Towards a characterization of fields leading to black hole hair

TL;DR

This paper investigates conditions under which black holes can have observable 'hair' from external fields, focusing on the behavior of the energy-momentum tensor and its trace.

Contribution

It characterizes the types of fields that can produce black hole hair based on the trace properties of their energy-momentum tensors.

Findings

Black holes can exhibit observable signatures of certain fields.

Tracefree or rapidly decreasing trace energy-momentum tensors allow for black hole hair.

Provides a framework for identifying fields that lead to black hole hair.

Abstract

In the present work, it is shown that an asymptotically flat spherical black hole can have a nontrivial signature of any field for an exterior observer if the energy momentum tensor of the corresponding field is either tracefree or if the trace falls off at least as rapidly as inverse cube of the radial distance. In the absence of a general No Hair Theorem, this result can provide a characterization of the fields leading to black hole hair.