Modification of the Coulomb potential from a Kaluza-Klein model with a Gauss-Bonnet term in the action

Details Modification of the Coulomb potential from a Kaluza-Klein model with a Gauss-Bonnet term in the action Modification of the Coulomb potential from a Kaluza-Klein model with a Gauss-Bonnet term in the action

1994-09-29

arxiv.org/abs/gr-qc/9409060v2

Ann.Phys.240:432-458,1995

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

27 pages, compressed and uuencoded postscript file with unpacking instructions; major revision to section IV.D.2 on pages 15-1

Scientific paper

10.1006/aphy.1995.1051

In four dimensions a Gauss-Bonnet term in the action corre- sponds to a total derivative, and it does not contribute to the classical equations of motion. For higher-dimensional geometries this term has the interesting property (shared with other dimensionally continued Euler densities) that when the action is varied with respect to the metric, it gives rise to a symmetric, covariantly conserved tensor of rank two which is a function of the metric and its first and second order derivatives. Here we review the unification of General Relativity and electromagnetism in the classical five-dimen- sional, restricted (with g_55 = 1) Kaluza-Klein model. Then we discuss the modifications of the Einstein-Maxwell theory that results from adding the Gauss-Bonnet term in the action. The resulting four-dimensional theory describes a non-linear U(1) gauge theory non-minimally coupled to gravity. For a point charge at rest, we find a perturbative solution for large distances which gives a mass-dependent correction to the Coulomb potential. Near the source we find a power-law solution which seems to cure the short-distance divergency of the Coulomb potential. Possible ways to obtain an experimen- tal upper limit to the coupling of the hypothetical Gauss- Bonnet term are also considered.

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