Boundary Conservation from Bulk Symmetry

TL;DR

This paper demonstrates that the boundary dynamics near a black hole horizon, modeled as a membrane fluid, can be derived from bulk symmetry invariance and that quantum effects like Hawking radiation restore broken covariance.

Contribution

It shows that boundary matter dynamics stem from bulk symmetry invariance and connects Hawking flux to boundary conservation laws in semi-classical gravity.

Findings

Boundary dynamics arise from bulk symmetry invariance.

Quantum flux restores broken covariance near horizons.

Hawking flux is incorporated into boundary conservation equations.

Abstract

The evolution of the black hole horizon can be effectively captured by a fictitious membrane fluid living on the stretched horizon. We show that the dynamics of this boundary matter arises from the invariance of the bulk action under local symmetries in the presence of the inner boundary. If general covariance is broken in a semi-classical treatment of a quantum field near a black hole horizon, we argue that it can be restored by the inclusion of a quantum flux into the membrane conservation equation which is exactly equal to the Hawking flux.