On Uniqueness of static Einstein-Maxwell-Dilation black holes

We prove uniqueness of static, asymptotically flat spacetimes with non-degenerate black holes for three special cases of Einstein-Maxwell-dilaton theory: For the coupling ''''$alpha = 1$'' (which is the low energy limit of string theory) on the one hand, and for vanishing magnetic or vanishing electric field (but arbitrary coupling) on the other hand. Our work generalizes in a natural, but non-trivial way the uniqueness result obtained by Masood-ul-Alam who requires both $alpha = 1$ and absence of magnetic fields, as well as relations between the mass and the charges. Moreover, we simplify Masood-ul-Alam's proof as we do not require any non-trivial extensions of Witten's positive mass theorem. We also obtain partial results on the uniqueness problem for general harmonic m

Minimal data at a given point of space for solutions to certain geometric systems

We consider a geometrical system of equations for a three dimensional Riemannian manifold. This system of equations has been constructed as to include several physically interesting systems of equations, such as the stationary Einstein vacuum field equations or harmonic maps coupled to gravity in three dimensions. We give a characterization of its solutions in a neighbourhood of a given point through sequences of symmetric trace free tensors (referred to as `null data'). We show that the null data determine a formal expansion of the solution and we obtain necessary and sufficient growth estimates on the null data for the formal expansion to be absolutely convergent in a neighbourhood of the given point. This provides a complete characterization of all the solutions to the given system of equations around that point.Comment: 26 pages, no figure

On marginally outer trapped surfaces in stationary and static spacetimes

In this paper we prove that for any spacelike hypersurface containing an untrapped barrier in a stationary spacetime satisfying the null energy condition, any marginally outer trapped surface cannot lie in the exterior region where the stationary Killing vector is timelike. In the static case we prove that any marginally outer trapped surface cannot penetrate into the exterior region where the static Killing vector is timelike. In fact, we prove these result at an initial data level, without even assuming existence of a spacetime. The proof relies on a powerful theorem by Andersson and Metzger on existence of an outermost marginally outer trapped surface.Comment: 22 pages, 3 figures; 1 reference added, 1 figure changed, other minor change

The Wahlquist-Newman solution

Based on a geometrical property which holds both for the Kerr metric and for the Wahlquist metric we argue that the Kerr metric is a vacuum subcase of the Wahlquist perfect-fluid solution. The Kerr-Newman metric is a physically preferred charged generalization of the Kerr metric. We discuss which geometric property makes this metric so special and claim that a charged generalization of the Wahlquist metric satisfying a similar property should exist. This is the Wahlquist-Newman metric, which we present explicitly in this paper. This family of metrics has eight essential parameters and contains the Kerr-Newman-de Sitter and the Wahlquist metrics, as well as the whole Pleba\'nski limit of the rotating C-metric, as particular cases. We describe the basic geometric properties of the Wahlquist-Newman metric, including the electromagnetic field and its sources, the static limit of the family and the extension of the spacetime across the horizon.Comment: LaTeX, 18 pages, no figures. Accepted for publication in Phys. Rev.

A simple proof of the recent generalisations of Hawking's black hole topology theorem

A key result in four dimensional black hole physics, since the early 1970s, is Hawking's topology theorem asserting that the cross-sections of an "apparent horizon", separating the black hole region from the rest of the spacetime, are topologically two-spheres. Later, during the 1990s, by applying a variant of Hawking's argument, Gibbons and Woolgar could also show the existence of a genus dependent lower bound for the entropy of topological black holes with negative cosmological constant. Recently Hawking's black hole topology theorem, along with the results of Gibbons and Woolgar, has been generalised to the case of black holes in higher dimensions. Our aim here is to give a simple self-contained proof of these generalisations which also makes their range of applicability transparent.Comment: 12 pages, 1 figur

Gravitational radiation from dynamical black holes

An effective energy tensor for gravitational radiation is identified for uniformly expanding flows of the Hawking mass-energy. It appears in an energy conservation law expressing the change in mass due to the energy densities of matter and gravitational radiation, with respect to a Killing-like vector encoding a preferred flow of time outside a black hole. In a spin-coefficient formulation, the components of the effective energy tensor can be understood as the energy densities of ingoing and outgoing, transverse and longitudinal gravitational radiation. By anchoring the flow to the trapping horizon of a black hole in a given sequence of spatial hypersurfaces, there is a locally unique flow and a measure of gravitational radiation in the strong-field regime.Comment: 5 revtex4 pages. Additional comment

Uniqueness properties of the Kerr metric

We obtain a geometrical condition on vacuum, stationary, asymptotically flat spacetimes which is necessary and sufficient for the spacetime to be locally isometric to Kerr. Namely, we prove a theorem stating that an asymptotically flat, stationary, vacuum spacetime such that the so-called Killing form is an eigenvector of the self-dual Weyl tensor must be locally isometric to Kerr. Asymptotic flatness is a fundamental hypothesis of the theorem, as we demonstrate by writing down the family of metrics obtained when this requirement is dropped. This result indicates why the Kerr metric plays such an important role in general relativity. It may also be of interest in order to extend the uniqueness theorems of black holes to the non-connected and to the non-analytic case.Comment: 30 pages, LaTeX, submitted to Classical and Quantum Gravit

The Simon and Simon-Mars Tensors for Stationary Einstein-Maxwell Fields

Modulo conventional scale factors, the Simon and Simon-Mars tensors are defined for stationary vacuum spacetimes so that their equality follows from the Bianchi identities of the second kind. In the nonvacuum case one can absorb additional source terms into a redefinition of the Simon tensor so that this equality is maintained. Among the electrovacuum class of solutions of the Einstein-Maxwell equations, the expression for the Simon tensor in the Kerr-Newman-Taub-NUT spacetime in terms of the Ernst potential is formally the same as in the vacuum case (modulo a scale factor), and its vanishing guarantees the simultaneous alignment of the principal null directions of the Weyl tensor, the Papapetrou field associated with the timelike Killing vector field, the electromagnetic field of the spacetime and even the Killing-Yano tensor.Comment: 12 pages, Latex IOP article class, no figure

On the topology of untrapped surfaces

Recently a simple proof of the generalizations of Hawking's black hole topology theorem and its application to topological black holes for higher dimensional ($n\geq 4$) spacetimes was given \cite{rnew}. By applying the associated new line of argument it is proven here that strictly stable untrapped surfaces do possess exactly the same topological properties as strictly stable marginally outer trapped surfaces (MOTSs) are known to have. In addition, a quasi-local notion of outwards and inwards pointing spacelike directions--applicable to untrapped and marginally trapped surfaces--is also introduced.Comment: 9 pages, no figure

Stability of marginally outer trapped surfaces and symmetries

We study properties of stable, strictly stable and locally outermost marginally outer trapped surfaces in spacelike hypersurfaces of spacetimes possessing certain symmetries such as isometries, homotheties and conformal Killings. We first obtain results for general diffeomorphisms in terms of the so-called metric deformation tensor and then particularize to different types of symmetries. In particular, we find restrictions at the surfaces on the vector field generating the symmetry. Some consequences are discussed. As an application we present a result on non-existence of stable marginally outer trapped surfaces in slices of FLRW.Comment: 23 pages, 3 figure