Gordon and Kerr-Schild ansatze in massive and bimetric gravity

TL;DR

This paper introduces the generalized Gordon and Kerr-Schild ansatze for massive and bimetric gravity, simplifying calculations and enabling explicit expressions for the square root matrix, with applications to cosmology and black hole physics.

Contribution

It develops a unified ansatz framework that simplifies the analysis of ghost-free massive and bimetric gravity theories, including explicit formulas for key matrices and stress-energy tensors.

Findings

The ansatz includes most physically interesting spacetimes.

Explicit calculation of the matrix square root gamma is achieved.

Implications for cosmology and black hole physics are discussed.

Abstract

We develop the "generalized Gordon ansatz" for the ghost-free versions of both massive and bimetric gravity, an ansatz which is general enough to include almost all spacetimes commonly considered to be physically interesting, and restricted enough to greatly simplify calculations. The ansatz allows explicit calculation of the matrix square root gamma = sqrt{g^{-1} f} appearing as a central feature of the ghost-free analysis. In particular, this ansatz automatically allows us to write the effective stress-energy tensor as that corresponding to a perfect fluid. A qualitatively similar "generalized Kerr-Schild ansatz" can also be easily considered, now leading to an effective stress-energy tensor that corresponds to a null fluid. Cosmological implications are considered, as are consequences for black hole physics. Finally we have a few words to say concerning the null energy condition in the framework provided by these ansatze.