Multi Black Holes and Earthquakes on Riemann surfaces with boundaries

Details Multi Black Holes and Earthquakes on Riemann surfaces with boundaries Multi Black Holes and Earthquakes on Riemann surfaces with boundaries

2006-10-13

arxiv.org/abs/math/0610429v5

Int. Math. Res. Not. 2011 (2011):3, 487-552

Mathematics

Geometric Topology

29 pages, several figures. v2: corrections, more detailed arguments, etc. Update to v3 was an error while trying to update ano

Scientific paper

10.1093/imrn/rnq070

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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