First-order flow equations for extremal black holes in very special geometry

Cardoso, Gabriel Lopes; Ceresole, Anna; Dall’Agata, Gianguido; Oberreuter, Johannes M.; Perz, Jan

doi:10.1088/1126-6708/2007/10/063

Cited by 117 publications

(197 citation statements)

References 46 publications

Supporting

Mentioning

194

Contrasting

Order By: Relevance

“…In particular, the Attractor Mechanism for extremal black holes [1,2,3,4,5] in four and five dimensions has been widely investigated for both N = 2 and extended supergravities [6]- [44] (see also [45], [46] and [47] for recent reviews).…”

Section: Introductionmentioning

confidence: 99%

“…for a given background spacetime geometry, by solving explicitly the equations of motion [5,6,7,15,28,62,63]. These are originally the second order differential field equations for the scalars and the warp factors, but they have been shown to be equivalent to first order flow equations for both supersymmetric and broad classes of nonsupersymmetric, static and rotating BH solutions [36,42,44]. In this context, the relation between five and four dimensions is implemented through dimensional reduction and by a Taub-NUT geometry for the black hole (see for instance [8,9,11,44,64]).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

4d/5d correspondence for the black hole potential and its critical points

Ceresole

Ferrara

Marrani

2007

Class. Quantum Grav.

Self Cite

118

View full text Add to dashboard Cite

We express the d = 4, N = 2 black hole effective potential for cubic holomorphic F functions and generic dyonic charges in terms of d = 5 real special geometry data. The 4d critical points are computed from the 5d ones, and their relation is elucidated. For symmetric spaces, we identify the BPS and non-BPS classes of attractors and the respective entropies. These always derive from simple interpolating formulae between four and five dimensions, depending on the volume modulus and on the 4d magnetic (or electric) charges.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

4d/5d correspondence for the black hole potential and its critical points

Ceresole

Ferrara

Marrani

2007

Class. Quantum Grav.

Self Cite

118

View full text Add to dashboard Cite

show abstract

“…The derivation of flow equations for extremal black holes presented here differs from their previous presentation [29,30,31] in two aspects: Firstly, no specific form of the relation between the fake and actual charges is assumed here, instead the derivation is based on the assumption of harmonicity of the variables H I . 13 Secondly, expressing the black hole potential directly by harmonic functions makes it possible to determine the fake charges by extremization.…”

Section: First-order Flow Equations For Extremal Black Holesmentioning

confidence: 97%

“…Being interested in spherically symmetric solutions black hole solutions we take φ x = φ x (ρ) and can solve the vector field equations of motion by putting 9) where the q's are the electric charges. Using the ansätze (2.6) and (2.9) in the remaining equations of motion, we see that they all reduce to the following equations…”

Section: H-variablesmentioning

confidence: 99%

“…Even though not all extremal black holes are supersymmetric [5,6] and all non-extremal black holes break all supersymmetries, it turns out [7] that analogous flow equations may be derived for four- [8] and five-dimensional extremal black holes [9], as well as for non-extremal p-branes [10] and black holes [11]. This fact alone already hints at a possibility that perhaps non-supersymmetric solutions could be obtained in a similar way to the supersymmetric ones.…”

Section: Introductionmentioning

confidence: 95%

See 1 more Smart Citation

Black holes and black strings of N = 2, d = 5 supergravity in the H-FGK formalism

Meessen

Ortı́n

Perz

et al. 2012

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

We study general classes and properties of extremal and non-extremal static black-hole solutions of N = 2, d = 5 supergravity coupled to vector multiplets using the recently proposed H-FGK formalism, which we also extend to static black strings. We explain how to determine in general the integration constants and physical parameters of the black-hole and black-string solutions. We derive some model-independent statements, including the transformation of nonextremal flow equations to the form of those for the extremal flow. We apply our methods to the construction of example solutions (among others a new extremal string solution of heterotic string theory on K 3 × S 1 ) and analyze their properties. In all the cases studied the product of areas of the inner and outer horizon of a non-extremal solution coincides with the square of the moduli-independent area of the horizon of the extremal solution with the same charges. a

show abstract

Black hole attractors and the entropy function in four‐ and five‐dimensional N = 2 supergravity

Perz

2007

Fortschritte der Physik

View full text Add to dashboard Cite

In this overview of selected aspects of the black hole attractor mechanism, after introducing the necessary foundations, we examine the relationship between two ways to describe the attractor phenomenon in four‐dimensional N = 2 supergravity: the entropy function and the black hole potential. We also exemplify their practical application to finding solutions to the attractor equations for a conifold prepotential. Next we describe an extension of the original definition of the entropy function to a class of rotating black holes in five‐dimensional N = 2 supergravity based on cubic polynomials, exploiting a connection between four‐ and five‐dimensional black holes. This link allows further the derivation of five‐dimensional first‐order differential flow equations governing the profile of the fields from infinity to the event horizon and construction of non‐supersymmetric interpolating solutions in four dimensions by dimensional reduction. Finally, since four‐dimensional extremal black holes in N = 2 supergravity can be viewed as certain two‐dimensional string compactifications with fluxes, we discuss implications of the conifold example in the context of the entropic principle, which postulates as a probability measure on the space of these string compactifications the exponentiated entropy of the corresponding black holes.

show abstract

First-order flow equations for extremal black holes in very special geometry

Cited by 117 publications

References 46 publications

4d/5d correspondence for the black hole potential and its critical points

4d/5d correspondence for the black hole potential and its critical points

Black holes and black strings of N = 2, d = 5 supergravity in the H-FGK formalism

Black hole attractors and the entropy function in four‐ and five‐dimensional N = 2 supergravity

Contact Info

Product

Resources

About