Transient scalar hair for nearly extreme black holes

Lior M Burko,Subir Sabharwal,Gaurav Khanna

doi:10.1103/physrevresearch.1.033106

Lior M Burko, Subir Sabharwal + Show 1 more

Open Access

https://doi.org/10.1103/physrevresearch.1.033106

Copy DOI

Abstract

It has been shown recently that extreme Reissner-Nordstr\"{o}m black holes perturbed by a minimally coupled, free, massless scalar field have permanent scalar hair. The hair - a conserved charge calculated at the black hole's event horizon - can be measured by a certain expression at future null infinity: the latter approaches the hair inversely in time. We generalize this newly discovered hair also for extreme Kerr black holes. We study the behavior of nearly extreme black hole hair and its measurement at future null infinity as a transient phenomenon. For nearly extreme black holes the measurement at future null infinity of the length of the newly grown hair decreases quadratically in time at intermediate times until its length becomes short and the rate at which the length shortens further slows down. Eventually, the nearly extreme BH becomes bald again like non-extreme BHs.

Highlights

Scalar fields, which are ubiquitous in theoretical physics and in astrophysics, have been proposed as candidates for black hole (BH) hair [1], in possible violation of the no-hair conjecture
In hyperboloidal coordinates (ρ, τ ), the initially spherical ( = 0) Gaussian pulse is centered at ρ = 1.0M with a width of 0.22M so that we have horizon penetrating initial data that lead to H[ψ] = 0 on the initial data surface [10]. (For example, the horizon is at ρ = 0.95M for extreme Reissner-Nordström (ERN) and extreme Kerr (EK) BHs in these coordinates.) The Gaussian is truncated beyond ρ = 8.0M and the outer boundary is located at S = ρ(I +) = 19.0M
Both fields vary as functions of time, the changes in H[ψ](v) are not visible on the scale of this figure

Summary

INTRODUCTION

Scalar fields, which are ubiquitous in theoretical physics (e.g., the Higgs field) and in astrophysics (e.g., the inflaton, certain dark matter, and dark energy models), have been proposed as candidates for black hole (BH) hair [1], in possible violation of the no-hair conjecture The latter states that all BH solutions of the Einstein-Maxwell equations of general relativity can be completely characterized by three and only three externally observable classical parameters, the BH’s mass M, charge q, and spin angular momentum a. We consider nearly extreme BHs (NERN or NEK BHs) and show the AAG hair as a transient behavior, including observational features from far away

NUMERICAL METHOD

EXTREME RN OR KERR BLACK HOLES

NEARLY EXTREME AND NONEXTREME RN OR