Superradiant instabilities for a charged black hole in de Rham-Gabadadze-Tolley theory

Abstract

In this paper, we study the superradiant instabilities for the charged furry black hole in massive gravity. In de Rham-Gabadadze-Tolley (dRGT) theory, the St\uckelberg field may provide St\uckelberg hair for the black hole solutions. To make the furry most obvious in large scale, we only consider to the next order of $1/{r}^{2}$ in the metric function. According to the horizon, we define two new conservation charge as the hair of black hole: one is positive charge ${k}_{+}$; the other is negative charge ${k}_{\ensuremath{-}}$. Both of them are known as St\uckelberg charge. Using a mirrorlike boundary condition, we show that there are superradiant instabilities for both types of black holes. As the St\uckelberg charge increases, the central black hole becomes more stable. The reason for this behavior is caused by the impact of St\uckelberg charge on the horizon. We also plot the parameter space for stabilities of two types black holes. As a matter of fact, the various configuration of St\uckelberg field led to this new feature in the dRGT theory.