Explicit form of the Mann-Marolf surface term in (3+1) dimensions
arXiv:0808.2068 · doi:10.1103/PhysRevD.79.024023
Abstract
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.
arXiv comment4 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 D
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