Schwarzschild/CFT from soft black hole hair?

TL;DR

This paper explores how relaxing boundary conditions in gravitational theories reveals new degrees of freedom, potentially explaining black hole microstates via a conformal field theory dual, and revisiting entropy counting methods.

Contribution

It proposes an enhancement of gravitational degrees of freedom at black hole horizons and connects them to a 2D conformal structure for Schwarzschild black holes.

Findings

Identification of new gravitational hair modes.

Proposal of a 2D conformal dual theory.

Reinterpretation of black hole entropy via Sugawara construction.

Abstract

Recent studies of asymptotic symmetries suggest, that a Hamiltonian phase space analysis in gravitational theories might be able to account for black hole microstates. In this context we explain, why the use of conventional Bondi fall-off conditions for the gravitational field is too restrictive in the presence of an event horizon. This implies an enhancement of physical degrees of freedom ($\mathcal{A}$-modes). They provide new gravitational hair and are responsible for black hole microstates. Using covariant phase space methods, for the example of a Schwarzschild black hole, we give a proposal for the surface degrees of freedom and their surface charge algebra. The obtained two-dimensional dual theory is conjectured to be conformally invariant as motivated from the criticality of the black hole. Carlip's approach to entropy counting reemerges as a Sugawara-construction of a 2D stress-tensor.