Soft thermodynamics of gravitational shock wave

TL;DR

This paper establishes a simple thermodynamic relation linking gravitational shock waves to microscopic horizon area changes, applicable to various static spacetimes and demonstrated within Gauss-Bonnet gravity, with implications for black hole entanglement.

Contribution

It derives a universal thermodynamic relation for gravitational shock waves using covariant phase space formalism, extending applicability beyond AdS spacetimes and connecting to horizon area deformations.

Findings

Derived a thermodynamic relation between shock waves and horizon area deformation.

Applied the formalism to Gauss-Bonnet gravity as an example.

Showed the scattering matrix exponential relates to horizon area.

Abstract

The gravitational shock waves have provided crucial insights into entanglement structures of black holes in the AdS/CFT correspondence. Recent progress on the soft hair physics suggests that these developments from holography may also be applicable to geometries beyond negatively curved spacetime. In this work, we derive a remarkably simple thermodynamic relation which relates the gravitational shock wave to a microscopic area deformation. Our treatment is based on the covariant phase space formalism and is applicable to any Killing horizon in generic static spacetime which is governed by arbitrary covariant theory of gravity. The central idea is to probe the gravitational shock wave, which shifts the horizon in the $u$ direction, by the Noether charge constructed from a vector field which shifts the horizon in the $v$ direction. As an application, we illustrate its use for the Gauss-Bonnet gravity. We also derive a simplified form of the gravitational scattering unitary matrix and show that its leading-order contribution is nothing but the exponential of the horizon area: $\mathcal{U}=\exp(i \text{Area})$.