Transient Instability of Rapidly Rotating Black Holes

TL;DR

This paper analytically investigates the transient instability phenomena near the horizon of near-extremal Kerr black holes caused by external perturbations, revealing long-lasting growth effects in the extremal limit.

Contribution

It provides a detailed analytical study of the linear response of near-extremal Kerr black holes to various field perturbations, elucidating the nature of horizon instabilities.

Findings

Transient growth of energy density, electromagnetic fields, and tidal forces near the horizon.

Growth duration becomes arbitrarily long as the black hole approaches extremality.

Results connect near-horizon geometry to observable instability effects.

Abstract

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.