Holography of 3D Asymptotically Flat Black Holes

TL;DR

This paper explores the holographic duality between three-dimensional asymptotically flat black holes and a contracted conformal field theory, deriving conserved charges and entropy consistent with thermodynamics and the Cardy-like formula.

Contribution

It introduces a duality framework for flat-space black holes using contracted conformal field theories and derives their conserved charges and entropy.

Findings

Conserved charges match the first law of thermodynamics.

Derived a Cardy-like formula reproducing Wald's entropy.

Constructed stress tensor for asymptotically flat black holes.

Abstract

We study the asymptotically flat rotating hairy black hole solution of a three-dimensional gravity theory which is given by taking the flat-space limit (zero cosmological constant limit) of new massive gravity. We propose that the dual field theory of the flat-space limit of new massive gravity can be described by a contracted conformal field theory which is invariant under the action of the BMS$_{3}$ group. Using the flat/contracted conformal field theory correspondence, we construct a stress tensor which yields the conserved charges of the asymptotically flat black hole solution. We check that our expressions of the mass and angular momentum fit with the first law of black hole thermodynamics. Furthermore, by taking the appropriate limit of the Cardy formula in the parent conformal field theory, we find a Cardy-like formula which reproduces the Wald's entropy of the 3D asymptotically flat black hole.