The Lynden-Bell and Katz definition of gravitational energy: Applications to singular solutions |
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Authors: | Fernando de Felice Yunqiang Yu Sandro Coriasco |
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Institution: | (1) Dipartimento di Fisica G. Galilei, Universitá di Padova, Via Marzolo 8, I-35131 Padova, Italy;(2) Sezione di Padova, INFN, Italy;(3) Department of Physics, Peking University, 100871 Beijing, China;(4) Istituto di Fisica Matematica J.-L. Lagrange, Universitá di Torino, Via C. Alberto 10, I-10123 Torino, Italy |
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Abstract: | We apply the Lynden-Bell and Katz (LK) definition of gravitational energy to static and spherically symmetric space-times which admit a curvature singularity. These are the 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 KL gravitational energy is positive definite everywhere in space time, this is not the case for the overcharged Reissner-Nordström 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 limit of validity to the Reissner-Nordström solution. |
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