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

TL;DR

This paper explores noncommutative D3-brane effective gravity, revealing extra dimensions, and demonstrates that black hole geometries in this framework match known extremal black holes in 4D string theory, with entropy calculations supporting the attractor mechanism.

Contribution

It shows that noncommutative D3-brane geometries are equivalent to known extremal black holes in 4D string theory, linking noncommutative geometry with established black hole solutions.

Findings

Extra dimensions exist in the gravity decoupling limit.

Black hole geometries in noncommutative D3-brane theory match 4D extremal black holes.

Macroscopic entropy computed via attractor mechanism confirms the equivalence.

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 $AdS_5$ 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.