On some properties of the attractor equations

Günaydın

et al. 2006

Int. J. Mod. Phys. A

Self Cite

152

409

We study the critical points of the black hole scalar potential V BH in N = 2, d = 4 supergravity coupled to n V vector multiplets, in an asymptotically flat extremal black hole background described by a 2 (n V + 1)-dimensional dyonic charge vector and (complex) scalar fields which are coordinates of a special Kähler manifold.For the case of homogeneous symmetric spaces, we find three general classes of regular attractor solutions with non-vanishing Bekenstein-Hawking entropy. They correspond to three (inequivalent) classes of orbits of the charge vector, which is in a 2 (n V + 1)-dimensional representation R V of the U-duality group. Such orbits are non-degenerate, namely they have non-vanishing quartic invariant (for rank-3 spaces). Other than the 1 2 -BPS one, there are two other distinct non-BPS classes of charge orbits, one of which has vanishing central charge.The three species of solutions to the N = 2 extremal black hole attractor equations give rise to different mass spectra of the scalar fluctuations, whose pattern can be inferred by using invariance properties of the critical points of V BH and some group theoretical considerations on homogeneous symmetric special Kähler geometry.

Section: Non-bps Solutionssupporting

confidence: 62%

Section: The Mass Spectra At Critical Pointsmentioning

confidence: 99%

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Charge Orbits of Symmetric Special Geometries and Attractors

Bellucci

Günaydın

et al. 2006

Int. J. Mod. Phys. A

Self Cite

152

409

“…It is useful to point out that in [48] a different normalization for the d = 5 (electric) effective BH potential was used: 22) due to a different normalization of the d = 5 vector kinetic matrix: which also shows that due to the identity [48] 26) where the d = 5 scalar metric in our convention reads 27) with λ i ≡ a ij λ j .…”

Section: Bps and Non-bps D = 5 And D = Relationsmentioning

confidence: 99%

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

Ceresole

Marrani

2007

Class. Quantum Grav.

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118

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.

“…ii ) non-BPS solutions with Z = 0 and D i Z = 0 for at least some i [5,13,15,16,23]. They do not preserve any supersymmetry and do not saturate the BPS bound; indeed, for symmetric spaces it holds that [27]:…”

mentioning

confidence: 99%

Black Hole Attractors in Extended Supergravity

AIP Conference Proceedings

Marrani

2007

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We review some aspects of the attractor mechanism for extremal black holes of (not necessarily supersymmetric) theories coupling Einstein gravity to scalars and Maxwell vector fields. Thence, we consider N = 2 and N = 8, d = 4 supergravities, reporting some recent advances on the moduli spaces associated to BPS and non-BPS attractor solutions supported by charge orbits with non-compact stabilizers.