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We revisit the 4D generalized black hole geometries, obtained by us [1], witha renewed interest, to unfold some aspects of effective gravity in anoncommutative D3-brane formalism. In particular, we argue for the existence ofextra dimensions in the gravity decoupling limit in the theory. We show thatthe theory is rather described by an ordinary geometry and is governed by aneffective string theory in 5D. The extremal black hole geometry $AdS_5$obtained in effective string theory is shown to be in precise agreement withthe gravity dual proposed for D3-brane in a constant magnetic field.Kaluza-Klein compactification is performed to obtain the corresponding chargedblack hole geometries in 4D. Interestingly, they are shown to be governed bythe extremal black hole geometries known in string theory. The attractormechanism is exploited in effective string theory underlying a noncommutativeD3-brane and the macroscopic entropy of a charged black hole is computed. Weshow that the generalized black hole geometries in a noncommutative D3-branetheory are precisely identical to the extremal black holes known in 4Deffective string theory.Comment: 17 page

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Noncommutative<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>D</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>-brane, black holes, and attractor mechanism

NoncommutativeD3-brane, black holes, and attractor mechanism