On the extremality bound of stringy black holes

Pablo A Cano,Pedro F Ramírez,Tomás Ortín

doi:10.1007/jhep02(2020)175

Abstract

A mild version of the weak gravity conjecture (WGC) states that extremal black holes have charge-to-mass ratio larger or equal than one when higher-curvature interactions are taken into account. Since these corrections become more relevant in the low-mass regime, this would allow the decay of extremal black holes in terms of energy and charge conservation. Evidence in this direction has been mainly given in the context of corrections to Einstein-Maxwell theory. Here we compute corrections to the charge-to-mass ratio of some dyonic extremal black holes explicitly embedded in the heterotic string effective theory. We find that modifications of the extremality bound depend on the solution considered, with the charge-to-mass ratio remaining unchanged or deviating positively from one. Additionally, we observe that the introduction of the higher-curvature terms increases the Wald entropy in all cases considered, whose variation does not seem to be correlated with the charge-to-mass ratio, contrary to the situation in Einstein-Maxwell theory.

Highlights

Case in which there is no binding energy between the products, while a strict inequality is expected in generic situations
A mild version of the weak gravity conjecture (WGC) states that extremal black holes have charge-to-mass ratio larger or equal than one when higher-curvature interactions are taken into account
The weak gravity conjecture proposes that the spectrum of a quantum theory of gravity must be such that extremal black holes can decay, as far as energy and charge conservation are concerned

Summary

A family of extremal black holes

C∞ and φ∞ are the asymptotic values of c and φ These are effective fourdimensional fields, while hatted objects represent ten-dimensional fields of the heterotic theory. From the effective four-dimensional action (2.2) one sees that, at the supergravity level, one could truncate V , H and c This would simplify the system to the Einstein-Maxwell-Dilaton model. Higher-derivative corrections to the Einstein-Maxwell-Dilaton effective model in the context of string theory may require the activation of additional fields. This is a well-known but often forgotten fact [34, 35]

Supergravity zeroth-order solution

Discussion

A The heterotic theory

B Solving the equations of motion

C Wald entropy