Extremal Tunneling and Anti-de Sitter Instantons

TL;DR

This paper derives a universal tunneling probability for charged black holes, confirms its relation to horizon entropy change, and connects it to Anti-de Sitter instantons, superradiance, and the Weak Gravity Conjecture.

Contribution

It extends the tunneling amplitude framework to charged black holes with backreaction, relates it to AdS instantons, and discusses implications for AdS stability and the Weak Gravity Conjecture.

Findings

Tunneling probability equals the exponential of horizon entropy change.

The approach captures superradiant decay regimes.

Connections established between black hole tunneling and AdS instantons.

Abstract

We rederive and extend the amplitude for charged spherical shells tunneling through the outer horizon of charged black holes. In particular, we explicitly confirm that an effective action approach with natural initial conditions for a spherical shell, including backreaction, reduces to the tunneling integral. Consequently, we establish a universal expression for the probability of emission in terms of the change in the horizon entropy. Notably, the result for the charged black hole also captures the superradiant regime of charged particle decay at low energies. We then explore an appropriately regulated extremal and near-horizon limit, relating the tunneling amplitude to a family of gravitational instantons in the near-horizon Anti-de Sitter geometry, reducing to the known result for $AdS_2$ domain walls to leading order in the probe limit. We comment on the relation to the Weak Gravity Conjecture and the conjectured instability of (non-supersymmetric) Anti-de Sitter vacua.