Black-Hole Solutions with Scalar Hair in Einstein-Scalar-Gauss-Bonnet Theories

By A. Bakopoulos, G. Antoniou, P. Kanti. 2017

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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 small number of constraints. 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 are found to be regular and to depend on the value of the coupling constant: for large values, they both exhibit in general a non-monotonic behaviour, an unusual feature that highlights the limitations of the existing no-hair theorems.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/0c5c0fb323015c8794f850d366e5e03eca5495f0

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Horndeski theory and beyond: a review (2019, background): “as a trivial proﬁle. The no-hair theorem can thus be extended to cover a wider class of theories [263, 264], though it can certainly be evaded, e.g., by a nonminimal coupling to the Gauss-Bonnet term [265, 266, 267, 268]. In light of the modern reformulation of the Horndeski theory, it has been argu”