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

Quasilocal Formalism and Black Ring Thermodynamics

The thermodynamical properties of a dipole black ring are derived using the quasilocal formalism. We find that the dipole charge appears in the first law in the same manner as a global charge. Using the Gibbs-Duhem relation, we also provide a non-trivial check of the entropy/area relationship for the dipole ring. A preliminary study of the thermodynamic stability indicates that the neutral ring is unstable to angular fluctuations.Comment: 10 pages, no figures; v2, expanded references, misprints corrected; v3: misprint corected in rel. (22); discussion unchange

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

Instability of Einstein-Yang-Mills Solitons for Arbitrary Gauge Groups

We prove that static, spherically symmetric, asymptotically flat, regular solutions of the Einstein-Yang-Mills equations are unstable for arbitrary gauge groups. The proof involves the following main steps. First, we show that the frequency spectrum of a class of radial perturbations is determined by a coupled system of radial "Schroedinger equations". Eigenstates with negative eigenvalues correspond to exponentially growing modes. Using the variational principle for the ground state it is then proven that there always exist unstable modes (at least for "generic" solitons). This conclusion is reached without explicit knowledge of the possible equilibrium solutions.Comment: 11 pages, Latex, ZU-TH 4\9

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