Volume renormalization for conformally compact asymptotically hyperbolic manifolds in dimension four

Abstract

We derive a new renormalized volume formula for conformally compact asymptotically hyperbolic manifolds in dimension four. The formula generalizes the ones given by Anderson, Albin, and Chang-Qing-Yang for the case of Poincare-Einstein manifolds. We also derive variational formulas for the renormalized seen as a functional on the manifold.

References in corpus (1)

• Renormalized area and properly embedded minimal surfaces in hyperbolic 3-manifolds

Cited by in corpus (1)

• Einstein-AdS action, renormalized volume/area and holographic Renyi entropies