Self-accelerating cosmologies and hairy black holes in ghost-free bigravity and massive gravity

TL;DR

This paper surveys various cosmological and black hole solutions in ghost-free bigravity and massive gravity theories, highlighting their classifications, properties, and the mechanisms for recovering General Relativity.

Contribution

It provides a comprehensive classification and analysis of known solutions in ghost-free bigravity and massive gravity, including new insights into their behaviors and properties.

Findings

Solutions with proportional metrics resemble GR with a cosmological term

Spherically symmetric solutions include non-bidiagonal and bidiagonal metrics

Matter sources enable asymptotically flat solutions with Vainshtein mechanism

Abstract

We present a survey of the known cosmological and black hole solutions in ghost-free bigravity and massive gravity theories. These can be divided into three classes. First, there are solutions with proportional metrics, which are the same as in General Relativity with a cosmological term, which can be positive, negative or zero. Secondly, for spherically symmetric systems, there are solutions with non-bidiagonal metrics. The g-metric fulfills Einstein equations with a positive cosmological term and a matter source, while the f-metric is anti-de Sitter. The third class contains solutions with bidiagonal metrics, and these can be quite complex. The time-dependent solutions describe homogeneous (isotropic or anisotropic) cosmologies which show a late-time self-acceleration or other types of behavior. The static solutions describe black holes with a massive graviton hair, and also globally regular lumps of energy. None of these are asymptotically flat. Including a matter source gives rise to asymptotically flat solutions which exhibit the Vainshtein mechanism of recovery of General Relativity in a finite region.