No-hair theorems in General Relativity and scalar-tensor theories

TL;DR

This review discusses the classification and no-hair theorems of black holes in scalar-tensor gravity, highlighting the complexities and recent results compared to general relativity.

Contribution

It provides a comprehensive overview of known and new no-hair results in scalar-tensor theories, including detailed proofs and mathematical techniques.

Findings

Complexity of scalar-tensor field equations hinders black hole classification.

Most known no-hair theorems are reviewed with some new results.

Comparison with general relativity black hole uniqueness theorems included.

Abstract

In the present review, we consider the status of the classification of the vacuum, stationary and asymptotically flat black holes in scalar-tensor gravity. Contrary to the similar problem in general relativity, the black hole classification in scalar-tensor theories is much more challenging due to the very complicated character of the field equations and the very complex mathematical structure of the scalar-tensor gravity as a whole. We review most of the known no-hair results, and where possible new ones, as well demonstrate some of the difficulties that appear in our attempts to classify the black holes within scalar-tensor gravity. The proofs of the theorems and the underlying mathematical techniques are given in sufficient detail. To make the review self-contained we also present the vacuum black hole uniqueness theorems in general relativity and their proofs.