Cosmological New Massive Gravity and Galilean Conformal Algebra in 2-dimensions

TL;DR

This paper explores the realization of 2D Galilean conformal algebra in the context of cosmological new massive gravity, deriving entropy formulas that match the non-relativistic limits of black hole entropies in specific solutions.

Contribution

It provides the first derivation of GCA_2 entropy formulas from cosmological new massive gravity solutions, connecting boundary algebra with bulk black hole thermodynamics.

Findings

Entropy formulas for GCA_2 match non-relativistic limits of BTZ and warped AdS_3 black hole entropies.

Derived explicit relations between GCA_2 parameters and black hole thermodynamics.

Extended the understanding of holography in non-AdS backgrounds.

Abstract

In the present paper we consider the realization of $2-$dimensional Galilean conformal algebra ($GCA_2$) on the boundary of cosmological new massive gravity. At first we consider the contracted BTZ black hole solution. We obtain entropy formula for the $GCA_2$ in term of contracted scaling dimension $\Delta$ and central charge $C_1$. This entropy formula exactly matches with the non-relativistic limit of Bekenstein-Hawking entropy of BTZ black hole. Then we extend our study to the contracted warped $AdS_3$ black hole solution of CNMG. We obtain the entropy of dual $GCA_2$ in terms of central charges and finite temperatures, $T_1, T_2$. Again this expression coincides with the non-relativistic limit of Bekenstein-Hawking entropy formula of warped $AdS_3$ black hole.