Stability of the Black Hole Horizon and the Landau Ghost

TL;DR

This paper investigates the stability of black hole horizons against attempts to exceed extremality, demonstrating that physical and quantum effects prevent such violations, thus supporting cosmic censorship and thermodynamic laws.

Contribution

It analyzes various processes adding charge to black holes and shows that classical and quantum effects prevent horizon destabilization, confirming the robustness of black hole stability principles.

Findings

Self-Coulomb repulsion prevents charged shells from crossing the horizon.

Classical charge radius constraints inhibit charge addition.

Quantum effects and Landau ghost considerations protect the horizon.

Abstract

The stability of the black hole horizon is demanded by both cosmic censorship and the generalized second law of thermodynamics. We test the consistency of these principles by attempting to exceed the black hole extremality condition in various process in which a U(1) charge is added to a nearly extreme Reissner--Nordstr\"om black hole charged with a {\it different\/} type of U(1) charge. For an infalling spherical charged shell the attempt is foiled by the self--Coulomb repulsion of the shell. For an infalling classical charge it fails because the required classical charge radius exceeds the size of the black hole. For a quantum charge the horizon is saved because in order to avoid the Landau ghost, the effective coupling constant cannot be large enough to accomplish the removal.