Convergent null data expansions at space-like infinity of stationary vacuum solutions

We present a characterization of the asymptotics of all asymptotically flat stationary vacuum solutions of Einstein's field equations. This characterization is given in terms of two sequences of symmetric trace free tensors (we call them the `null data'), which determine a formal expansion of the solution, and which are in a one to one correspondence to Hansen's multipoles. We obtain necessary and sufficient growth estimates on the null data to define an absolutely convergent series in a neighbourhood of spatial infinity. This provides a complete characterization of all asymptotically flat stationary vacuum solutions to the field equations.Comment: 71 pages, no figure

Extremal black hole initial data deformations

We study deformations of axially symmetric initial data for Einstein-Maxwell equations satisfying the time-rotation ($t$-$\phi$) symmetry and containing one asymptotically cylindrical end and one asymptotically flat end. We find that the $t$-$\phi$ symmetry implies the existence of a family of deformed data having the same horizon structure. This result allows us to measure how close solutions to Lichnerowicz equation are when arising from nearby free data.Comment: 21 pages, no figures, final versio

Convergent null data expansions at space-like infinity of stationary vacuum solutions

We present a characterization of the asymptotics of all asymptotically flat stationary vacuum solutions of Einstein's field equations. This characterization is given in terms of two sequences of symmetric trace free tensors (we call them the `null data'), which determine a formal expansion of the solution, and which are in a one to one correspondence to Hansen's multipoles. We obtain necessary and sufficient growth estimates on the null data to define an absolutely convergent series in a neighbourhood of spatial infinity. This provides a complete characterization of all asymptotically flat stationary vacuum solutions to the field equations.Comment: 71 pages, no figure

Constant mean curvature surfaces and area-charge inequality for a spheroidal electrically counterpoised dust spacetime

We consider the spacetime presented by Bonnor in 1998, whose matter content is a spheroid of electrically counterpoised dust, in the context of the geometrical inequalities between area and charge. We determine numerically the constant mean curvature surfaces that are candidates to be stable isoperimetric surfaces and analyze the relation between area and charge for them, showing that both a previously proved inequality and a conjectured inequality are far from being saturated. We also show that the maximal initial data has a cylindrical limit where the minimum of the area-charge relation is attained.Fil: Aceña, Andrés Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Interdisciplinario de Ciencias Básicas. - Universidad Nacional de Cuyo. Instituto Interdisciplinario de Ciencias Básicas; Argentin

Horizon area--angular momentum inequality for a class of axially symmetric black holes

We prove an inequality between horizon area and angular momentum for a class of axially symmetric black holes. This class includes initial conditions with an isometry which leaves fixed a two-surface. These initial conditions have been extensively used in the numerical evolution of rotating black holes. They can describe highly distorted black holes, not necessarily near equilibrium. We also prove the inequality on extreme throat initial data, extending previous results.Comment: 23 pages, 5 figures. We improved the hypothesis of the main theore

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

Stable isoperimetric surfaces in super-extreme Reissner-Nordström

We study isoperimetric surfaces in the Reissner-Nordström spacetime, with emphasis on the cuasilocal inequality between area and charge. We analyze the stability of the isoperimetric spheres and we found that there is a lower bound on the area in terms of the charge, and that the inequality is saturated in the transition from the superextremal to the subextremal case. We also derive a general inequality between area and charge for stable isoperimetric surfaces in maximal electro-vacuum initial data.Fil: Aceña, Andrés Esteban. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; ArgentinaFil: Dain, Sergio Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Córdoba. Instituto de Física "Enrique Gaviola"; Argentina. Albert Einstein Institut. Max-Planck-Institut fur Gravitationsphysik; Alemania. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin