Re: Papers that Calculate BH potential energy Lawrence
Spino...@aol.com
On Monday, February 29, 2016 at 12:10:13 AM UTC-6, Spino...@aol.com wrote:Bruce you may not be aware of where this conversation ended up. I don't think I was correct in arguing that the BH ADM mass is twice the total Hawking radiation energy. I think Birkoff's theorem is a no go for this to be true. We would have the emission of gravity waves on a spherically symmetric collapse and this is not the case.What I said , I think did make sense in terms of MTW with regard to Gravitational energy localization, but the Wiki article on this says that MTW assert that gravitational IS localized for this type of system.In physics, the Cooperstock's energy-localization hypothesis is a hypothesis proposed by Fred Cooperstock that in general relativity, energy only exists in regions of non-vanishing energy–momentum tensor.[1]
Since the creation of general relativity there have been questions about the energy of gravitational fields. Among the proposals for the energy are the Landau–Lifshitz pseudotensor,Einstein pseudotensor, and the Møller superpotential.
In Misner, Thorne & Wheeler[2] the authors claimed that energy can only be localized for spherical systems, which Cooperstock & Sarracino [3] demonstrated implies that energy must be localized for all systems, while Bondi [4] argued that non-localizable energy is not allowed in general relativity.
The energy localization hypothesis has also been proven for a number of specific examples (see for example Ref [5]), but has not been proven or disproven in general.
Feynman's sticky bead argument shows that energy is transported by gravitational waves, which is difficult to make compatible with the Cooperstock's hypothesis.
I can't find where MTW say this, but it must be the case or symmetrical collapse would generate gravity waves. It seems the question of Gravitational energy localization is not a settled issue. I don't see how the assertion of Ha, Brown, York and Maluf put the equivalence principle in jeopardy. I think what they are saying makes sense in contrast to my original claim.
Bob Zannelli
A completely spherical collapse would not generate gravitational waves. It requires quadupole moments in the collapse.
LC