Gravitational Corner Conditions in Holography

Abstract: Contrary to popular belief, asymptotically anti-de Sitter solutions of gravitational theories cannot be obtained by taking initial data (satisfying the constraints) on a spacelike surface, and choosing an arbitrary conformal metric on the timelike boundary at infinity. There are an infinite number of corner conditions that also must be satisfied where the initial data surface hits the boundary. These are well known to mathematical relativists, but to make them more widely known we give a simple explanation of why these conditions exist and discuss some of their consequences. An example is given which illustrates their power. Some implications for holography are also mentioned.