Near-Horizon Geometry and Warped Conformal Symmetry

TL;DR

This work introduces boosted near-horizon (quasi-Rindler) boundary conditions in 3D gravity and shows that the resulting asymptotic symmetries form a Witt algebra with a twisted, vanishing-level u(1) current, describable by a warped conformal structure. A nonstandard charge construction—integrating over retarded time—reveals a centrally extended warped Virasoro algebra whose mixed bracket carries a nontrivial cocycle, connecting to BMS3 via a twisted Sugawara map. The authors derive microscopic (Cardy-like) and macroscopic (on-shell action) entropies for zero-mode solutions, demonstrating precise agreement and extending the analysis to boosted Rindler–AdS, with a consistent Rindler limit recovering the area law. They also explore the unusual implications of retarded-time dependence and periodicity, discuss the relation to ultrarelativistic CFTs, and outline generalizations to other gravity theories and higher dimensions.

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.