Role of Mann Counterterm in Gravitational Energy

2020/07/27 by Shoichiro Miyashita, Miyashita, Shoichiro
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th

paper · pdf · doi:10.48550/arxiv.2007.13294

4 pages; v2; typos corrected, footnote and references added

arxiv created 2020/11/14 · arxiv updated 2020/11/17

Abstract

In 1999, R. B. Mann proposed a counterterm that is some sort of generalization of the well-known Holographic counterterm and that can eliminate the divergence of the gravitational action of asymptotically AdS and flat spacetimes (Phys. Rev. D \boldsymbol60 (1999) 104047 [1]). I show it is not only for eliminating the divergence of such spacetimes but also for setting the ground state energy to zero for any d-dimensional spacetimes with an S^d-2 × ℝ boundary geometry, and speculate it is also true for spacetimes with any (suitable) boundary geometry and topology.

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