The equivalence principle in Kaluza-Klein gravity

In four-dimensional general relativity the spacetime outside of an isolated spherical star is described by an unique line element, which is the Schwarzschild metric. However, theories that envision our world as embedded in a larger universe, with more than four dimensions, lead to a number of possible non-Schwarzschild exteriors. In five-dimensional Kaluza-Klein gravity the condition that in the weak-field limit we recover the usual Newtonian physics singles out an unique static exterior. In this work we show that this unique exterior also guarantees the equality between the inertial and gravitational masses of a star. PACS: 04.50.+h; 04.20.Cv