We apply the Lynden-Bell and Katz (LK) definition of gravitational energy to static and sperically symmetric space-times which admit a curvature singularity. These are Tolman V, Tolman VI and the interior Schwarzschild solutions, the latter with the boundary limit of 9/8th of the gravitational radius. We show that the LK definition can still be applied to these solutions despite the presence of a singularity which nonetheless appears to carry no energy in the LK sense. While in the solutions that we mentioned the LK gravitational energy is positive definite everywhere, we show that this is not the case for the overcharged Reissner-Nordström space-time.
The Lynden-Bell and Katz definition of gravitational energy: application to singular solutions
CORIASCO, Sandro
1994-01-01
Abstract
We apply the Lynden-Bell and Katz (LK) definition of gravitational energy to static and sperically symmetric space-times which admit a curvature singularity. These are Tolman V, Tolman VI and the interior Schwarzschild solutions, the latter with the boundary limit of 9/8th of the gravitational radius. We show that the LK definition can still be applied to these solutions despite the presence of a singularity which nonetheless appears to carry no energy in the LK sense. While in the solutions that we mentioned the LK gravitational energy is positive definite everywhere, we show that this is not the case for the overcharged Reissner-Nordström space-time.
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