Is there a breakdown of effective field theory at the horizon of an extremal black hole?

TL;DR

This paper investigates whether the Aretakis instability in extremal black holes leads to a breakdown of effective field theory at the horizon, concluding that higher derivative corrections remain small in most cases.

Contribution

The study shows that, despite the Aretakis instability, higher derivative corrections do not significantly affect the equations of motion in extremal Reissner-Nordstrom and Kerr black holes under certain conditions.

Findings

Higher derivative corrections stay small in extremal Reissner-Nordstrom due to general covariance.

In extremal Kerr, backreaction is complex, but corrections are still expected to be small near extremality.

Effective field theory remains valid despite the Aretakis instability in typical scenarios.

Abstract

Linear perturbations of extremal black holes exhibit the Aretakis instability, in which higher derivatives of a scalar field grow polynomially with time along the event horizon. This suggests that higher derivative corrections to the classical equations of motion may become large, indicating a breakdown of effective field theory at late time on the event horizon. We investigate whether or not this happens. For extremal Reissner-Nordstrom we argue that, for a large class of theories, general covariance ensures that the higher derivative corrections to the equations of motion appear only in combinations that remain small compared to two derivative terms so effective field theory remains valid. For extremal Kerr, the situation is more complicated since backreaction of the scalar field is not understood even in the two derivative theory. Nevertheless we argue that the effects of the higher derivative terms will be small compared to the two derivative terms as long as the spacetime remains close to extremal Kerr.