Near-Horizon Geometry and Warped Conformal Symmetry

TL;DR

This paper explores the near-horizon geometry of non-extremal black holes using novel boundary conditions in three-dimensional gravity, revealing a twisted warped conformal symmetry algebra that relates to BMS and matches entropy calculations.

Contribution

It introduces new boundary conditions for near-horizon geometries leading to a twisted warped CFT symmetry algebra and connects it to BMS through a twisted Sugawara construction.

Findings

Identified a twisted warped CFT symmetry algebra for near-horizon geometries.

Established a relation between the symmetry algebra and BMS via a twisted Sugawara construction.

Matched micro- and macroscopic entropy calculations for zero-mode solutions.

Abstract

We provide boundary conditions for three-dimensional gravity including boosted Rindler spacetimes, representing the near-horizon geometry of non-extremal black holes or flat space cosmologies. These boundary conditions force us to make some unusual choices, like integrating the canonical boundary currents over retarded time and periodically identifying the latter. The asymptotic symmetry algebra turns out to be a Witt algebra plus a twisted u(1) current algebra with vanishing level, corresponding to a twisted warped CFT that is qualitatively different from the ones studied so far in the literature. We show that this symmetry algebra is related to BMS by a twisted Sugawara construction and exhibit relevant features of our theory, including matching micro- and macroscopic calculations of the entropy of zero-mode solutions. We confirm this match in a generalization to boosted Rindler-AdS. Finally, we show how Rindler entropy emerges in a suitable limit.