Black hole hair in generalized scalar-tensor gravity: An explicit example

By T. Sotiriou, Shuang-Yong Zhou. 2014

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In a recent paper we showed that in shift-symmetric Horndeski theory the scalar field is forced to obtain a nontrivial configuration in black hole spacetimes, unless a linear coupling with the Gauss--Bonnet invariant is tuned away. As a result, black holes generically have hair in this theory. In this companion paper, we first review our argument and discuss it in more detail. We then present actual black hole solutions in the simplest case of a theory with the linear scalar-Gauss--Bonnet coupling. We generate exact solutions numerically for a wide range of values of the coupling and also construct analytic solutions perturbatively in the small-coupling limit. Comparison of the two types of solutions indicates that nonlinear effects that are not captured by the perturbative solution lead to a finite area, as opposed to a central, singularity. Remarkably, black holes have a minimum size, controlled by the length scale associated with the scalar-Gauss--Bonnet coupling. We also compute some phenomenological observables for the numerical solution for a wide range of values of the scalar-Gauss--Bonnet coupling. Deviations from the Schwarzschild geometry are generically very small.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a175ef746bb8828c8c059a99f8ef5a7040176d1f

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Citations in the corpus

Horndeski theory and beyond: a review (2019, background): “lore how one can circumvent the no-hair theorem in the context of the Horndeski/beyond Horndeski theories. For example, by tuning the form of the Horndeski functions one can evade the no-hair theorem [270, 271]. Another possibility is relaxing the assumptions on the time independence of φand/orits a”
Asymptotically flat black holes in Horndeski theory and beyond (2017, methodology): “[24] has shown that, under some assumptions, black holes have no hair (see [28, 32] for more details).”