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- W3045596908 abstract "Kartik Prabhu Enrico Fermi Institute and Department of Physics, The University of Chicago, Chicago, IL 60637, USA Abstract We derive the first law of black hole mechanics for physical theories based on a local covariant and gauge-invariant Lagrangian where the dynamical fields transform non-trivially under the action of some internal gauge group. The theories of interest include General Relativity formulated in terms of tetrads, Einstein-Yang-Mills theory and Einstein-Dirac theory. Since the dynamical fields of these theories have some internal gauge freedom, we argue that there is no natural group action of diffeomorphisms of spacetime on such dynamical fields. In general, such fields cannot even be represented as smooth, globally well-defined tensor fields on spacetime. Consequently the derivation of the first law by Iyer and Wald cannot be used directly. Nevertheless, we show how such theories can be formulated on a principal bundle and that there is a natural action of automorphisms of the bundle on the fields. These bundle automorphisms encode both spacetime diffeomorphisms and internal gauge transformations. Using this reformulation we define the Noether charge associated to an infinitesimal automorphism and the corresponding notion of stationarity and axisymmetry of the dynamical fields. We can then obtain a general first law of black hole mechanics for such theories. The first law relates the perturbed Hamiltonians at spatial infinity and the horizon and, that the horizon contributions take the form of a “potential times perturbed charge” term. We further identify the gravitational potential and perturbed charge as the temperature and perturbed entropy of the black hole. We also comment on the ambiguities in defining a prescription for the total entropy for black holes." @default.
- W3045596908 created "2020-08-03" @default.
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- W3045596908 date "2016-01-01" @default.
- W3045596908 modified "2023-09-23" @default.
- W3045596908 title "The first law of black hole mechanics for fields with internal gauge freedom" @default.
- W3045596908 hasPublicationYear "2016" @default.
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