Massive Gravitons on Bohmian Congruences

Abstract

Taking a quantum corrected form of Raychaudhuri equation in a geometric background described by a Lorentz-violating massive theory of gravity, we go through investigating a time-like congruence of massive gravitons affected by a Bohmian quantum potential. We find some definite conditions upon which these gravitons are confined to diverging Bohmian trajectories. The respective behaviour of those quantum potentials are also derived and discussed. Additionally, and through a relativistic quantum treatment of a typical wave function, we demonstrate schematic conditions on the associated frequency to the gravitons, in order to satisfy the necessity of divergence.