Static Black Hole Solutions Research Articles

Mass of colored black holes

New results pertaining to colored static black hole solutions to the Einstein-Yang-Mills equations are obtained. The isolated horizons framework is used to define the concept of Hamiltonian Horizon Mass of the black hole. An unexpected relation between the ADM and Horizon masses of the black hole solution with the ADM mass of the corresponding Bartnik-McKinnon soliton is found. These results can be generalized to other non-linear theories and they suggest a general testing bed for the instability of the corresponding hairy black holes.

Regular (2+1)-dimensional black holes within nonlinear electrodynamics

(2+1)-regular static black hole solutions with a nonlinear electric field are derived. The source to the Einstein equations is an energy momentum tensor of nonlinear electrodynamics, which satisfies the weak energy conditions and in the weak field limit becomes the (2+1)-Maxwell field tensor. The derived class of solutions is regular; the metric, curvature invariants and electric field are regular everywhere. The metric becomes, for a vanishing parameter, the (2+1)-static charged BTZ solution. A general procedure to derive solutions for the static BTZ (2+1)-spacetime, for any nonlinear Lagrangian depending on the electric field is formulated; for relevant electric fields one requires the fulfillment of the weak energy conditions.

Violation of the cosmic no hair conjecture in the Einstein-Maxwell-dilaton system

The cosmic no hair conjecture is tested in the spherically symmetric Einstein-Maxwell-dilaton (EMD) system with a positive cosmological constant \ensuremath{\Lambda}. First, we analytically show that once gravitational collapse occurs in the massless dilaton case, the system of field equations breaks down inevitably in outer communicating regions or at the boundary provided that a future null infinity ${\mathcal{I}}^{+}$ exists. Next, we find numerically the static black hole solutions in the massive dilaton case and investigate their properties for comparison with the massless case. It is shown that their Abbott-Deser (AD) mass is infinite, which implies that a spacetime with finite AD mass does not approach a black hole solution after gravitational collapse. These results suggest that ${\mathcal{I}}^{+}$ cannot appear in the EMD system once gravitational collapse occurs and hence the cosmic no hair conjecture is violated in both the massless and massive cases, in contrast with general relativity.

Mechanics of isolated horizons

A set of boundary conditions defining an undistorted, non-rotating isolated horizon are specified in general relativity. A spacetime representing a black hole which is itself in equilibrium but whose exterior contains radiation admits such a horizon. However, the definition is applicable in a more general context, such as cosmological horizons. Physically motivated, (quasi-)local definitions of the mass and surface gravity of an isolated horizon are introduced and their properties analysed. Although their definitions do not refer to infinity, these quantities assume their standard values in the static black-hole solutions. Finally, using these definitions, the zeroth and first laws of black-hole mechanics are established for isolated horizons.

Remarks on conserved quantities and entropy of BTZ black hole solutions. I. The general setting

The BTZ stationary black hole solution is considered and its mass and angular momentum are calculated by means of Noether theorem. In particular, relative conserved quantities with respect to a suitably fixed background are discussed. Entropy is then computed in a geometric and macroscopic framework, so that it satisfies the first principle of thermodynamics. In order to compare this more general framework to the prescription by Wald et al. we construct the maximal extension of the BTZ horizon by means of Kruskal-like coordinates. A discussion about the different features of the two methods for computing entropy is finally developed.

Brown-York quasilocal energy, gravitational charge, and black hole horizons

We study a recently proposed horizon defining identity for certain black hole spacetimes. It relates the difference of the Brown-York quasilocal energy and the Komar charge at the horizon to the total energy of the spacetime. The Brown-York quasilocal energy is evaluated for some specific choices of spacetime foliations. With a certain condition imposed on the matter distribution, we prove this identity for spherically symmetric static black hole solutions of general relativity. For these cases, we show that the identity can be derived from a Gauss-Codacci condition that any three-dimensional timelike boundary embedded around the hole must obey. We also demonstrate the validity of the identity in other cases by explicitly applying it to several static, non-static, asymptotically flat, and asymptotically non-flat black hole solutions. These include the asymptotically FRW solutions and the case of a black hole with a global monopole charge.

LETTER: Newman–Janis Method and Rotating Dilaton-Axion Black Hole

It is shown that the dilaton-axion rotating black hole solution can be obtained from GGHS static charged dilaton black hole solution via the Newman–Janis method.

New black hole solutions in Brans-Dicke theory of gravity

An existence check of nontrivial, stationary axisymmetric black hole solutions in the Brans-Dicke theory of gravity in different directions from those of Penrose, Thorne and Dykla, and Hawking is performed. Namely, working directly with the known explicit spacetime solutions in Brans-Dicke theory, it is found that nontrivial Kerr-Newman-type black hole solutions different from general relativistic solutions could occur for the generic Brans-Dicke parameter values $\ensuremath{-}5/2<~\ensuremath{\omega}<\ensuremath{-}3/2.$ Finally, issues such as whether these new black holes carry scalar hair and can really arise in nature, and if they can, what the associated physical implications would be, are discussed carefully.

Do Naked Singularities Generically Occur in Generalized Theories of Gravity?

A new mechanism for causing naked singularities is found in an effective superstring theory. We investigate the gravitational collapse in a spherically symmetric Einstein-Maxwell-dilaton system in the presence of a pure cosmological constant "potential", where the system has no static black hole solution. We show that once gravitational collapse occurs in the system, naked singularities necessarily appear in the sense that the field equations break down in the domain of outer communications. This suggests that in generalized theories of gravity, the non-minimally coupled fields generically cause naked singularities in the process of gravitational collapse if the system has no static or stationary black hole solution.

Stationary black holes in a generalized three-dimensional theory of gravity

We consider a generalized three-dimensional theory of gravity which is specified by two fields, the graviton and the dilaton, and one parameter. This theory contains, as particular cases, three-dimensional General Relativity and three-dimensional String Theory. Stationary black hole solutions are generated from the static ones using a simple coordinate transformation. The stationary black holes solutions thus obtained are locally equivalent to the corresponding static ones, but globally distinct. The mass and angular momentum of the stationary black hole solutions are computed using an extension of the Regge and Teitelboim formalism. The causal structure of the black holes is described.

Properties of naked black holes

We investigate the properties of a class of near-extreme static black hole solutions called naked black holes. These black holes, which occur in string theory, have small curvature invariants but large tidal forces outside their event horizons. We show that these large tidal forces are due to a concentration of dilaton stress-energy near the horizon. We study infalling test strings and find that they are highly excited by the large tidal forces, but remain small. Perhaps most importantly, it turns out that a small amount of infalling matter will cause the curvature invariants to become large outside the horizon. Nevertheless, an exact calculation shows that both the matter trajectories and the classical black hole background are not significantly altered.

Black holes in N = 2 supergravity theories and harmonic functions

We present dyonic BPS static black hole solutions for general d = 4, N = 2 supergravity theories coupled to vector and hypermultiplets. These solutions are generalisations of the spherically symmetric Majumdar-Papapetrou black hole solutions of Einstein-Maxwell gravity and are completely characterised by a set of constrained harmonic functions. In terms of the underlying special geometry, these harmonic functions are identified with the imaginary part of the holomorphic sections defining the special Kähler manifold and the metric is expressed in terms of the symplectic invariant Kähler potential. The relations of the holomorphic sections to the harmonic functions constitute the “ generalised stabilisation equations” for the moduli fields. In addition to asymptotic flatness, the harmonic functions are also constrained by the requirement that the Kähler connection of the underlying Hodge-Kähler manifold has to vanish in order to obtain static solutions. The behaviour of these solutions near the horizon is also explained.

General Static N=2 Black Holes

We find general static BPS black hole solutions for general N=2, d=4 supergravity theories with an arbitrary number of vector multiplets. These solutions are completely specified by the Kähler potential of the underlying special Kähler geometry and a set of constrained harmonic functions.

Static Black-Hole Solutions with Axial Symmetry

We construct a new class of asymptotically flat black hole solutions in Einstein-Yang-Mills and Einstein-Yang-Mills-dilaton theory. These black hole solutions are static, and they have a regular event horizon. However, they possess only axial symmetry. Like their regular counterparts, the black hole solutions are characterized by two integers, the winding number $n$ and the node number $k$ of the gauge field functions.

Black holes in N = 2 supergravity theories and harmonic functions

We present dyonic BPS static black hole solutions for general d=4, N=2 supergravity theories coupled to vector and hypermultiplets. These solutions are generalisations of the spherically symmetric Majumdar-Papapetrou black hole solutions of Einstein-Maxwell gravity and are completely characterised by a set of constrained harmonic functions. In terms of the underlying special geometry, these harmonic functions are identified with the imaginary part of the holomorphic sections defining the special K\"ahler manifold and the metric is expressed in terms of the symplectic invariant K\"ahler potential. The relations of the holomorphic sections to the harmonic functions constitute the generalised stabilisation equations for the moduli fields. In addition to asymptotic flatness, the harmonic functions are also constrained by the requirement that the K\"ahler connection of the underlying Hodge-K\"ahler manifold has to vanish in order to obtain static solutions. The behaviour of these solutions near the horizon is also explained.

Static N = 2 black holes for quadratic prepotentials

We employ the principle of minimal central charge and study the entropy of N = 2 black holes corresponding to the most general quadratic prepotential. We also give a static black hole solution for these models in which the scalar moduli are non constants. Finally, we speculate on the microscopic origin for our solution.

Effective Lagrangian and Static Black Holes in 2-D Dilatonic Gravity Inspired by Quantum Effects

We study the effective action in 2-D dilaton-Maxwell quantum gravity. Working with the one-loop renormalizable subset of such theories, we construct the improved effective Lagrangian which contains curvature under logarithm. This effective Lagrangian leads to new classical dilatonic gravity inspired by quantum effects. The static black holes (BH) solutions which may play the role of a remnant after the Hawking radiation for such theory are carefully investigated. The effective Lagrangian for Gross–Neveu-dilaton gravity is also constructed (in 1/N expansion).

Modifications of the BTZ black hole by a dilaton and scalar

We investigate some modifications of the static BTZ black hole solution due to a chosen asymptotically constant dilaton/scalar. New classes of static black hole solutions are obtained. One of the solutions contains the Martinez-Zanelli conformal black hole solution as a special case. Using quasilocal formalism, we calculate their mass for a finite spatial region that contains the black hole. Their temperatures are also computed. Finally, using some of the curvature singularities as examples, we investigate whether a quantum particle behaves singularly or not.

Ehlers-Harrison transformations and black holes in dilaton-axion gravity with multiple vector fields

Dilaton-axion gravity with $p U(1)$ vector fields is studied on space-times admitting a timelike Killing vector field. Three-dimensional sigma-model is derived in terms of K\"ahler geometry, and holomorphic representation of the SO(2,2+p) global symmetry is constructed. A general static black hole solution depending on $2p+5$ parameters is obtained via SO(2,2+p) covariantization of the Schwarzschild solution. The metric in the curvature coordinates looks as the variable mass Reissner-Nordstr\"om one and generically possesses two horizons. The inner horizon is pushed to the singularity if electric and magnetic SO(p) charge vectors are parallel. For non-parallel charges the inner horizon has a finite area except for an extremal limit when this property is preserved only for orthogonal charges. Extremal dyon configurations with orthogonal charges have finite horizon radii continuously varying from zero to the ADM mass. New general solution is endowed with a NUT parameter, asymptotic values of dilaton and axion, and a gauge parameter which can be used to ascribe any given value to one of scalar charges.

Dimensionally continued Oppenheimer-Snyder gravitational collapse: Solutions in even dimensions

The extension of the general relativity theory to higher dimensions, so that the field equations for the metric remain of second order, is done through the Lovelock action. This action can also be interpreted as the dimensionally continued Euler characteristics of lower dimensions. The theory has many constant coefficients apparently without any physical meaning. However, it is possible, in a natural way, to reduce to two (the cosmological and Newton's constant) these several arbitrary coefficients, yielding a restricted Lovelock gravity. In this process one separates theories in even dimensions from theories in odd dimensions. These theories have static black hole solutions. In general relativity, black holes appear as the final state of gravitational collapse. In this work, gravitational collapse of a regular dust fluid in even dimensional restricted Lovelock gravity is studied. It is found that black holes emerge as the final state for these regular initial conditions.