Extreme mass ratio head-on collisions of black holes in Einstein-scalar-Gauss-Bonnet theory

Abstract

The evolution of the event horizon when two black holes merge can be determined by resorting to ray-tracing techniques on a single black hole spacetime, under the assumption that the binary's mass ratio is infinite and the underlying gravity theory respects the equivalence principle. We extend this analysis to the head-on collision of non-spinning hairy black holes in Einstein-scalar-Gauss-Bonnet gravity. In such theories the scalar field is coupled to a higher curvature operator, leading to possible modifications of the background geometry and consequently of photon propagation. We study three families of coupling functions: linear, quadratic, and a particular exponential form. The first choice enjoys a shift symmetry and forces the presence of scalar hair in the spectrum of black hole solutions. The latter two couplings break the shift symmetry and allow for spontaneously scalarized hairy black holes, which coexist with the Schwarzschild black hole. For all three classes of theories studied, we find a merger duration that is longer than the corresponding time in general relativity, when keeping the size of the small black hole fixed, and for viably small values of the coupling constant. However, the case of the exponential coupling yields a non-monotonic merger duration, which can become shorter than the general relativity value for a sufficiently large coupling constant. We observe that the merger duration and the area increment generically track the behavior of the small black hole's photon ring. Finally, we also compare our results with recent numerical simulations by other groups, despite the dissimilar mass ratios considered.