Horizon Shells: Classical Structure at the Horizon of a Black Hole

TL;DR

This paper investigates the uniqueness of Schwarzschild black holes, revealing that while they are unique solutions elsewhere, an infinite family of solutions exists at the horizon, challenging traditional views on black hole structure.

Contribution

It demonstrates the non-uniqueness of solutions at the black hole horizon, showing an infinite set of solutions can match Schwarzschild outside the horizon, which is a novel insight.

Findings

Solutions are unique outside the horizon.

Infinite solutions exist at the horizon.

Implications for black hole physics are discussed.

Abstract

We address the question of the uniqueness of the Schwarzschild black hole by considering the following question: How many meaningful solutions of the Einstein equations exist that agree with the Schwarzschild solution (with a fixed mass m) everywhere except maybe on a codimension one hypersurface? The perhaps surprising answer is that the solution is unique (and uniquely the Schwarzschild solution everywhere in spacetime) *unless* the hypersurface is the event horizon of the Schwarzschild black hole, in which case there are actually an infinite number of distinct solutions. We explain this result and comment on some of the possible implications for black hole physics.