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.

arXiv comment17 pages

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• Entropy function and attractors for AdS black holes
• Stationary black holes and attractor mechanism
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• Generalizations of the Smarr formula for black holes with nonlinear electromagnetic fields
• Hawking radiation in a Rotating Kaluza-Klein Black Hole with Squashed Horizons
• Greybody factor for a scalar field coupling to Einstein's tensor
• On Attractor Mechanism and Entropy Function for Non-extremal Black Holes/Branes
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• Non-Supersymmetric Unattractors in Born-Infeld Black Holes
• Phantom scalar emission in the Kerr black hole spacetime
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• Entropy Function for Non-extremal D1D5 and D2D6NS5-branes
• Geodesic structure of a noncommutative black hole