2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131851We prove two related results. The first is an ``Earthquake Theorem'' for closed hyperbolic surfaces with cone singularities where the total angle is less than $π$: any two such metrics in are connected by a unique left earthquake. The second result is that the space of ``globally hyperbolic'' AdS manifolds with ``particles'' -- cone singularities (of given angle) along time-like lines -- is parametrized by the product of two copies of the Teichmüller space with some marked points (corresponding to the cone singularities). The two statements are proved together.18 pages, several figures. v2: improved exposition, several correctionsGeometric TopologyDifferential Geometrytext