The Hawking energy or Hawking mass is one of the possible definitions of mass in general relativity. It is a measure of the bending of ingoing and outgoing rays of light that are orthogonal to a 2-sphere surrounding the region of space whose mass is to be defined.
Contents
Definition
Let
where
Properties
In the Schwarzschild metric, the Hawking mass of any sphere
A result of Geroch implies that Hawking mass satisfies an important monotonicity condition. Namely, if
where
Said otherwise, Hawking mass is increasing for the inverse mean curvature flow.
Hawking mass is not necessarily positive. However, it is asymptotic to the ADM or the Bondi mass, depending on whether the surface is asymptotic to spatial infinity or null infinity.