On the global existence and the asymptotic behavior of solutions to the Einstein-Maxwell-Yang-Mills equations
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This article is published in Journal of Differential Geometry.The article was published on 1991-01-01 and is currently open access. It has received 223 citations till now. The article focuses on the topics: Asymptotic analysis & Asymptotology.read more
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A Higher dimensional stationary rotating black hole must be axisymmetric
TL;DR: In this paper, it was shown that in spacetimes of dimension greater than 4, it is no longer true that the orbits of the stationary Killing field on the horizon must return to the same null geodesic generator.
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On the regularity of solutions to the Yamabe equation and the existence of smooth hyperboloidal initial data for Einstein's field equations
TL;DR: The regularity of the solutions to the Yamabe Problem in the case of conformally compact manifolds and negative scalar curvature is investigated in this article, and the existence of smooth hyperboloidal initial data for Einstein's field equations is demonstrated.
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Einstein equations and conformal structure: Existence of Anti-de Sitter-type space-times
TL;DR: In this paper, a conformally invariant Caftan connection representation of the equations was derived and the existence of asymptotically simple solutions to Einstein's equations with a positive cosmological constant was shown.
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On the rigidity theorem for spacetimes with a stationary event horizon or a compact Cauchy horizon
TL;DR: In this article, the authors considered smooth electrovac spacetimes which represent either an asymptotically flat, stationary black hole or a cosmological spacetime with a compact Cauchy horizon ruled by closed null geodesics and showed that there exists a Killing vector field in a one-sided neighborhood of the horizon which is normal to the horizon.
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Hyperbolic reductions for Einstein's equations
TL;DR: In this paper, the authors consider the problem of reducing initial value problems for Einstein's field equations to hyperbolic systems, a problem of importance for numerical as well as analytical investigations of gravitational fields.
References
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Book
The Large Scale Structure of Space-Time
TL;DR: In this paper, the authors discuss the General Theory of Relativity in the large and discuss the significance of space-time curvature and the global properties of a number of exact solutions of Einstein's field equations.
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Cosmological Event Horizons, Thermodynamics, and Particle Creation
TL;DR: In this article, it was shown that the relationship between event horizons and thermodynamics can be extended to cosmological models with a repulsive cosmology constant, and that the spacetime metric itself appears to be observer-dependent.
Book
Spinors and space-time
Roger Penrose,Wolfgang Rindler +1 more
TL;DR: The calculus of 2-spinors was introduced and systematically developed in this article, which leads not only to a deeper understanding of the structure of space-time, but also provides shortcuts to some very tedious calculations.
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Conformal deformation of a Riemannian metric to constant scalar curvature
TL;DR: In this paper, a new global idea was introduced to solve the Yamabe problem in dimensions 3, 4, and 5, and the existence of a positive solution u on M of the equation was proved in all remaining cases.