Transient instability of rapidly rotating black holes

We analytically study the linear response of a near-extremal Kerr black hole to external scalar, electromagnetic, and gravitational field perturbations. We show that the energy density, electromagnetic field strength, and tidal force experienced by infalling observers exhibit transient growth near the horizon. The growth lasts arbitrarily long in the extremal limit, reproducing the horizon instability of extremal Kerr. We explain these results in terms of near-horizon geometry and discuss potential astrophysical implications.

Figure 1

Plot of the magnitude of the Hartle-Hawking tetrad Weyl scalar ${\mathrm{\Psi }}_4$ associated with near-horizon quasinormal modes excited by a distant pulse of $\ell =m=2$ initial data. [That is, we plot the $\ell =m=2$ term of Eq. (17) with $s=2$.] We normalize ${\mathrm{\Psi }}_4$ by the maximum value it attains on the horizon, $|{\mathrm{\Psi }}_4^{\mathrm{H}}|$. The gravitational perturbations grow for a time $V\sim 1/\sigma$, and overall ${\mathrm{\Psi }}_4\sim {\sigma }^{-3/2}$, as determined by the scaling in Eq. (17).