Black Hole Geometries in Noncommutative String Theory

TL;DR

This paper derives generalized black hole solutions in noncommutative string theory, revealing their behavior across different regimes and connecting them to 2D black holes and Hawking radiation phenomena.

Contribution

It introduces a unified effective gravity framework on a curved D3-brane with noncommutative gauge fields, extending classical black hole geometries to all orders in noncommutativity.

Findings

GRN-black hole reduces to GS-black hole in the Planckian regime

Classical regime describes Reissner-Nordstrom and Schwarzschild geometries independently

Near horizon geometry of D-string resembles 2D black hole

Abstract

We obtain a generalized Schwarzschild (GS-) and a generalized Reissner-Nordstrom (GRN-) black hole geometries in (3+1)-dimensions, in a noncommutative string theory. In particular, we consider an effective theory of gravity on a curved $D_3$-brane in presence of an electromagnetic (EM-) field. Two different length scales, inherent in its noncommutative counter-part, are exploited to obtain a theory of effective gravity coupled to an U(1) noncommutative gauge theory to all orders in $\Theta$. It is shown that the GRN-black hole geometry, in the Planckian regime, reduces to the GS-black hole. However in the classical regime it may be seen to govern both Reissner-Nordstrom and Schwarzschild geometries independently. The emerging notion of 2D black holes evident in the frame-work are analyzed. It is argued that the $D$-string in the theory may be described by the near horizon 2D black hole geometry, in the gravity decoupling limit. Finally, our analysis explains the nature of the effective force derived from the nonlinear EM-field and accounts for the Hawking radiation phenomenon in the formalism.