THE LYNDEN-BELL AND KATZ DEFINITION OF GRAVITATIONAL ENERGY - APPLICATIONS TO SINGULAR SOLUTIONS

We apply the Lynden-Bell and Katz (LK) definition of gravitational ene rgy to static and spherically symmetric space-times which admit a curv ature singularity. These are the Tohnan V, Tolman VI and the interior Schwarzschild solutions, the latter with the boundary limit of 9/8th o f the gravitational radius. We show that the LK definition can still b e applied to these solutions despite the presence of a singularity whi ch nonetheless appears to carry no energy in the LK sense. While in th e solutions that we mentioned the KL gravitational energy is positive definite everywhere in space time, this is not the case for the overch arged Reissner-Nordstrom space-time. In the latter case in fact the LK energy density becomes negative sufficiently close to the singularity hence we use the positivity criterion to impose a more stringent limi t of validity to the Reissner-Nordstrom solution.