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

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.

34 pages

References in corpus (4)

• Near-horizon symmetries of extremal black holes
• Introduction to Effective Field Theory
• No Dynamics in the Extremal Kerr Throat
• Kerr-CFT and gravitational perturbations

Cited by in corpus (5)

• Sudden breakdown of effective field theory near cool Kerr-Newman black holes
• Aspects of Holography of Taub-NUT-AdS4
• The Aretakis constants and instability in general spherically symmetric extremal black hole spacetimes: higher multipole modes, late-time tails, and geometrical meanings
• Revisiting the Aretakis constants and instability in two-dimensional Anti-de Sitter spacetimes
• EFT Corrections to Majumdar-Papapetrou Black Holes