α′ corrections of Reissner-Nordström black holes

Abstract

We study the first-order in α corrections to non-extremal 4-dimensional dyonic Reissner-Nordström (RN) black holes with equal electric and magnetic charges in the context of Heterotic Superstring effective field theory (HST) compactified on a T 6 . The particular embedding of the dyonic RN black hole in HST considered here is not supersymmetric in the extremal limit. We show that, at first order in α , consistency with the equations of motion of the HST demands additional scalar and vector fields become active, and we provide explicit expressions for all of them. We determine analytically the position of the event horizon of the black hole, as well as the corrections to the extremality bound, to the temperature and to the entropy, checking that they are related by the first law of black-hole thermodynamics, so that ∂S/∂M = 1/T. We discuss the implications of our results in the context of the Weak Gravity Conjecture, clarifying that entropy corrections for fixed mass and charge at extremality do not necessarily imply corrections to the extremal chargeto-mass ratio. a pabloantonio.cano[at]kuleuven.be

T duality and Wald entropy formula in the Heterotic Superstring effective action at first-order in α′

“…(5.2b) that we are going to derive in section 5 has been applied to a non-extremal version of the 4-dimensional Reissner-Nordström black hole we just discussed, in ref. [21]. While the microscopic interpretation of the entropy of this black hole is unknown, being a black hole with finite temperature, one can check that the first law of thermodynamics is indeed satisfied because the temperature computed from the α -corrected metric and the entropy computed from the α -corrected metric with the αcorrected entropy formula are related by the thermodynamic relation…”

“…[17] and [18][19][20], respectively and, more recently, to 4-dimensional non-extremal Reissner-Nordström black holes in ref. [21]. The question of the regularity of the so-called small black holes has also been reviewed in refs.…”

On the extremality bound of stringy black holes

“…Of course, the details depend on the UV theory on which the system is embedded. It is interesting to mention here the example of the dyonic Reissner-Nordstrom black hole solution of Einstein-Maxwell-Dilaton theory embedded in the heterotic theory (f (q, 0) configuration), which requires the activation of additional fields that can be truncated at the two-derivative level [35].…”

“…In other words, 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].…”

“…The study of the non-extremal black holes of that type will be the object of a coming publication[35]. α ′ -corrections seem to introduce pathologies in the extremal case even though the zeroth-order solution is regular.…”