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

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

2008-08-14

arxiv.org/abs/0808.2068v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages; revtex4; V2: Now 5 pages. Improved discussion of the degenerate case where some eigenvalues of the Einstein tensor ar

Scientific paper

10.1103/PhysRevD.79.024023

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.

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