Abstract
Using the Wentzel–Kramers–Brillouin (WKB) approximation we study the formation and propagation of quantum bound states in the vicinity of a Galileon black hole. We show that for various ranges of the derivative coupling to the Einstein tensor, which appears in the metric of the Galileon black hole, a Regge–Wheeler potential containing a local well is formed. Varying the strength of the derivative coupling we investigate the behaviour of the bound states trapped in the potential well or penetrating the horizon of the Galileon black hole.
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