"No-Scalar-Hair" Theorems for Nonminimally Coupled Fields with Quartic Self-Interaction

TL;DR

This paper proves that static black holes cannot support nontrivial scalar fields with nonminimal coupling and quartic self-interaction, confirming the no-scalar-hair conjecture in this context.

Contribution

It establishes a no-hair theorem for scalar fields with quartic self-interaction and nonminimal coupling, extending the validity of Bekenstein's conjecture.

Findings

No static black hole solutions with nonminimal scalar hair exist.

The result holds for all values of the nonminimal coupling parameter.

Confirms the no-scalar-hair conjecture for this class of scalar fields.

Abstract

Self-gravitating scalar fields with nonminimal coupling to gravity and having a quartic self-interaction are considered in the domain of outer communications of a static black hole. It is shown that there is no value of the nonminimal coupling parameter $\zeta$ for which nontrivial static black hole solutions exist. This result establishes the correctness of Bekenstein ``no-scalar-hair'' conjecture for quartic self-interactions.