Extended Near Horizon Symmetries of Extremal BTZ Black Holes in 3D Massive Gravity

TL;DR

This paper investigates the near-horizon symmetries of extremal BTZ black holes in 3D massive gravity theories, revealing dual Virasoro algebras with consistent central charges, thus extending the understanding of black hole symmetries in higher derivative gravities.

Contribution

It demonstrates the existence of two centrally extended Virasoro algebras in near-horizon extremal BTZ black holes within higher derivative gravity theories, confirming the robustness of the regularization method.

Findings

Two Virasoro algebras with central charges consistent with spatial infinity results

Regularization procedure relates near-horizon and asymptotic geometries

Symmetry structure extends to higher derivative gravity theories

Abstract

We study the asymptotic symmetries of near-horizon extremal BTZ black holes in higher derivative theories of gravity, such as New Massive Gravity and Topological Massive Gravity. By employing a particular boundary condition and the regularization prescription proposed earlier for the Einstein gravity, we demonstrate the existence of two centrally extended Virasoro algebras. The central charges evaluated within this framework are in agreement with their corresponding expressions evaluated at the spatial infinity. We also discuss the robustness of the regularization procedure by relating asymptotic and near-horizon geometries.