Critical Solutions of Scalarized Black Holes

Jose Luis Blázquez-Salcedo,Jutta Kunz,Sarah Kahlen

doi:10.3390/sym12122057

Jose Luis Blázquez-Salcedo, Jutta Kunz + Show 1 more

Open Access

https://doi.org/10.3390/sym12122057

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Abstract

We consider charged black holes with scalar hair obtained in a class of Einstein–Maxwell– scalar models, where the scalar field is coupled to the Maxwell invariant with a quartic coupling function. Besides the Reissner–Nordström black holes, these models allow for black holes with scalar hair. Scrutinizing the domain of existence of these hairy black holes, we observe a critical behavior. A limiting configuration is encountered at a critical value of the charge, where space time splits into two parts: an inner space time with a finite scalar field and an outer extremal Reissner–Nordström space time. Such a pattern was first observed in the context of gravitating non-Abelian magnetic monopoles and their hairy black holes.

Highlights

In the SO(3)-EYMH case, these solitons correspond to gravitating magnetic monopoles and dyons, which can be endowed with a horizon, generating hairy black holes [46,47,48,49,50,51,52]
As the critical solution is approached, the space time splits into two parts, an exterior part r > rcr corresponding to the exterior region of an extremal RN black hole and an interior part r < rcr with a finite scalar field that vanishes at rcr
We have focused the discussion on the fundamental branch of scalarized black holes, with scalar field functions that possess no nodes

Summary

Introduction

Studies of black holes with scalar hair received much interest, both in the context of generalized gravity theories such as Einstein–scalar–Gauß–Bonnet (EsGB) theories [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22] and in the context of simpler models such as Einstein–Maxwell–scalar (EMs) models [23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40]. In the SO(3)-EYMH case, these solitons correspond to gravitating magnetic monopoles and dyons, which can be endowed with a horizon, generating hairy black holes [46,47,48,49,50,51,52] These non-Abelian solutions do not exist for arbitrary values of the coupling constant or horizon radius but possess a limited domain of existence. As the critical solution is approached, the space time splits into two parts, an exterior part r > rcr corresponding to the exterior region of an extremal RN black hole and an interior part r < rcr with a finite scalar field that vanishes at rcr.

EMs Theory

Branches of Black Holes

Excited Solutions

Conclusions