A Schwarzian on the Stretched Horizon

TL;DR

This paper demonstrates that replacing the black hole horizon with a stretched horizon introduces a Schwarzian boundary term, akin to those in nearly AdS gravity, revealing new boundary dynamics.

Contribution

It introduces a Schwarzian action at the stretched horizon, extending the understanding of boundary terms in black hole physics beyond the classical horizon.

Findings

A new boundary term appears at the stretched horizon.

The boundary term is described by a Schwarzian action.

Connections to nearly AdS gravity boundary dynamics.

Abstract

It is well known that the Euclidean black hole action has a boundary term at the horizon proportional to the area. I show that if the horizon is replaced by a stretched horizon with appropriate boundary conditions, a new boundary term appears, described by a Schwarzian action similar to the recently discovered boundary actions in "nearly anti-de Sitter" gravity.