Observations on holographic aspects of four-dimensional asymptotically flat ${\cal N}=2$ black holes

TL;DR

This paper investigates the holographic properties of four-dimensional near-extremal Reissner-Nordstrom black holes in ${ m extbf{N}=2}$ supergravity, demonstrating how bulk features are encoded in a boundary theory via deformations of $AdS_2$ space.

Contribution

It introduces a novel approach to relate near-extremal black hole properties to boundary theories through solution space deformations and extends the attractor mechanism to non-extremal cases.

Findings

Bulk properties like mass and entropy are holographically encoded in boundary theories.

Near-extremal black holes can be described as deformations of BPS black holes in solution space.

The nAdS$_2$ attractor mechanism is reformulated as a deformation of BPS flow equations.

Abstract

In this note, we explore holographic attributes of four-dimensional near-extremal Reissner-Nordstrom black hole solutions in ungauged ${\cal N}=2$ supergravity theories at the two-derivative level by recasting them as a specific first-order deformation in solution space, associated with an infinitesimal Harrison transformation, of black holes in an $AdS_2$ space-time. Specifically, we use this link to exhibit how bulk properties, such as mass and entropy, of four-dimensional near-extremal black holes are holographically encoded in the one-dimensional boundary theory dual to gravity in an infinitesimally deformed $AdS_2$ space-time. We do so for the case of four-dimensional near-extremal black holes that arise as deformations in solution space of BPS black holes by changing the non-extremality parameter. For these near-extremal black holes, we further show that the nAdS$_2$ attractor mechanism can be recast as a specific deformation of the BPS flow equations in four dimensions. Additionally, we also discuss time-dependent perturbations of the four-dimensional near-extremal Reissner-Nordstrom solutions from a two-dimensional point of view.