Black-hole solutions with scalar hair in Einstein-scalar-Gauss-Bonnet theories

Abstract

In the context of the Einstein-scalar-Gauss-Bonnet theory, with a general coupling function between the scalar field and the quadratic Gauss-Bonnet term, we investigate the existence of regular black-hole solutions with scalar hair. Based on a previous theoretical analysis, which studied the evasion of the old and novel no-hair theorems, we consider a variety of forms for the coupling function (exponential, even and odd polynomial, inverse polynomial, and logarithmic) that, in conjunction with the profile of the scalar field, satisfy a basic constraint. Our numerical analysis then always leads to families of regular, asymptotically flat black-hole solutions with nontrivial scalar hair. The solution for the scalar field and the profile of the corresponding energy-momentum tensor, depending on the value of the coupling constant, may exhibit a nonmonotonic behavior, an unusual feature that highlights the limitations of the existing no-hair theorems. We also determine and study in detail the scalar charge, horizon area, and entropy of our solutions.

Spinning and excited black holes in Einstein-scalar-Gauss–Bonnet theory

“…Later it was realized that spontaneous scalarization can occur for charged black holes in Einstein-Maxwell-scalar (EMs) theory, for certain choices of the scalar coupling function and coupling strength [36][37][38][39][40][41]. This "charge-induced" spontaneous scalarization presents many similarities with the case of curvature-induced spontaneous scalarization of black holes [24][25][26][27][28][29][30][31][32].…”

Einstein-scalar–Gauss-Bonnet black holes: Analytical approximation for the metric and applications to calculations of shadows

“…All the known black hole solutions in the fourdimensional Einstein-scalar-Gauss-Bonnet gravity are obtained either numerically [9][10][11], or perturbatively [12,13], what makes it either difficult or impossible to use a number of tools for analysis of behavior of such solutions. Analytical expressions for such numerical blackhole metrics, which are valid in the whole space outside the event horizon, would allow us to see the explicit dependence of the metric on physical parameters of the system and to work with the metric as, essentially, with an exact solution.…”

“…In [17] the analytical approximation was found for the particular choice of the scalar field coupling -the dilaton, exponential coupling, which was considered numerically in [9]. Recently this approach was extended in [10] to various types of the scalar field function and allowed therefore, to look whether there are some common features for all the considered couplings of the scalar field. A similar problem was attacked numerically for case of the Einstein-scalar-Maxwell theory [25] and the study of its analytical approximation [18] showed that the radius of the black-hole shadow is increased for any of the considered couplings of the scalar field.…”

Collapsing spherical star in Scalar-Einstein-Gauss-Bonnet gravity with a quadratic coupling

“…[57]. In this context, existence of regular black-hole solutions with scalar hair in the Einstein-scalar-Gauss-Bonnet theory was investigated by Antoniou, Bakopoulos and Kanti [58,59], with a general coupling function between the scalar field and the quadratic Gauss-Bonnet term which highlighted the limitations of the existing no-hair theorems. In a recent study Kanti, Gannouji and Dadhich have addressed the importance of such a coupling from a cosmological purview and proved by some simple analytical calculation that a quadratic coupling function, although a special choice, allows for inflationary, de Sitter-type solutions to emerge [60].…”