A Schwarzian on the Stretched Horizon

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.

8 pages; v2: 9 pages, extended explanation of boundary conditions, other minor changes, to appear in a special issue of Gen. Rel. Grav. in memory of Prof. Thanu Padmanabhan ("Paddy")

References in corpus (3)

• Entropy of Null Surfaces and Dynamics of Spacetime
• Classifying boundary conditions in JT gravity: from energy-branes to $\alpha$-branes
• Near-Horizon BMS Symmetry, Dimensional Reduction, and Black Hole Entropy

Cited by in corpus (2)

• Freelance Holography, Part I: Setting Boundary Conditions Free in Gauge/Gravity Correspondence
• A note on the action with the Schwarzian at the stretched horizon