Schwarzschild horizon dynamics and SU(2) Chern-Simons theory

TL;DR

This paper explores how different gauge fixing choices affect the description of Schwarzschild black hole horizons as SU(2) and ISO(2) Chern-Simons theories, showing their physical equivalence and reduction to U(1) invariance.

Contribution

It demonstrates the equivalence of various gauge-fixed descriptions of horizon degrees of freedom in Schwarzschild black holes, connecting SU(2), ISO(2), and U(1) Chern-Simons theories.

Findings

Different gauge fixings lead to equivalent horizon theories.

SU(2) and ISO(2) descriptions can be reduced to U(1) gauge invariance.

The approach unifies disparate horizon characterization methods.

Abstract

We discuss the effect of different choices in partial gauge fixing of bulk local Lorentz invariance, on the description of the horizon degrees of freedom of a Schwarzschild black hole as an SU(2) Chern-Simons theory with specific sources. A classically equivalent description in terms of an ISO(2) Chern-Simons theory is also discussed. Further, we demonstrate that both these descriptions can be partially gauge fixed to a horizon theory with U(1) local gauge invariance, with the solder form sources being subject to extra constraints in directions orthogonal to an internal vector field left invariant by U(1) transformations. Seemingly disparate approaches on characterization of the horizon theory for the Schwarzschild black hole (as well as spherical Isolated Horizons in general) are thus shown to be equivalent physically.