Black Holes with Surrounding Matter in Scalar-Tensor Theories

We uncover two mechanisms that can render Kerr black holes unstable in scalar-tensor gravity, both associated with the presence of matter in the vicinity of the black hole and the fact that this introduces an effective mass for the scalar. Our results highlight the importance of understanding the structure of spacetime in realistic, astrophysical black holes in scalar-tensor theories.

Figure 1

The internal mass, $M_{\mathrm{int}}\equiv M-C/2$, shell radius $R$, and Kretschmann scalar $K=R_{abcd}{R}^{abcd}$ at the horizon for a hairy BH as function of the scalar charge $Q$, normalized by their value in GR, $Q=0$.

Figure 2

Superradiant instability details for a matter profile characterized by $\mathcal{G}=\Theta [r-r_0]\beta (r-r_0)/r^3$. Top panel: modes as a function of $r_0$ for fixed $\beta$. Bottom panel: modes as a function of $\beta$ for fixed $r_0$. For large $\beta$ the system behaves as a BH enclosed in a cavity with radius $r_0$. All curves are truncated when the modes become stable.