Normalization conventions for Newton's constant and the Planck scale in arbitrary spacetime dimension

Details Normalization conventions for Newton's constant and the Planck scale in arbitrary spacetime dimension Normalization conventions for Newton's constant and the Planck scale in arbitrary spacetime dimension

2006-09-17

arxiv.org/abs/gr-qc/0609060v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages, 2 figures, RevTeX4

Scientific paper

We calculate, in d spacetime dimensions, the relationship between the coefficient 1/K^2 of the Einstein-Hilbert term in the action of general relativity and the coefficient G_N of the force law that results from the Newtonian limit of general relativity. The result is K^2=2[(d-2)/(d-3)]Vol(S^[d-2])G_N, where Vol(S^n) 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]

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