Supersymmetry and attractors

453

816

We study extremal black hole solutions in D dimensions with near horizon geometry AdS 2 × S D−2 in higher derivative gravity coupled to other scalar, vector and antisymmetric tensor fields. We define an entropy function by integrating the Lagrangian density over S D−2 for a general AdS 2 × S D−2 background, taking the Legendre transform of the resulting function with respect to the parameters labelling the electric fields, and multiplying the result by a factor of 2π. We show that the values of the scalar fields at the horizon as well as the sizes of AdS 2 and S D−2 are determined by extremizing this entropy function with respect to the corresponding parameters, and the entropy of the black hole is given by the value of the entropy function at this extremum. Our analysis relies on the analysis of the equations of motion and does not directly make use of supersymmetry or specific structure of the higher derivative terms.

Section: Entropy Of Extremal Black Holesmentioning

confidence: 99%

Black hole entropy function and the attractor mechanism in higher derivative gravity

Sen

2005

453

816

“…The term proportional to q A G AB q B is the so-called black hole potential [3,31] which, with the help of (A.12), can be written as…”

Section: Flow Equations In Five Dimensionsmentioning

confidence: 99%

“…Such solutions are given in terms of harmonic functions [1,3,8,9,10,11]. Furthermore, these black holes can be connected to supersymmetric black hole solutions [12,13,14,15] in five-dimensional N = 2 supergravity theories.…”

Section: Introductionmentioning

confidence: 99%

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

Cardoso

Ceresole

Dall’Agata

et al. 2007

117

194

We construct interpolating solutions describing single-center static extremal non-supersymmetric black holes in four-dimensional N = 2 supergravity theories with cubic prepotentials. To this end, we derive and solve first-order flow equations for rotating electrically charged extremal black holes in a Taub-NUT geometry in five dimensions. We then use the connection between five-and four-dimensional extremal black holes to obtain four-dimensional flow equations and we give the corresponding solutions.

“…From the perspective of four dimensional Calabi-Yau black holes in N = 2 supergravity, the above truncation on the spectrum is also expected. To understand this, we first recall some facts about the attractor mechanism for four dimensional BPS black holes in asymptotically flat space [27,28,29,30]. Although the entropy of such black holes depends on the near horizon values of the vector multiplet moduli, these values are fixed by the charges of the black hole.…”

Section: Extra Charges Attractors and Ghostsmentioning

confidence: 99%

Crystal melting and black holes

Heckman

Vafa

2007

It has recently been shown that the statistical mechanics of crystal melting maps to A-model topological string amplitudes on non-compact Calabi-Yau spaces. In this note we establish a one to one correspondence between two and three dimensional crystal melting configurations and certain BPS black holes given by branes wrapping collapsed cycles on the orbifolds C 2 /Z n and C 3 /Z n × Z n in the large n limit. The ranks of gauge groups in the associated gauged quiver quantum mechanics determine the profiles of crystal melting configurations and the process of melting maps to flop transitions which leave the background Calabi-Yau invariant. We explain the connection between these two realizations of crystal melting and speculate on the underlying physical meaning.