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On the uniqueness of smooth, stationary black holes in vacuum,
 Invent. Math.
, 2009
"... Abstract. The goal of the paper is to prove a perturbative result, concerning the uniqueness of Kerr solutions; result which we believe to be useful in the proof of their nonlinear stability. Following the program started in ..."
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Cited by 35 (6 self)
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Abstract. The goal of the paper is to prove a perturbative result, concerning the uniqueness of Kerr solutions; result which we believe to be useful in the proof of their nonlinear stability. Following the program started in
From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
, 2007
"... This article reviews some aspects in the current relationship between mathematical and numerical General Relativity. Focus is placed on the description of isolated systems, with a particular emphasis on recent developments in the study of black holes. Ideas concerning asymptotic flatness, the initia ..."
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Cited by 5 (3 self)
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This article reviews some aspects in the current relationship between mathematical and numerical General Relativity. Focus is placed on the description of isolated systems, with a particular emphasis on recent developments in the study of black holes. Ideas concerning asymptotic flatness, the initial value problem, the constraint equations, evolution formalisms, geometric inequalities and quasilocal black hole horizons are discussed on the light of the interaction between numerical and mathematical relativists.
Spacetime Ehlers group: Transformation law for the
, 2001
"... The spacetime Ehlers group, which is a symmetry of the Einstein vacuum field equations for strictly stationary spacetimes, is defined and analyzed in a purely spacetime context (without invoking the projection formalism). In this setting, the Ehlers group finds its natural description within an infi ..."
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Cited by 4 (1 self)
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The spacetime Ehlers group, which is a symmetry of the Einstein vacuum field equations for strictly stationary spacetimes, is defined and analyzed in a purely spacetime context (without invoking the projection formalism). In this setting, the Ehlers group finds its natural description within an infinite dimensional group of transformations that maps Lorentz metrics into Lorentz metrics and which may be of independent interest. The Ehlers group is shown to be well defined independently of the causal character of the Killing vector (which may become null on arbitrary regions). We analyze which global conditions are required on the spacetime for the existence of the Ehlers group. The transformation law for the Weyl tensor under Ehlers transformations is explicitly obtained. This allows us to study where, and under which circumstances, curvature singularities in the transformed spacetime will arise. The results of the paper are applied to obtain a local characterization of the KerrNUT metric.
Alfonso GarcíaParrado GómezLobo
, 805
"... Abstract. Exploiting a 3+1 analysis of the MarsSimon tensor, conditions on a vacuum initial data set ensuring that its development is isometric to a subset of the Kerr spacetime are found. These conditions are expressed in terms of the vanishing of a positive scalar function defined on the initial ..."
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Abstract. Exploiting a 3+1 analysis of the MarsSimon tensor, conditions on a vacuum initial data set ensuring that its development is isometric to a subset of the Kerr spacetime are found. These conditions are expressed in terms of the vanishing of a positive scalar function defined on the initial data hypersurface. Applications of this result are discussed.
domains
, 2011
"... Given a compact domain of a 3dimensional hypersurface on a vacuum spacetime, a scalar (the “nonKerrness”) is constructed by solving a Dirichlet problem for a second order elliptic system. If such scalar vanishes, and a set of conditions are satisfied at a point, then the domain of dependence of th ..."
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Given a compact domain of a 3dimensional hypersurface on a vacuum spacetime, a scalar (the “nonKerrness”) is constructed by solving a Dirichlet problem for a second order elliptic system. If such scalar vanishes, and a set of conditions are satisfied at a point, then the domain of dependence of the compact domain is isometric to a portion of a member of the Kerr family of solutions to the Einstein field equations. This construction is expected to be of relevance in the analysis of numerical simulations of black hole spacetimes. PACS: 04.20.Ex, 04.20.Jb, 04.25.dg 1