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.

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