Symmetry inheritance of scalar fields

TL;DR

This paper classifies when scalar fields inherit spacetime symmetries, focusing on real and complex cases, and explores implications for boson stars and black hole scalar hair, including effects on mass and angular momentum.

Contribution

It provides a classification of obstructions to symmetry inheritance for scalar fields and analyzes their impact on black hole solutions and scalar hair.

Findings

Identifies conditions for symmetry inheritance in scalar fields.

Analyzes the role of symmetry noninheritance in boson stars.

Examines contributions to black hole mass and angular momentum.

Abstract

Matter fields don't necessarily have to share the symmetries with the spacetime they live in. When this happens, we speak of the symmetry inheritance of fields. In this paper we classify the obstructions of symmetry inheritance by the scalar fields, both real and complex, and look more closely at the special cases of stationary and axially symmetric spacetimes. Since the symmetry noninheritance is present in the scalar fields of boson stars and may enable the existence of the black hole scalar hair, our results narrow the possible classes of such solutions. Finally, we define and analyse the symmetry noninheritance contributions to Komar mass and angular momentum of the black hole scalar hair.