Noncommutative $D_3$-brane, Black Holes and Attractor Mechanism

Abstract

We revisit the 4D generalized black hole geometries, obtained by us [1], with a renewed interest, to unfold some aspects of effective gravity in a noncommutative D3-brane formalism. In particular, we argue for the existence of extra dimensions in the gravity decoupling limit in the theory. We show that the theory is rather described by an ordinary geometry and is governed by an effective string theory in 5D. The extremal black hole geometry $Ad{S}_5$ obtained in effective string theory is shown to be in precise agreement with the gravity dual proposed for D3-brane in a constant magnetic field. Kaluza-Klein compactification is performed to obtain the corresponding charged black hole geometries in 4D. Interestingly, they are shown to be governed by the extremal black hole geometries known in string theory. The attractor mechanism is exploited in effective string theory underlying a noncommutative D3-brane and the macroscopic entropy of a charged black hole is computed. We show that the generalized black hole geometries in a noncommutative D3-brane theory are precisely identical to the extremal black holes known in 4D effective string theory.

17 pages

References in corpus (3)

• Non-Supersymmetric Attractors and Entropy Function
• On Euclidean and Noetherian Entropies in AdS Space
• Higher derivative corrections to near-extremal black holes in type IIB supergravity

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• Stationary black holes and attractor mechanism
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• Tunneling between de Sitter and anti de Sitter black holes in a noncommutative D3-brane formalism
• Greybody Factors for Rotating Black Holes on Codimension-2 Branes
• Black hole evaporation in a spherically symmetric non-commutative space-time
• Scalar emission in a rotating Gödel black hole
• Moeller's Energy-Momentum Complex for a Spacetime Geometry on a Noncommutative Curved D3-Brane
• Non-Supersymmetric Attractors in BI black holes
• Non-Supersymmetric Unattractors in Born-Infeld Black Holes
• Entropy Function for Non-extremal D1D5 and D2D6NS5-branes