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, that 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 non-trivial 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 non-monotonic behaviour, 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.
Highlights
The construction of generalized gravitational theories, with the inclusion of extra fields or higher-curvature terms in the action, has attracted an enormous interest during the last decades [1,2]
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
As the old no-hair theorem imposes in general mild constraints on a theory, in Ref. [31], we considered in addition the novel no-hair theorem [7] that applies in theories with a conformal coupling of the scalar fields to gravity
Summary
The construction of generalized gravitational theories, with the inclusion of extra fields or higher-curvature terms in the action, has attracted an enormous interest during the last decades [1,2]. In the context of these modified gravitational theories, different aspects of gravity, from black-hole solutions to cosmological solutions, have been readdressed and, on several occasions, shown to lead to novel, interesting solutions Such a class of solutions was the one describing regular black holes with a nontrivial scalar field in the exterior region, a type of solutions forbidden by General Relativity. This was soon outdated by the discovery of black holes with Yang-Mills [4], Skyrme fields [5], or a conformal coupling to gravity [6] These led to the formulation of the novel no-hair theorem [7] that was recently extended to cover the case of standard scalar-tensor theories [8]; a new form that covers the case of Galileon fields was proposed [9]. Further characteristics of the produced solutions, such as the scalar charge, horizon area, and entropy, are determined, studied in detail, and compared to the corresponding Schwarzschild values
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