Uniqueness of (dilatonic) charged black holes and black p-branes in higher dimensions

We prove the uniqueness of higher dimensional (dilatonic) charged black holes in static and asymptotically flat spacetimes for arbitrary vector-dilaton coupling constant. An application to the uniqueness of a wide class of black p-branes is also given.Comment: 6 page

Uniqueness Theorem for Generalized Maxwell Electric and Magnetic Black Holes in Higher Dimensions

Based on the conformal energy theorem we prove the uniqueness theorem for static higher dimensional electrically and magnetically charged black holes being the solution of Einstein (n-2)-gauge forms equations of motion. Black hole spacetime contains an asymptotically flat spacelike hypersurface with compact interior and non-degenerate components of the event horizon.Comment: 7 pages, RevTex, to be published in Phys.Rev.D1

Static perfect fluids with Pant-Sah equations of state

We analyze the 3-parameter family of exact, regular, static, spherically symmetric perfect fluid solutions of Einstein's equations (corresponding to a 2-parameter family of equations of state) due to Pant and Sah and "rediscovered" by Rosquist and the present author. Except for the Buchdahl solutions which are contained as a limiting case, the fluids have finite radius and are physically realistic for suitable parameter ranges. The equations of state can be characterized geometrically by the property that the 3-metric on the static slices, rescaled conformally with the fourth power of any linear function of the norm of the static Killing vector, has constant scalar curvature. This local property does not require spherical symmetry; in fact it simplifies the the proof of spherical symmetry of asymptotically flat solutions which we recall here for the Pant-Sah equations of state. We also consider a model in Newtonian theory with analogous geometric and physical properties, together with a proof of spherical symmetry of the asymptotically flat solutions.Comment: 32 p., Latex, minor changes and correction

TIME-SYMMETRIC INITIAL DATA SETS IN 4--D DILATON GRAVITY

I study the time--symmetric initial--data problem in theories with a massless scalar field (dilaton), free or coupled to a Maxwell field in the stringy way, finding different initial--data sets describing an arbitrary number of black holes with arbitrary masses, charges and asymptotic value of the dilaton. The presence of the scalar field gives rise to a number of interesting effects. The mass and charges of a single black hole are different in its two asymptotically flat regions across the Einstein--Rosen bridge. The same happens to the value of the dilaton at infinity. This forbids the identification of these asymptotic regions in order to build (Misner) wormholes in the most naive way. Using different techniques, I find regular initial data for stringy wormholes. The price payed is the existence singularities in the dilaton field. The presence of a single--valued scalar seems to constrain strongly the allowed topologies of the initial space--like surface. Other kinds of scalar fields (taking values on a circle or being defined up to an additive constant) are also briefly considered.Comment: latex file, 38 pages

Topological and geometrical restrictions, free-boundary problems and self-gravitating fluids

Let (P1) be certain elliptic free-boundary problem on a Riemannian manifold (M,g). In this paper we study the restrictions on the topology and geometry of the fibres (the level sets) of the solutions f to (P1). We give a technique based on certain remarkable property of the fibres (the analytic representation property) for going from the initial PDE to a global analytical characterization of the fibres (the equilibrium partition condition). We study this analytical characterization and obtain several topological and geometrical properties that the fibres of the solutions must possess, depending on the topology of M and the metric tensor g. We apply these results to the classical problem in physics of classifying the equilibrium shapes of both Newtonian and relativistic static self-gravitating fluids. We also suggest a relationship with the isometries of a Riemannian manifold.Comment: 36 pages. In this new version the analytic representation hypothesis is proved. Please address all correspondence to D. Peralta-Sala

Time-Independent Gravitational Fields

This article reviews, from a global point of view, rigorous results on time independent spacetimes. Throughout attention is confined to isolated bodies at rest or in uniform rotation in an otherwise empty universe. The discussion starts from first principles and is, as much as possible, self-contained.Comment: 47 pages, LaTeX, uses Springer cl2emult styl

Non-existence theorems for Yang-Mills fields outside the black hole of the Schwarzschild spacetime

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