Newton's Law on an Einstein ``GaussBonnet" Brane
Abstract
It is known that Newton's law of gravity holds asymptotically on a flat ``brane" embedded in an antide Sitter ``bulk"; this was shown not only when gravity in the bulk is described by Einstein's theory but also in Einstein ``Lanczos Lovelock GaussBonnet"'s theory. We give here the expressions for the corrections to Newton's potential in both theories, in analytic form and valid for all distances. We find that in Einstein's theory the transition from the 1/r behaviour at small r to the 1/r^{2} one at large r is quite slow. In the Einstein GaussBonnet case on the other hand, we find that the correction to Newton's potential can be small for all r. Hence, Einstein GaussBonnet equations in the bulk (rather than simply Einstein's) induce on the brane a better approximation to Newton's law.
 Publication:

Progress of Theoretical Physics
 Pub Date:
 September 2003
 DOI:
 10.1143/PTP.110.441
 arXiv:
 arXiv:grqc/0306032
 Bibcode:
 2003PThPh.110..441D
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics;
 High Energy Physics  Theory
 EPrint:
 typos corrected, reference added, version to be published in Progress of Theoretical Physics