Firewall black holes and echoes from an action principle

Abstract

It is often said that there is no gravity theory based on local action principles giving rise to firewall black hole solutions. Additionally, Guo and Mathur [Int. J. Mod. Phys. D 31, 2242009 (2022).] have cast doubt on the observability of firewall echoes due to the closed trapped surface produced by a backreaction of macroscopic in-falling wave packets. In this paper, we bring Einstein-Maxwell-Dilaton action as a toy model that serves as counterexample to these assertions. Actions with Maxwell and dilaton fields emerge from several fundamental theories, such as the low energy limit of (super) string theory or Kaluza-Klein compactifications. In these systems, the black hole solution has two curvature singularities. We will show that the outer singularity inside the event horizon can cause significant change to the outside, close to the extremal limit, making a macroscopic reflective barrier near the event horizon that would lead to “observable” gravitational wave echoes in this toy model. Additionally, we also call into question the argument by Guo et al. [J. High Energy Phys. 07 (2018) 162.] claiming that a very small fraction of the backscattered photons will be able to escape back to infinity from the firewall, using these black holes as a counterexample.