Finite Energy of Black Holes in Massive Gravity

TL;DR

This paper demonstrates that in certain four-dimensional massive gravity theories, there exist spherically symmetric solutions with finite total energy despite having nonstandard asymptotic behavior, challenging traditional notions of gravitational energy.

Contribution

The authors show that massive gravity theories admit solutions with finite energy and unconventional asymptotics, expanding the understanding of gravitational configurations.

Findings

Existence of finite-energy solutions with asymptotics slower than 1/r

Nonstandard asymptotics can be physically viable in massive gravity

Extra gravitationally coupled field balances infinite energy contributions

Abstract

In GR the static gravitational potential of a self-gravitating body goes as 1/r at large distances and any slower decrease leads to infinity energy. We show that in a class of four-dimensional massive gravity theories there exists spherically symmetric solutions with finite total energy, featuring an asymptotic behavior slower than 1/r and generically of the form $r^\gamma$. This suggests that configurations with nonstandard asymptotics may well turn out to be physical. The effect is due to an extra field coupled only gravitationally, which allows for modifications of the static potential generated by matter, while counterbalancing the apparently infinite energy budget.