On the Uniqueness of the Papapetrou--Majumdar Metric

We establish the equality of the ADM mass and the total electric charge for asymptotically flat, static electrovac black hole spacetimes with completely degenerate, not necessarily connected horizon.Comment: 9 pages, latex, no figures, to appear in Class. Quantum Gra

Stationary perturbations and infinitesimal rotations of static Einstein-Yang-Mills configurations with bosonic matter

Using the Kaluza-Klein structure of stationary spacetimes, a framework for analyzing stationary perturbations of static Einstein-Yang-Mills configurations with bosonic matter fields is presented. It is shown that the perturbations giving rise to non-vanishing ADM angular momentum are governed by a self-adjoint system of equations for a set of gauge invariant scalar amplitudes. The method is illustrated for SU(2) gauge fields, coupled to a Higgs doublet or a Higgs triplet. It is argued that slowly rotating black holes arise generically in self-gravitating non-Abelian gauge theories with bosonic matter, whereas, in general, soliton solutions do not have rotating counterparts.Comment: 8 pages, revtex, no figure

Dressing a black hole with non-minimally coupled scalar field hair

We investigate the possibility of dressing a four-dimensional black hole with classical scalar field hair which is non-minimally coupled to the space-time curvature. Our model includes a cosmological constant but no self-interaction potential for the scalar field. We are able to rule out black hole hair except when the cosmological constant is negative and the constant governing the coupling to the Ricci scalar curvature is positive. In this case, non-trivial hairy black hole solutions exist, at least some of which are linearly stable. However, when the coupling constant becomes too large, the black hole hair becomes unstable.Comment: 17 pages, 7 figures, uses iopart.cls. Minor changes, accepted for publication in Classical and Quantum Gravit

The 2+1 charged black hole in topologically massive Electrodynamics

The 2+1 black hole coupled to a Maxwell field can be charged in two different ways. On the one hand, it can support a Coulomb field whose potential grows logarithmically in the radial coordinate. On the other, due to the existence of a non-contractible cycle, it also supports a topological charge whose value is given by the corresponding Abelian holonomy. Only the Coulomb charge, however, is given by a constant flux integral with an associated continuity equation. The topological charge does not gravitate and is somehow decoupled from the black hole. This situation changes abruptly if one turns on the Chern-Simons term for the Maxwell field. First, the flux integral at infinity becomes equal to the topological charge. Second, demanding regularity of the black hole horizon, it is found that the Coulomb charge (whose associated potential now decays by a power law) must vanish identically. Hence, in 2+1 topologically massive electrodynamics coupled to gravity, the black hole can only support holonomies for the Maxwell field. This means that the charged black hole, as the uncharged one, is constructed from the vacuum by means of spacetime identifications.Comment: 4 pages, no figures, LaTex, added reference

A Mass Bound for Spherically Symmetric Black Hole Spacetimes

Requiring that the matter fields are subject to the dominant energy condition, we establish the lower bound $(4\pi)^{-1} \kappa {\cal A}$ for the total mass $M$ of a static, spherically symmetric black hole spacetime. (${\cal A}$ and $\kappa$ denote the area and the surface gravity of the horizon, respectively.) Together with the fact that the Komar integral provides a simple relation between $M - (4\pi)^{-1} \kappa A$ and the strong energy condition, this enables us to prove that the Schwarzschild metric represents the only static, spherically symmetric black hole solution of a selfgravitating matter model satisfying the dominant, but violating the strong energy condition for the timelike Killing field $K$ at every point, that is, $R(K,K) \leq 0$. Applying this result to scalar fields, we recover the fact that the only black hole configuration of the spherically symmetric Einstein-Higgs model with arbitrary non-negative potential is the Schwarzschild spacetime with constant Higgs field. In the presence of electromagnetic fields, we also derive a stronger bound for the total mass, involving the electromagnetic potentials and charges. Again, this estimate provides a simple tool to prove a ``no-hair'' theorem for matter fields violating the strong energy condition.Comment: 16 pages, LATEX, no figure

A no-go on strictly stationary spacetimes in four/higher dimensions

We show that strictly stationary spacetimes cannot have non-trivial configurations of form fields/complex scalar fields and then the spacetime should be exactly Minkowski or anti-deSitter spacetimes depending on the presence of negative cosmological constant. That is, self-gravitating complex scalar fields and form fields cannot exist.Comment: 8 page

Pulsation of Spherically Symmetric Systems in General Relativity

The pulsation equations for spherically symmetric black hole and soliton solutions are brought into a standard form. The formulae apply to a large class of field theoretical matter models and can easily be worked out for specific examples. The close relation to the energy principle in terms of the second variation of the Schwarzschild mass is also established. The use of the general expressions is illustrated for the Einstein-Yang-Mills and the Einstein-Skyrme system.Comment: 21 pages, latex, no figure

Black Rings, Boosted Strings and Gregory-Laflamme

We investigate the Gregory-Laflamme instability for black strings carrying KK-momentum along the internal direction. We demonstrate a simple kinematical relation between the thresholds of the classical instability for the boosted and static black strings. We also find that Sorkin's critical dimension depends on the internal velocity and in fact disappears for sufficiently large boosts. Our analysis implies the existence of an analogous instability for the five-dimensional black ring of Emparan and Reall. We also use our results for boosted black strings to construct a simple model of the black ring and argue that such rings exist in any number of space-time dimensions.Comment: 26 pages, 6 figure

Skyrme Black Holes in the Isolated Horizons Formalism

We study static, spherically symmetric, Skyrme black holes in the context of the assumption that they can be viewed as bound states between ordinary bare black holes and solitons. This assumption and results stemming from the isolated horizons formalism lead to several conjectures about the static black hole solutions. These conjectures are tested against the Skyrme black hole solutions. It is shown that, while there is in general good agreement with the conjectures, a crucial aspect seems to violate one of the conjectures.Comment: Full journal version, 6 pages, 5 figure

A classification (uniqueness) theorem for rotating black holes in 4D Einstein-Maxwell-dilaton theory

In the present paper we prove a classification (uniqueness) theorem for stationary, asymptotically flat black hole spacetimes with connected and non-degenerate horizon in 4D Einstein-Maxwell-dilaton theory with an arbitrary dilaton coupling parameter $\alpha$. We show that such black holes are uniquely specified by the length of the horizon interval, angular momentum, electric and magnetic charge and the value of the dilaton field at infinity when the dilaton coupling parameter satisfies $0\le \alpha^2\le3$. The proof is based on the nonpositivity of the Riemann curvature operator on the space of the potentials. A generalization of the classification theorem for spacetimes with disconnected horizons is also given.Comment: 15 pages, v2 typos correcte