New boundary conditions in Einstein-scalar gravity in three dimensions

TL;DR

This paper explores new boundary conditions in three-dimensional Einstein-scalar gravity, constructing exact solutions that interpolate between AdS vacuum and scalar field fixed points, revealing novel properties of surface charges and their algebraic structure.

Contribution

It introduces a new class of boundary conditions and exact solutions in 3D Einstein-scalar gravity, demonstrating a modified conformal algebra with a field-dependent central extension.

Findings

Surface charges are finite but non-integrable.

The integrable part of charges realizes the conformal algebra.

Central extension depends on the scalar field configuration.

Abstract

We analyze the backreaction of a class of scalar field self-interactions with the possibility of evolving from an AdS vacuum to a fixed point where the scalar field potential vanishes. Exact solutions which interpolate between these regions, ranging from stationary black hole to dynamical spacetimes are constructed. Their surface charges are finite but non-integrable. We study the properties of these charges on the solutions. In particular, we show that the integrable part of the charges provides a realization of the conformal algebra by means of a modification of the Dirac bracket proposed by Barnich and Troessaert. The latter construction allows for a field dependent central extension, whose value tends to the Brown-Henneaux central charge at late times.