Non-supersymmetric attractors and entropy function

Physical Review D, 2008

We generalize the description of the d = 4 Attractor Mechanism based on an effective black hole (BH) potential to the presence of a gauging which does not modify the derivatives of the scalars and does not involve hypermultiplets. The obtained results do not rely necessarily on supersymmetry, and they can be extended to d > 4, as well.

General Relativity and Gravitation, 2008

We investigate four-dimensional spherically symmetric black hole solutions in gravity theories with massless, neutral scalars non-minimally coupled to gauge fields. In the non-extremal case, we explicitly show that, under the variation of the moduli, the scalar charges appear in the first law of black hole thermodynamics. In the extremal limit, the near horizon geometry is AdS 2 × S 2 and the entropy does not depend on the values of moduli at infinity. We discuss the attractor behaviour by using Sen's entropy function formalism as well as the effective potential approach and their relation with the results previously obtained through special geometry method. We also argue that the attractor mechanism is at the basis of the matching between the microscopic and macroscopic entropies for the extremal non-BPS Kaluza-Klein black hole.

Journal of High Energy Physics, 2008

We study the attractor equations for a quantum corrected prepotential F = t 3 + iλ, with λ ∈ R,which is the only correction which preserves the axion shift symmetry and modifies the geometry.

Journal of High Energy Physics, 2007

We examine in details the entropy function formalism for non-extremal D3, M 2, and M 5-branes that their throat approximation is given by Schwarzschild black hole in AdS p+2 × S D−(p+2) . We show that even though there is no attractor mechanism in the non-extremal black holes/branes, the entropy function formalism does work and the entropy is given by the entropy function at its saddle point.

Physical Review D, 2008

We investigate extremal dyon black holes in the Einstein-Maxwell-dilaton (EMD) theory with higher curvature corrections in the form of the Gauss-Bonnet density coupled to the dilaton. In the same theory without the Gauss-Bonnet term the extremal dyon solutions exist only for discrete values of the dilaton coupling constant a. We show that the Gauss-Bonnet term acts as a dyon hair tonic enlarging the allowed values of a to continuous domains in the plane (a, qm) the second parameter being the magnetic charge. In the limit of the vanishing curvature coupling (a large magnetic charge) the dyon solutions obtained tend to the Reissner-Nordström solution but not to the extremal dyons of the EMD theory. Both solutions have the same values of the horizon radius as a function of charges. The entropy of new dyonic black holes interpolates between the Bekenstein-Hawking value in the limit of the large magnetic charge (equivalent to the vanishing Gauss-Bonnet coupling) and twice this value for the vanishing magnetic charge. Although an expression for the entropy can be obtained analytically using purely local near-horizon solutions, its interpretation as the black hole entropy is legitimate only once the global black hole solution is known to exist, and we obtain numerically the corresponding conditions on the parameters. Thus, a purely local analysis is insufficient to fully understand the entropy of the curvature corrected black holes. We also find dyon solutions which are not asymptotically flat, but approach the linear dilaton background at infinity. They describe magnetic black holes on the electric linear dilaton background. the present paper for extremal dyon black holes with the AdS 2 × S 2 horizon in the Gauss-Bonnet gravity.

The European Physical Journal C, 2019

It has been shown that the entropy function formalism is an efficient way to calculate the entropy of black holes in string theory. We check this formalism for the extremal charged dilaton black hole. We find the general four-derivative correction on the black hole entropy from the value of the entropy function at its extremum point.

Journal of High Energy Physics, 2013

We discuss the fate of flat directions in higher derivative gravity by studying two explicit examples, namely higher derivative gauged supergravity in five dimensions and higher derivative type IIB string theory in ten dimensions. In the first case, the supersymmetric spinning black hole solution in asymptotically AdS spacetime, found by Gutowski and Reall, is analyzed. In this case we find that the flat direction at the two derivative level is not lifted after addition of higher derivative terms, and as it turns out, this result holds even for non-supersymmetric deformations of the higher derivative action. For the rotating D3-brane solutions in type IIB theory, the dilaton parametrizes a flat direction at leading order, but its fate changes upon including order (α ′) 3 supersymmetric higher derivative corrections to the type IIB action, i.e. its leading value gets fixed.

Physical Review D, 2010

Small black holes in heterotic string theory have vanishing horizon area at the supergravity level, but the horizon is stretched to the finite radius AdS2 × S D−2 geometry once higher curvature corrections are turned on. This has been demonstrated to give good agreement with microscopic entropy counting. Previous considerations, however, were based on the classical local solutions valid only in the vicinity of the event horizon. Here we address the question of global existence of extremal black holes in the D-dimensional Einstein-Maxwell-Dilaton theory with the Gauss-Bonnet term introducing a variable dilaton coupling a as a parameter. We show that asymptotically flat black holes exist only in a bounded region of the dilaton couplings 0 < a < acr where acr depends on D. For D ≥ 5 (but not for D = 4) the allowed range of a includes the heterotic string values. For a > acr numerical solutions meet weak naked singularities at finite radii r = rcusp (spherical cusps), where the scalar curvature diverges as |r − rcusp| −1/2. For D ≥ 7 cusps are met in pairs, so that solutions can be formally extended to asymptotically flat infinity choosing a suitable integration variable. We show, however, that radial geodesics cannot be continued through the cusp singularities, so such a continuation is unphysical.

Physical Review D, 2007

We show that four-dimensional Einstein-Maxwell-Dilaton-Gauss-Bonnet gravity admits asymptotically flat black hole solutions with a degenerate event horizon of the Reissner-Nordström type AdS2 × S 2. Such black holes exist for the dilaton coupling constant within the interval 0 ≤ a 2 < a 2 cr. Black holes must be endowed with an electric charge and (possibly) with magnetic charge (dyons) but they can not be purely magnetic. Purely electric solutions are constructed numerically and the critical dilaton coupling is determined acr ≃ 0.488219703. For each value of the dilaton coupling a within this interval and for a fixed value of the Gauss-Bonnet coupling α we have a family of black holes parameterized by their electric charge. Relation between the mass, the electric charge and the dilaton charge at both ends of the allowed interval of a is reminiscent of the BPS condition for dilaton black holes in the Einstein-Maxwell-Dilaton theory. The entropy of the DGB extremal black holes is twice the Bekenstein-Hawking entropy.

Journal of High Energy Physics, 2017

In the context of applications of the AdS/CFT correspondence to condensed matter physics, we compute conductivities for field theory duals of dyonic planar black holes in 3+1-dimensional Einstein-Maxwell-dilaton theories at zero temperature. We combine the near-horizon data obtained via Sen's entropy function formalism with known expressions for conductivities. In this way we express the conductivities in terms of the extremal black hole charges. We apply our approach to three different examples for dilaton theories for which the background geometry is not known explicitly. For a constant scalar potential, the thermoelectric conductivity explicitly scales as α xy ∼ N 3/2 , as expected. For the same model, our approach yields a finite result for the heat conductivity κ/T ∝ N 3/2 even for T → 0.

Journal of High Energy Physics, 2007

We consider the entropy of four-dimensional near-extremal N = 2 black holes. Without R 2 -terms, the Bekenstein-Hawking entropy formula has the structure of the extremal black holes entropy with a shift of the charges depending on the non-extremality parameter and the moduli at infinity. We derive a generalized Wald entropy formula for non-extremal N = 2 black holes with R 2 -terms. We construct a class of small near-extremal horizon solutions with R 2 -terms. In this case the entropy is the same as in the extremal case to order O(µ 2 ), and does not exhibit the charge shift behavior.