Quasi-local mass integrals and the total mass

Abstract

On asymptotically flat and asymptotically hyperbolic manifolds, by evaluating the total mass via the Ricci tensor, we show that the limits of certain Brown-York type and Hawking type quasi-local mass integrals equal the total mass of the manifold in all dimensions.

References updated, introduction revised

References in corpus (1)

• Chern's magic form and the Gauss-Bonnet-Chern mass

Cited by in corpus (2)

• Quasi-local energy with respect to de Sitter/anti-de Sitter reference
• Some functionals on compact manifolds with boundary