Fierz-Pauli equation for massive gravitons from Induced Matter theory of gravity

TL;DR

This paper derives a Fierz-Pauli type equation for massive gravitational waves within a 5D induced matter framework, showing how graviton mass arises from extra-dimensional geometry and affects wave dynamics.

Contribution

It introduces a novel derivation of massive graviton equations from 5D induced matter theory, linking graviton mass to extra-dimensional foliation and background connections.

Findings

Gravitational waves obey a Fierz-Pauli type equation in this model.

Graviton mass is induced by static foliation of the extra dimension.

Interaction with 5D background connections influences GW behavior.

Abstract

Starting with a 5D physical vacuum described by a 5D Ricci-flat background metric, we study the emergence of gravitational waves (GW) from the Induce Matter (IM) theory of gravity. We obtain the equation of motion for GW on an 4D curved spacetime which has the form of a Fierz-Pauli one. In our model the mass of gravitons $m_g$ is induced by a static foliation on the noncompact space-like extra dimension and the source-term is originated in the interaction of the GW with the induced connections of the background 5D metric. Here, relies the main difference of this formalism with the original Fierz-Pauli one.