Spacetimes dressed with stealth electromagnetic fields

TL;DR

This paper investigates stealth electromagnetic fields that have zero energy-momentum tensor, explores conditions for their existence in nonlinear models, and presents black hole solutions with stealth electromagnetic hair that do not affect the core gravitational relations.

Contribution

It establishes the conditions for stealth electromagnetic fields in nonlinear models and provides explicit black hole solutions with stealth electromagnetic hair.

Findings

Stealth fields have vanishing energy-momentum tensor in certain models.

Black holes can be dressed with stealth electromagnetic hair.

Stealth hair influences Komar charges but not the Smarr formula.

Abstract

Stealth field configurations by definition have a vanishing energy-momentum tensor, thus do not contribute to the gravitational field equations. While only trivial fields can be stealth in Maxwell's electrodynamics, nontrivial stealth fields appear in some nonlinear models of electromagnetism. We find the necessary and sufficient conditions for the electromagnetic fields to be stealth and analyse which models admit such configurations. Furthermore, we present some concrete exact solutions, featuring a class of black holes dressed with the stealth electromagnetic hair, closely related to force-free solutions. Stealth hair does not alter the generalized Smarr formula, but may contribute to the Komar charges.