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

An Asymptotic Preserving and Energy Stable Scheme for the Euler-Poisson System in the Quasineutral Limit

An asymptotic preserving and energy stable scheme for the Euler-Poisson system under the quasineutral scaling is designed and analysed. Correction terms are introduced in the convective fluxes and the electrostatic potential, which lead to the dissipation of mechanical energy and the entropy stability. The resolution of the semi-implicit in time finite volume in space fully-discrete scheme involves two steps: the solution of an elliptic problem for the potential and an explicit evaluation for the density and velocity. The proposed scheme possesses several physically relevant attributes, such as the the entropy stability and the consistency with the weak formulation of the continuous Euler-Poisson system. The AP property of the scheme, i.e. the boundedness of the mesh parameters with respect to the Debye length and its consistency with the quasineutral limit system, is shown. The results of numerical case studies are presented to substantiate the robustness and efficiency of the proposed method.Comment: 29 pages, research paper. arXiv admin note: text overlap with arXiv:2206.0606

ANTIDIABETIC ACTIVITY OF CLERODENDRUM PHILIPPINUM SCHAUER LEAVES IN STREPTOZOTOCIN INDUCED DIABETIC RATS

Objective: The present study has been undertaken to evaluate the antidiabetic activity of Clerodendrum philippinum Schauer leaves.Methods: The fresh leaves were collected from Kuruan village of Jajpur district in the state of Odisha, India and extracted successively with n-hexane, methanol and water. The effect of extracts at the dose level of 400 mg/kg body weight was studied in normal, glucose loaded and streptozotocin-induced diabetic rats.Results: The test extracts showed significant reduction of blood glucose level in normal, glucose loaded and streptozotocin-induced diabetic rats. Methanol extract demonstrated maximum blood glucose lowering potential as compared to other extracts.Conclusion: The leaf of Clerodendrum philippinum Schauer is endowed with blood sugar lowering potential in both normal and diabetic rats.Â