Expanded evasion of the black hole no-hair theorem in dilatonic Einstein-Gauss-Bonnet theory

Abstract

We study a hairy black hole solution in the dilatonic Einstein-Gauss-Bonnet theory of gravitation, in which the Gauss-Bonnet term is nonminimally coupled to the dilaton field. Hairy black holes with spherical symmetry seem to be easily constructed with a positive Gauss-Bonnet (GB) coefficient α within the coupling function, f (φ) = αe γφ , in an asymptotically flat spacetime, i.e., no-hair theorem seems to be easily evaded in this theory. Therefore, it is natural to ask whether this construction can be expanded into the case with the negative coefficient α. In this paper, we numerically present the dilaton black hole solutions with a negative α, and we analyze the properties of GB term through the aspects of the black hole mass. We construct the new integral constraint allowing the existence of the hairy solutions with the negative α. Through this procedure, we expand the evasion of the no-hair theorem for hairy black hole solutions.

Rotating black holes with an anisotropic matter field

“…Sometimes, one could not have intuitive predictions and interpretations. Thus, in most cases, one studies static black holes first [58,59,60,61,62] and deals with the rotating black holes based on this static one. Of course, the study begins with the rotating black hole when considering some phenomena that only occurred in the rotating black hole geometry.…”

Scalarized black holes in the presence of the coupling to Gauss-Bonnet gravity

“…*1 The static and spherically symmetric BH solutions have been investigated in Refs. [26][27][28][29][30][31][32][33][34][35] and then generalized to slowly rotating [36][37][38] and full rotating [39,40] solutions accordingly.…”

Μαύρες Οπές Και Σκουληκότρυπες Στα Πλαίσια Γενικευμένων Θεωριών Βαρύτητας Με Βαθμωτά Πεδία Και Ανώτερους Βαρυτικούς Όρους

“…f (φ) > 0, was found to lead indeed to novel solutions when satisfied but it could not exclude their emergence in the opposite case. An analysis of the old no-hair theorem that bypasses the constraint on the sign of the coupling function, and allows solutions with f (φ) < 0, may be found here [333].…”

“…In both cases new solutions for asymptotically flat black holes were found [23,24,57]. Also, the last twenty years many other solutions for black holes have been found in the framework of the Einstein-scalar-Gauss-Bonnet theory [109,292,293], including solutions with rotation [37- 47,75], solutions in the presence of an electromagnetic field [88,99,294] or even solutions with a cosmological constant [76,295,296].…”

“…Employing, then, several different forms of the coupling function f (φ), a large number of asymptotically-flat black-hole solutions with scalar hair were determined [1,2]. Additional studies presenting novel black holes or compact objects in generalised gravitational theories have appeared [80][81][82][83][84][85][86][87][88][89][90][91] as well as further studies of the properties of these novel solutions [45,46,67,69,[92][93][94][95][96][97][98][99][100][101][102][103][104][105][106][107][108][109][110]. Finally the stability of scalarized black holes of EsGB theories has been addressed in detail by analyzing their radial perturbations and revealing a distinct dependence on the coupling function [69,70].…”