Multi Black Holes and Earthquakes on Riemann surfaces with boundaries
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.