Multi Black Holes and Earthquakes on Riemann surfaces with boundaries

Francesco Bonsante; Kirill Krasnov; Jean-Marc Schlenker

doi:10.1093/imrn/rnq070

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arXiv · math/0610429

Multi Black Holes and Earthquakes on Riemann surfaces with boundaries

Francesco Bonsante·Kirill Krasnov·Jean-Marc Schlenker

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Abstract

We prove an "Earthquake Theorem" for hyperbolic metrics with geodesic boundary on a compact surfaces $S$ with boundary: given two hyperbolic metrics with geodesic boundary on a surface with $k$ boundary components, there are $2^k$ right earthquakes transforming the first in the second. An alternative formulation arises by introducing the enhanced Teichmueller space of S: We prove that any two points of the latter are related by a unique right earthquake. The proof rests on the geometry of ``multi-black holes'', which are 3-dimensional anti-de Sitter manifolds, topologically the product of a surface with boundary by an interval.

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BibTeX RIS

Francesco Bonsante, Kirill Krasnov, Jean-Marc Schlenker. 2009-07-19. Multi Black Holes and Earthquakes on Riemann surfaces with boundaries. https://doi.org/10.1093/imrn%2Frnq070

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