Positivity of energy for asymptotically locally AdS spacetimes

Abstract

We derive necessary conditions for the spinorial Witten-Nester energy to be well-defined for asymptotically locally AdS spacetimes. We find that the conformal boundary should admit a spinor satisfying certain differential conditions and in odd dimensions the boundary metric should be conformally Einstein. We show that these conditions are satisfied by asymptotically AdS spacetimes. The gravitational energy (obtained using the holographic stress energy tensor) and the spinorial energy are equal in even dimensions and differ by a bounded quantity related to the conformal anomaly in odd dimensions.

Figures (1)

• Figure 1: We illustrate in this figure the various slices used in this paper. The shaded area is the initial value surface, $\partial M$ is the conformal boundary of the spacetime and $\Sigma_r$ is the regulated surface.