Multi-black holes and earthquakes on Riemann surfaces with boundaries

International audienceWe prove an "Earthquake Theorem" for hyperbolic metrics with geodesic boundary on a compact surface 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 Teichmuller 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 three-dimensional Anti-de Sitter manifolds, topologically the product of a surface with boundary by an interval