De-singularizing the extremal GMGHS black hole via higher derivatives corrections

Carlos Herdeiro,Eugen Radu,Kunihito Uzawa

doi:10.1016/j.physletb.2021.136357

De-singularizing the extremal GMGHS black hole via higher derivatives corrections

Carlos Herdeiro, Eugen Radu + Show 1 more

Open Access

https://doi.org/10.1016/j.physletb.2021.136357

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Abstract

The Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) black hole is an influential solution of the low energy heterotic string theory. As it is well known, it presents a singular extremal limit. We construct a regular extension of the GMGHS extremal black hole in a model with O(α′) corrections in the action, by solving the fully non-linear equations of motion. The de-singularization is supported by the O(α′)-terms. The regularised extremal GMGHS BHs are asymptotically flat, possess a regular (non-zero size) horizon of spherical topology, with an AdS2×S2 near horizon geometry, and their entropy is proportional to the electric charge. The near horizon solution is obtained analytically and some illustrative bulk solutions are constructed numerically.

Highlights

Low energy string theory compactified to four spacetime dimensions admits a famous black hole (BH) solution, found by Gibbons and Maeda [1] and, independently, by Garfinkle, Horowitz and Strominger [2] – on dubbed the GMGHS BH
In this work we have confirmed that α corrections can de-singularize the extremal GMGHS solution, an influential stringy BH whose extremal limit is long known to be singular
This gives an illustrative example of how higher order corrections motivated by quantum gravity can be key to understand the BH geometry on and outside a horizon

Summary

Introduction

Low energy string theory compactified to four spacetime dimensions admits a famous black hole (BH) solution, found by Gibbons and Maeda [1] and, independently, by Garfinkle, Horowitz and Strominger [2] – on dubbed the GMGHS BH. It is well known that such near horizon geometry is a key feature of static supersymmetric BHs, providing the attractor mechanism by which horizon scalar fields values are determined by the charges carried by the BH and insensitive to the asymptotic values of the scalar fields [32,33,34,35] The entropy of these BHs is consistent with the microscopic states counting of the associated D-brane system. In this work we shall provide numerical evidence for the existence of non-perturbative extensions of the GMGHS BHs which are extremal, asymptotically flat and regular, on and outside the horizon. These solutions represent global (bulk) extensions of the aforementioned attractors found analytically and possess a variety of interesting properties.

The action

Ansatz and entropy

The attractors

The bulk extremal BHs

Discussion