Stealth Scalar Field Overflying a 2+1 Black Hole

TL;DR

This paper reports the existence of stealth scalar field configurations around 2+1 black holes, which have no gravitational influence and can be absorbed by the black hole without affecting its properties.

Contribution

It demonstrates the existence of nontrivial, nonminimally coupled scalar fields with zero energy-momentum that do not alter the black hole metric, expanding understanding of scalar field configurations in lower-dimensional gravity.

Findings

Stealth scalar fields exist for static 2+1 black holes with any nonzero nonminimal coupling.

These fields can be absorbed by the black hole without changing its geometry.

The potential is bounded from below for certain coupling ranges, and the field can fall into the black hole exponentially.

Abstract

A nontrivial scalar field configuration of vanishing energy-momentum is reported. These matter configurations have no influence on the metric and therefore they are not be "detected" gravitationally. This phenomenon occurs for a time-dependent nonminimally coupled and self-interacting scalar field on the 2+1 (BTZ) black hole geometry. We conclude that such stealth configurations exist for the static 2+1 black hole for any value of the nonminimal coupling parameter $\zeta\neq0$ with a fixed self-interaction potential $U_\zeta(\Phi)$. For the range $0<\zeta\leq1/2$ potentials are bounded from below and for the range $0<\zeta<1/4$ the stealth field falls into the black hole and is swallowed by it at an exponential rate, without any consequence for the black hole.