Penrose quasi-local energy and Kerr-Schild metrics

Abstract

Specialising to the case of Kerr-Schild spacetimes, which include the Kerr black hole and gravitational wave solutions, we propose a modification of the Penrose quasi-local energy. The modification relies on the existence of a natural Minkowski background for Kerr-Schild spacetimes. We find that the modified surface integral reduces to a volume integral of the Einstein tensor, which has been proposed previously as an appropriate definition for quasi-local energy for Kerr-Schild backgrounds. Furthermore, in the special case that the Kerr-Schild null vector is normal to the surface of interest, we construct a 1-1 map between the 2-surface twistors in the Kerr-Schild background and Minkowski twistors projected onto the surface.

arXiv comment18 pages, appendix added

References in corpus (9)

• The Dynamics of General Relativity
• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Energy and angular momentum of charged rotating black holes
• Quasilocal mass in general relativity
• Isometric embeddings into the Minkowski space and new quasi-local mass
• Møller Energy for the Kerr-Newman metric
• Two dimensional Sen connections in general relativity
• Two dimensional Sen connections and quasi-local energy-momentum
• Entanglement entropy, the Einstein equation and the Sparling construction