Black Hole Geometries in Noncommutative String Theory

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.Comment: 30 pages, 2 figure

The Generalised Raychaudhuri Equations : Examples

Specific examples of the generalized Raychaudhuri Equations for the evolution of deformations along families of $D$ dimensional surfaces embedded in a background $N$ dimensional spacetime are discussed. These include string worldsheets embedded in four dimensional spacetimes and two dimensional timelike hypersurfaces in a three dimensional curved background. The issue of focussing of families of surfaces is introduced and analysed in some detail.Comment: 8 pages (Revtex, Twocolumn format). Corrected(see section on string worldsheets), reorganised and shortened slightl