54 research outputs found
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 (-) symmetry and containing one
asymptotically cylindrical end and one asymptotically flat end. We find that
the - 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
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