Geometry of the 2+1 black hole.
Máximo Bañados,Máximo Bañados,Marc Henneaux,Marc Henneaux,Claudio Teitelboim,Claudio Teitelboim,Jorge Zanelli,Jorge Zanelli +7 more
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The geometry of the spinning black holes of standard Einstein theory in 2+1 dimensions, with a negative cosmological constant, and without couplings to matter, is analyzed in detail.Abstract:
The geometry of the spinning black holes of standard Einstein theory in 2+1 dimensions, with a negative cosmological constant, and without couplings to matter, is analyzed in detail. It is shown that the black hole arises from identifications of points of anti\char21{}de Sitter space by a discrete subgroup of SO(2,2). The generic black hole is a smooth manifold in the metric sense. The surface r=0 is not a curvature singularity but, rather, a singularity in the causal structure. Continuing past it would introduce closed timelike lines. However, simple examples show the regularity of the metric at r=0 to be unstable: couplings to matter bring in a curvature singularity there. Kruskal coordinates and Penrose diagrams are exhibited. Special attention is given to the limiting cases of (i) the spinless hole of zero mass, which differs from anti\char21{}de Sitter space and plays the role of the vacuum, and (ii) the spinning hole of maximal angular momentum. A thorough classification of the elements of the Lie algebra of SO(2,2) is given in an appendix.read more
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Quotients of anti de Sitter space
Owen Madden,Simon F. Ross +1 more
TL;DR: In this article, the quotient of n+1-dimensional anti-de Sitter space was studied by one-parameter subgroups of its isometry group SO(2,n) for general n.
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Revisiting the asymptotic dynamics of General Relativity on AdS$_3$
TL;DR: In this article, the dual dynamics of Einstein gravity on AdS$_3$ supplemented with boundary conditions of KdV-type is identified, and the theory at the boundary is non-relativistic and possesses anisotropic scaling of Lifshitz type.
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Functional determinants, generalized BTZ geometries and Selberg zeta function
Rodrigo Aros,D. E. Diaz +1 more
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References
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Gravitationally collapsing dust in 2+1 dimensions.
Robert B. Mann,Simon F. Ross +1 more
TL;DR: The circumstances under which gravitationally collapsing dust can form a black hole in three-dimensional spacetime are investigated.