A New Boundary Counterterm for Asymptotically AdS Spacetimes

We present a modified version of the boundary counterterm method for removing divergences from the action of an asymptotically AdS spacetime. The standard approach renders the action finite but leaves diffeomorphism invariance partially broken if the dimension of the spacetime is odd. We show that this symmetry is restored by a new boundary counterterm, needed to cancel a divergence that appears in dimensional regularization. The result is a finite, diffeomorphism invariant action appropriate for gravitational physics. As an example we calculate the action for the Kerr-AdS5 black hole. Unlike the standard boundary counterterm results, our action yields conserved charges that are consistent with the first law of black hole thermodynamics.