Gravitomagnetism in Massive Gravity

TL;DR

This paper investigates gravitomagnetic effects in massive gravity, revealing notable differences from General Relativity in spin and orbital interactions, especially at large distances relevant for cosmic structures.

Contribution

It provides the first detailed calculation of gravitomagnetic interactions in massive gravity, including extensions to quadratic gravity theories, highlighting their distinct behaviors from General Relativity.

Findings

Spin-spin, spin-orbit, and orbit-orbit interactions differ discretely from GR.

Calculations applicable to large-scale cosmic interactions like galaxies.

Quadratic gravity shows different small-separation behavior than GR.

Abstract

Massive gravity in the weak field limit is described by the Fierz-Pauli theory with 5 degrees of freedom in four dimensions. In this theory, we calculate the gravitomagnetic effects (potential energy) between two point-like, spinning sources that also orbit around each other in the limit where the spins and the velocities are small. Spin-spin, spin-orbit and orbit-orbit interactions in massive gravity theory have rather remarkable, discrete differences from their counterparts in General Relativity. Our computation is applicable for large distances, for example, for interaction between galaxies or galaxy clusters where massive gravity is expected to play a role. We also extend the computations to quadratic gravity theories in four dimensions and find the lowest order gravitomagnetic effects and show that at small separations quadratic gravity behaves differently than General Relativity.