Five-dimensional PPN formalism and experimental test of Kaluza–Klein theory

Abstract

The parametrized post-Newtonian formalism for 5-dimensional metric theories with a compact extra dimension is developed. The relation of the 5-dimensional and 4-dimensional formulations is then analyzed, in order to compare the higher dimensional theories of gravity with experiments. It turns out that the value of post-Newtonian parameter γ in the reduced 5-dimensional Kaluza–Klein theory is two times smaller than that in 4-dimensional general relativity. The departure is due to the existence of an extra dimension in the Kaluza–Klein theory. Thus the confrontation between the reduced 4-dimensional formalism and Solar system experiments raises a severe challenge to the classical Kaluza–Klein theory.