New Bi-Gravities

TL;DR

This paper introduces New Bi-Gravities, a class of theories that resolve ghost issues in critical gravity by adding dynamics to an auxiliary field, ensuring stability at linear and possibly nonlinear levels.

Contribution

It proposes a novel class of bi-gravity models that eliminate ghosts in critical gravity and its higher-dimensional extensions by dynamizing an auxiliary field.

Findings

Ghosts are eliminated at linear level around AdS vacuum.

Black hole solutions have positive energy and entropy within certain parameters.

Models potentially free of ghost instabilities at nonlinear level.

Abstract

We show that the problem of ghosts in critical gravity and its higher dimensional extensions can be resolved by giving dynamics to the symmetric rank two auxiliary field existing in the action of these theories. These New Bi-Gravities, at linear level around the AdS vacuum, are free of Boulware-Deser ghost, kinetic ghost and tachyonic instability within the particular range of parameters. Moreover, we show that the energy and entropy of AdS-Schwarzschild black hole solutions of these new models are positive in the same range of parameters. This may be the sign that these new models are also free of ghost instabilities at the non-linear level.