holes in static vacuum space-times

An extension of Israel's theorem on the regularity of Killing horizons is proven. Well behaved asymptotically flat vacuum solutions of the Einstein equations which represent the exterior of a non-rotating black hole are considered. It is shown that the black hole has spherical topology and that the equipotential surfaces g ₀₀=constant are non-intersecting two-spheres. The solutions must therefore be members of the one-parameter family of spherically symmetric Schwarzschild solutions.This work has been carried out under a NATO Research Fellowship.     

LETTER: Generalized Vaidya Solutions

A large family of solutions, representing, ingeneral, spherically symmetric Type II fluid, ispresented, which includes most of the known solutions tothe Einstein field equations, such as, the monopole-de Sitter-charged Vaidya ones.     

Spherically symmetric configurations of General Relativity in presence of scalar fields: separation of circular orbits

We show that the test body stable circular orbits around the spherically symmetric black hole (BH) configuration can form disjoint structures in presence of a minimally coupled nonlinear scalar field. General conditions for the disjoint structures to exist are formulated. To present examples we construct a two-parametric family of exact solutions to Einstein equations with scalar fields for appropriate self-interaction potentials. For different values of the family parameters the solutions describe either BH or naked singularity (NS). We found numerically regions of the parameters when there exist two disjoint regions of stable circular orbits; such nonconnected structures indeed can exist in case of both BH and NS solutions.     

Supersymmetric coloured/hairy black holes

We discuss all possible spherically symmetric black hole type solutions to an N=2 supergravity model with SO(3) gauging. The solutions consist of a one parameter family of black hole solutions evading the no-hair theorem and an isolated solution that is a supersymmetric analogue of a coloured black hole.     

Vacuum nonsingular black hole

The spherically symmetric vacuum stress-energy tensor with one assumption concerning its specific form generates the exact analytic solution of the Einstein equations which for larger coincides with the Schwarzschild solution, for smallr behaves like the de Sitter solution and describes a spherically symmetric black hole singularity free everywhere.This essay received the fifth award from the Gravity Research Foundation, 1991     

Dynamics of phantom matter

A spherically symmetric evolution model of self-gravitating matter with the equation of state p = ?(1 + δ)? (where δ = const) is considered. The equations of the model are written in the frame of reference co-moving with matter. A criterion for the existence and formation of a horizon is defined. Part of the Einstein equations is integrated analytically. The initial conditions and the constraints imposed on these conditions in the presence of a horizon are determined. For small δ, an analytic solution to spherically symmetric time-dependent Einstein equations is obtained. Conditions are determined under which the dynamics of matter changes from collapse to expansion. Characteristic times of the evolution of the system are evaluated. It is proved that the accretion of phantom matter (for δ > 0) onto a black hole leads to the decreases of the horizon radius of the black hole (i.e., the black hole is dissolved).     

Matching Spherical Dust Solutions to Construct Cosmological Models

Conditions for smooth cosmological models are set out and applied to inhomogeneous spherically symmetric models constructed by matching together different Lemaître–Tolman–Bondi solutions to the Einstein field equations. As an illustration the methods are applied to a collapsing dust sphere in a curved background. This describes a region which expands and then collapses to form a black hole in an Einstein de Sitter background. We show that in all such models if there is no vacuum region then the singularity must go on accreting matter for an infinite LTB time.     

The model of the black hole enclosed in dust: the flat space case

The model is constructed to describe the Schwarzschild-like black hole enclosed in the dust cosmological background. It is an exact solution of Einstein equations for spherically symmetric dust distribution, and is a special case of Lemaitre–Tolman–Bondi solutions. The motion of the test particle in the model is investigated in comoving coordinate frame. Observable velocity of the particle is found from geodesic equations. It is shown that chosen reference system does not allow to solve the problem of ’all or nothing’ behavior.     

Gravitational Lensing by Charged Black Holes

We formulate the lensing effects of a spherically symmetric electrically charged black hole using thin lens equations. The charged black hole leads to three images and could lead to three Einstein rings provided the parameters such as the mass, charge and the distances satisfy certain constraints. We have computed the exact positions of images and magnification properties for a super-massive black hole with electric charge.     

The Boulware–Deser class of spacetimes radiates

We establish the result that the standard Boulware–Deser spacetime can radiate. This allows us to model the dynamics of a spherically symmetric radiating dynamical star in five-dimensional Einstein–Gauss–Bonnet gravity with three spacetime regions. The local internal region is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the vacuum Boulware–Deser exterior. Our approach allows for all three spacetime regions to be modeled by the same class of metric functions. A large family of solutions to the field equations are presented for various realistic equations of state. A comparison of our solutions with earlier well known results is undertaken and we show that Einstein–Gauss–Bonnet analogues of these solutions, including those of Husain, are contained in our family. We also generalise our results to higher dimensions.     

Computational soliton solutions to $$$$-dimensional generalised Kadomtsev–Petviashvili and $$(2+1)$$(2+1)-dimensional Gardner–Kadomtsev–Petviashvili models and their applications

In this paper, we present a formalism to generate a family of interior solutions to the Einstein–Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere matched to the exterior Reissner–Nordström space–time. By reducing the Einstein–Maxwell system to a recurrence relation with variable rational coefficients, we show that it is possible to obtain closed-form solutions for a specific range of model parameters. A large class of solutions obtained previously are shown to be contained in our general class of solutions. We also analyse the physical viability of our new class of solutions.     

Letter: Generating Static Black Holes in Higher Dimensional Space-Times

In this article we extend to higher dimensional space-times a recent theorem proved by Salgado which characterizes a three-parameter family of static and spherically symmetric solutions to the Einstein Field Equations. As it happens in four dimensions, it is shown that the Schwarzschild, Reissner-Nordström and global monopole solutions in higher dimensions are particular cases from this family.     

Some general properties of the renormalized stress-energy tensor for static quantum states on (<Emphasis Type="Italic">n</Emphasis> + 1)-dimensional spherically symmetric black holes

We study the renormalized stress-energy tensor (RSET) for static quantum states on (n + 1)-dimensional, static, spherically symmetric black holes. By solving the conservation equations, we are able to write the stress-energy tensor in terms of a single unknown function of the radial co-ordinate, plus two arbitrary constants. Conditions for the stress-energy tensor to be regular at event horizons (including the extremal and “ultra-extremal” cases) are then derived using generalized Kruskal-like co-ordinates. These results should be useful for future calculations of the RSET for static quantum states on spherically symmetric black hole geometries in any number of space-time dimensions.     

Scalar hairy black holes and solitons in a gravitating Goldstone model

We study black hole solutions of Einstein gravity coupled to a specific global symmetry breaking Goldstone model described by an O(3) isovector scalar field in four spacetime dimensions. Our configurations are static and spherically symmetric, approaching at infinity a Minkowski spacetime background. A set of globally regular, particle-like solutions are found in the limit of vanishing event horizon radius. These configurations can be viewed as ‘regularised’ global monopoles, since their mass is finite and the spacetime geometry has no deficit angle. As an unusual feature, we notice the existence of extremal black holes in this model defined in terms of gravity and scalar fields only.     

An investigation of embeddings for spherically symmetric spacetimes into Einstein manifolds

Embeddings into higher dimensions are very important in the study of higher-dimensional theories of our Universe and in high-energy physics. Theorems which have been developed recently guarantee the existence of embeddings of pseudo-Riemannian manifolds into Einstein spaces and more general pseudo-Riemannian spaces. These results provide a technique that can be used to determine solutions for such embeddings. Here we consider local isometric embeddings of four-dimensional spherically symmetric spacetimes into five-dimensional Einstein manifolds. Difficulties in solving the five-dimensional equations for given four-dimensional spaces motivate us to investigate embedded spaces that admit bulks of a specific type. We show that the general Schwarzschild–de Sitter spacetime and Einstein Universe are the only spherically symmetric spacetimes that can be embedded into an Einstein space of a particular form, and we discuss their five-dimensional solutions.     

Are all static black hole solutions spherically symmetric?

The static black hole solutions to the Einstein-Maxwell equations are all spherically symmetric, as are many of the recently discovered black hole solutions in theories of gravity coupled to other forms of matter. However, counterexamples demonstrating that static black holes need not be spherically symmetric exist in theories, such as the standard electroweak model, with electrically charged massive vector fields. In such theories, a magnetically charged Reissner-Nordström solution with sufficiently small horizon radius is unstable against the development of a nonzero vector field outside the horizon. General arguments show that, for generic values of the magnetic charge, this field cannot be spherically symmetric. Explicit construction of the solution shows that it in fact has no rotational symmetry at all.This essay received the second award from the Gravity Research Foundation, 1995-Ed.     

Static spherically symmetric solutions of the Einstein-Yang-Mills equations

We study the global behaviour of static, spherically symmetric solutions of the Einstein-Yang-Mills equations with gauge groupSU(2). Our analysis results in three disjoint classes of solutions with a regular origin or a horizon. The 3-spaces (t=const.) of the first, generic class are compact and singular. The second class consists of an infinite family of globally regular, resp. black hole solutions. The third type is an oscillating solution, which although regular is not asymptotically flat.This article was processed by the author using the Springer-Verlag TEX CoMaPhy macro package 1991.     

Perfect fluid and scalar field in the Reissner-Nordström metric

We describe the spherically symmetric steady-state accretion of perfect fluid in the Reissner-Nordström metric. We present analytic solutions for accretion of a fluid with linear equations of state and of the Chaplygin gas. We also show that under reasonable physical conditions, there is no steady-state accretion of a perfect fluid onto a Reissner-Nordström naked singularity. Instead, a static atmosphere of fluid is formed. We discuss a possibility of violation of the third law of black hole thermodynamics for a phantom fluid accretion.     

Einstein equations for a fluid sphere and the mass function

A mass function is used to study the Einstein equations in the case of a spherically symmetric ideal fluid. A new system of Einstein equations is proposed and it is shown that this system is simpler than the standard system for the given solutions. The mass function is used to obtain certain exact solutions, including the general solution for a uniform fluid sphere.Dnepropetrovsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 90–95, April, 1995.     

Applications of Lie Symmetries to Higher Dimensional Gravitating Fluids

We consider a radiating shear-free spherically symmetric metric in higher dimensions. Several new solutions to the Einstein’s equations are found systematically using the method of Lie analysis of differential equations. Using the five Lie point symmetries of the fundamental field equation, we obtain either an implicit solution or we can reduce the governing equations to a Riccati equation. We show that known solutions of the Einstein equations can produce infinite families of new solutions. Earlier results in four dimensions are shown to be special cases of our generalised results.