Solar System Tests of Higher-Dimensional Gravity

TL;DR

This paper tests five-dimensional Kaluza-Klein gravity against classical solar system experiments, constraining the extra-dimensional parameter and proposing future measurements to improve these limits.

Contribution

It extends classical tests of general relativity to five-dimensional Kaluza-Klein gravity, including new calculations for scenarios with non-zero momentum and spin along the extra dimension.

Findings

Parameter b constrained to |b| < 0.07 by current data

Future measurements could improve sensitivity by an order of magnitude

Gravity Probe B will significantly tighten constraints on extra dimensions

Abstract

The classical tests of general relativity - light deflection, time delay and perihelion shift - are applied, along with the geodetic precession test, to the five-dimensional extension of the theory known as Kaluza-Klein gravity, using an analogue of the four-dimensional Schwarzschild metric. The perihelion advance and geodetic precession calculations are generalized for the first time to situations in which the components of momentum and spin along the extra coordinate do not vanish. Existing data on light- bending around the Sun using long- baseline radio interferometry, ranging to Mars using the Viking lander, and the perihelion precession of Mercury all constrain a small parameter b associated with the extra part of the metric to be less than |b| < 0.07 in the solar system. An order-of-magnitude increase in sensitivity is possible from perihelion precession, if better limits on solar oblateness become available. Measurement of geodetic precession by the Gravity Probe B satellite will improve this significantly, probing values of b with an accuracy of one part in 10^4 or more.