Massive Gravitons in General Relativity

Abstract

In the framework of a generalisation of linear gravitation to the case when the gravitons have nonzero rest mass, we obtain a result analogous to that obtained by Regge and Wheeler, that is, the energy of the gravitational waves is trapped in the ‘material’ (interior) metric of the curved space–time. We show that the concept of a nonzero rest mass graviton may be defined in two ways: (i) phenomenologically, by introducing of a mass term in the linear Lagrangian density, as in Proca electrodynamics, and (ii) self-consistently, by solving Einstein’s equations in the conformally flat case. We find that the rest mass of the graviton may be given in terms of the three fundamental constants (gravitational, Planck, and light velocity constants) and it is a function of the density of cosmic matter.