Vacuum space-times with controlled singularities and without symmetries
We present a family of four-dimensional vacuum space-times with asymptotically velocity dominated singularities and without symmetries.
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arXiv subjects
Piotr T. Chruściel
Publications and source records attributed to Piotr T. Chruściel.
Hamiltonian dynamics in the space of asymptotically Kerr-de Sitter spacetimes
We determine all spacetime flows which lead to a Hamiltonian dynamics in the space of general relativistic initial data sets with asymptotically Kerr-de Sitter ends. The corresponding Hamiltonians are calculated. Some implications for black-hole thermodynamics are pointed out.
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Initial data sets with ends of cylindrical type: I. The Lichnerowicz equation
We construct large classes of vacuum general relativistic initial data sets, possibly with a cosmological constant Lambda, containing ends of cylindrical type.
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Characteristic initial data and smoothness of Scri. I. Framework and results
We analyze the Cauchy problem for the vacuum Einstein equations with data on a complete light-cone in an asymptotically Minkowskian space-time. We provide conditions on the free initial data which guarantee existence of global solutions of the characteristic constraint equations. We present necessary-and-sufficient conditions on characteristic initial data in $3+1$ dimensions to have no logarithmic terms in an asymptotic expansion at null infinity.
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The mass of light-cones
We give an elementary proof of positivity of total gravitational energy in space-times containing complete smooth light-cones.
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A2: Mathematical relativity and other progress in classical gravity theory - a session report
We report on selected oral contributions to the A2 session "Mathematical relativity and other progress in classical gravity theory" of "The 20th International Conference on General Relativity and Gravitation (GR20)" in Warsaw.
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Solutions of the vacuum Einstein equations with initial data on past null infinity
We prove existence of vacuum space-times with freely prescribable cone-smooth initial data on past null infinity.
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KIDs like cones
We analyze vacuum Killing Initial Data on characteristic Cauchy surfaces. A general theorem on existence of Killing vectors in the domain of dependence is proved, and some special cases are analyzed in detail, including the case of bifurcate Killing horizons.
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On maximal globally hyperbolic vacuum space-times
We prove existence and uniqueness of maximal global hyperbolic developments of vacuum general relativistic initial data sets with initial data (g,K) in Sobolev spaces $H^s\oplus H^{s-1}$ with integer s > n/2 +1.
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Space-time diagrammatics
We introduce a new class of two-dimensional diagrams, the \emph{projection diagrams}, as a tool to visualize the global structure of space-times. We construct the diagrams for several metrics of interest, including the Kerr-Newman - (anti) de Sitter family, with or without cosmological constant, and the Emparan-Reall black rings.
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The existence theorem for the general relativistic Cauchy problem on the light-cone
We prove existence of solutions of the vacuum Einstein equations with initial data induced by a smooth metric on a light-cone.
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The many ways of the characteristic Cauchy problem
We review various aspects of the characteristic initial value problem for the Einstein equations, presenting new approaches to some of the issues arising.
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Cauchy problem with data on a characteristic cone for the Einstein-Vlasov equations
We show how to solve the Cauchy problem for the Einstein-Vlasov equations with geometric initial data on a light-cone.
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Stationary Black Holes: Uniqueness and Beyond
The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are characterized by their mass, angular momentum and global charges. Moreover, the high degree of symmetry displayed by vacuum and electro-vacuum black-hole spacetimes ceases to exist in self-gravitating non-linear field theories. This text aims to review some developments in the subject and to discuss them in light of the uniqueness theorem for the Einstein-Maxwell system.
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On Lorentzian causality with continuous metrics
We present a systematic study of causality theory on Lorentzian manifolds with continuous metrics. Examples are given which show that some standard facts in smooth Lorentzian geometry, such as light-cones being hypersurfaces, are wrong when metrics which are merely continuous are considered. We show that existence of time functions remains true on domains of dependence with continuous metrics, and that $C^{0,1}$ differentiability of the metric suffices for many key results of the smooth causality theory.
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Initial data sets with ends of cylindrical type: II. The vector constraint equation
We construct solutions of the vacuum vector constraint equations on manifolds with cylindrical ends.
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Existence of singularities in two-Kerr black holes
We show that the angular momentum - area inequality 8π|J| =< A for weakly stable minimal surfaces would apply to (I^+)-regular many-Kerr solutions, if any existed. Hence we remove the undesirable hypothesis in the Hennig-Neugebauer proof of non-existence of well behaved two-component solutions.
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Elements of causality theory
These notes present some elements of causality theory. While they are not as complete as other treatments of the topic, there is some originality in that the whole approach is based on a definition of causal curves which allows to simplify many arguments. We keep track of the differentiability needed for various statements, obtaining a coherent theory for twice-continuously-differentiable metrics.
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