Universal low temperature theory of charged black holes with AdS 2 horizons

Abstract

We consider the low temperature quantum theory of a charged black hole of zero temperature horizon radius R h in a spacetime which is asymptotically AdS D (D > 3) far from the horizon. At temperatures T a 1/R h , the near-horizon geometry is AdS 2 , and the black hole is described by a universal 0+1 dimensional effective quantum theory of time diffeomorphisms with a Schwarzian action and a phase mode conjugate to the U(1) charge. We obtain this universal 0+1 dimensional effective theory starting from the full D-dimensional Einstein-Maxwell theory, while keeping quantitative track of the couplings. The couplings of the effective theory are found to be in agreement with those expected from the thermodynamics of the D-dimensional black hole.