The perihelion problem in Kaluza-Klein gravity

Abstract

To help decide if there are extra dimensions to spacetime, we examine the classical problem of the perihelion advance of an object in orbit around a spherically symmetric star in a simple Kaluza-Klein theory, in which general relativity is extended by the addition of one extra spatial dimension. There is a canonical class of solutions in this theory, which depends on two dimensionless parameters, special values of which give back the standard 4D Schwarzschild solution. However, a consistency relation between these parameters means that even a small extra (curved) dimension can affect the dominant term in the potential (metric), thereby altering the theoretical value of the perihelion shift. The value of the perihelion shift for Mercury indicates that our solar system is well described by 4D general relativity. But the parameters of the 5D Kaluza-Klein theory are not universal constants and could presumably have different values in different systems. We therefore suggest that the dimensionality of spacetime could be tested more rigorously by observations of extrasolar planetary systems and suitable binary pulsar systems.