2006/09/17 by Sean P. Robinson, Robinson, Sean P. · 1 citation
Physics and Astronomy · #Advanced Mathematical Theories and Applications #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Relativity and Gravitational Theory #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0609060
4 pages, 2 figures, RevTeX4
arxiv created 2006/09/17 · openalex publication_date 2006/09/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We calculate, in d spacetime dimensions, the relationship between the coefficient 1/K2 of the Einstein-Hilbert term in the action of general relativity and the coefficient GN of the force law that results from the Newtonian limit of general relativity. The result is K2=2[(d-2)/(d-3)]Vol(S^[d-2])GN, where Vol(Sn) is the volume of the unit n-sphere. While the d=4 case is an elementary calculation in any general relativity text, the arbitrary case presented here is slightly less well known. We discuss the relevance of this result for the definition of the so-called "reduced Planck mass" and comment very briefly on the implications for brane world models. [abstract abridged]