466 research outputs found

    Explicit form of the Mann-Marolf surface term in (3+1) dimensions

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    The Mann-Marolf surface term is a specific candidate for the "reference background term" that is to be subtracted from the Gibbons-Hawking surface term in order make the total gravitational action of asymptotically flat spacetimes finite. That is, the total gravitational action is taken to be: (Einstein-Hilbert bulk term) + (Gibbons-Hawking surface term) - (Mann-Marolf surface term). As presented by Mann and Marolf, their surface term is specified implicitly in terms of the Ricci tensor of the boundary. Herein I demonstrate that for the physically interesting case of a (3+1) dimensional bulk spacetime, the Mann-Marolf surface term can be specified explicitly in terms of the Einstein tensor of the (2+1) dimensional boundary.Comment: 4 pages; revtex4; V2: Now 5 pages. Improved discussion of the degenerate case where some eigenvalues of the Einstein tensor are zero. No change in physics conclusions. This version accepted for publication in Physical Review

    Rastall gravity is equivalent to Einstein gravity

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    Rastall gravity, originally developed in 1972, is currently undergoing a significant surge in popularity. Rastall gravity purports to be a modified theory of gravity, with a non-conserved stress-energy tensor, and an unusual non-minimal coupling between matter and geometry, the Rastall stress-energy satisfying nabla_b [T_R]^{ab} = {\lambda/4} g^{ab} nabla_b R. Unfortunately, a deeper look shows that Rastall gravity is completely equivalent to Einstein gravity --- usual general relativity. The gravity sector is completely standard, based as usual on the Einstein tensor, while in the matter sector Rastall's stress-energy tensor corresponds to an artificially isolated part of the physical conserved stress-energy.Comment: V1: 5 pages. V2: 6 pages; 5 added references, some added discussion, no changes in physics conclusions. V3: 7 pages, 2 added references, some added discussion, no changes in physics conclusion

    Thermality of the Hawking flux

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    Is the Hawking flux "thermal"? Unfortunately, the answer to this seemingly innocent question depends on a number of often unstated, but quite crucial, technical assumptions built into modern (mis-)interpretations of the word "thermal". The original 1850's notions of thermality --- based on classical thermodynamic reasoning applied to idealized "black bodies" or "lamp black surfaces" --- when supplemented by specific basic quantum ideas from the early 1900's, immediately led to the notion of the black-body spectrum, (the Planck-shaped spectrum), but "without" any specific assumptions or conclusions regarding correlations between the quanta. Many (not all) modern authors (often implicitly and unintentionally) add an extra, and quite unnecessary, assumption that there are no correlations in the black-body radiation; but such usage is profoundly ahistorical and dangerously misleading. Specifically, the Hawking flux from an evaporating black hole, (just like the radiation flux from a leaky furnace or a burning lump of coal), is only "approximately" Planck-shaped over a bounded frequency range. Standard physics (phase space and adiabaticity effects) explicitly bound the frequency range over which the Hawking flux is "approximately" Planck-shaped from both above and below --- the Hawking flux is certainly not exactly Planckian, and there is no compelling physics reason to assume the Hawking photons are uncorrelated.Comment: V1: 13 pages. V2: Now 17 pages. 3 references added; other references updated; new section on the relationship between past and future null infinity; small edits throughout the text. V3: Now 19 pages. 4 more references added; extra discussion/small edits. No physics change