Universal Relation between Corrections to Entropy and Extremality

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

Section: Discussionmentioning

confidence: 97%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

α′ corrections of Reissner-Nordström black holes

Cano

Chimento

Linares

et al. 2020

“…Scalar fields usually affect the thermodynamic description of black holes -see e.g. [39] -and it would be interesting to explore whether this could modify the conclusions of [23]. The string coupling constant and the curvature can be kept sufficiently small in the exterior region of the black hole for the cases we have considered, hence the low energy field theory description gives a good approximate description of the system.…”

Section: Discussionmentioning

confidence: 99%

“…Subsequent works have proposed that, demanding analyticity of scattering amplitudes, unitarity and causality constrain these coefficients such that there is a positive deviation of the charge-to-mass ratio of extremal black holes [18][19][20]. Likewise, it has been proposed that this can be related to the positivity of the corrections to the entropy of the black hole induced by higher-derivative operators [21][22][23]. The study of black holes in Einstein-Maxwell theory is well justified and interesting, as it provides a relatively simple arena to explore this question while making contact with dominant interactions in real world experiences.…”

Section: Introductionmentioning

confidence: 99%

On the extremality bound of stringy black holes

Cano

Ortı́n

Ramírez

2020

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 chargeto-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.

D = 5 rotating black holes in Einstein-Gauss-Bonnet gravity: mass and angular momentum in extremality

Lü

2021

We consider perturbative solutions in Einstein gravity with higher-derivative extensions and address some subtle issues of taking extremal limit. As a concrete new result, we construct the perturbative rotating black hole in five dimensions with equal angular momenta J and general mass M in Einstein-Gauss-Bonnet gravity, up to and including the linear order of the standard Gauss-Bonnet coupling constant α. We obtain the near horizon structure of the near extremal solution, with the blackening factor of the order α. In the extremal limit, the mass-angular momentum relation reduces to $$ M=\frac{3}{2}{\pi}^{\frac{1}{3}}{J}^{\frac{2}{3}}+\pi \alpha $$ M = 3 2 π 1 3 J 2 3 + πα . The positive sign of the α-correction implies that the centrifugal repulsion associated with rotations becomes weaker than the gravitational attraction under the unitary requirement for the Gauss-Bonnet term.