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Energy, Hamiltonian, Noether charge, and black holes
1999
Physical Review D, Particles and fields
It is shown that in general the energy E and the Hamiltonian H of matter fields on the black hole exterior play different roles. H is a generator of the time evolution along the Killing time while E enters the first law of black hole thermodynamics. For non-minimally coupled fields the difference H- E is not zero and is a Noether charge Q analogous to that introduced by Wald to define the black hole entropy. If fields vanish at the spatial boundary, Q is reduced to an integral over the horizon.
doi:10.1103/physrevd.59.064020
fatcat:zglfctxmvbeinakg5brdc2erau