Holographic Duals of Near-extremal Reissner-Nordstrom Black Holes

TL;DR

This paper explores the holographic duality between near-extremal Reissner-Nordstrom black holes and a two-dimensional conformal field theory, analyzing their uplifted geometries and scalar scattering processes.

Contribution

It provides a detailed analysis of the $ ext{AdS}_3/ ext{CFT}_2$ correspondence for uplifted near-extremal Reissner-Nordstrom black holes, including scalar scattering and absorption cross section calculations.

Findings

Absorption cross section matches CFT two-point function

Near horizon geometry is $ ext{AdS}_3 imes ext{S}^2$

Scalar scattering amplitude computed successfully

Abstract

We consider the $\mathrm{AdS}_3/\mathrm{CFT}_2$ description of Reissner-Nordstr{\o}m black holes by studying their uplifted counterparts in five dimensions. Assuming a natural size of the extra dimension, the near horizon geometries for the extremal limit are exactly $\mathrm{AdS}_3 \times \mathrm{S}^2$. We compute the scattering amplitude of a scalar field, with a mode near threshold of frequency and extra dimensional momentum, by a near extremal uplifted black hole. The absorption cross section agrees with the two point function of the CFT dual to the scalar field.