Constraints on "rare" dyon decays

We obtain the complete set of constraints on the moduli of N=4 superstring compactifications that permit "rare" marginal decays of 1/4-BPS dyons to take place. The constraints are analysed in some special cases. The analysis extends in a straightforward way to multi-particle decays. We discuss the possible relation between general multi-particle decays and multi-centred black holes.Comment: 27 page

Tri-generative Stochastic Model of Population Growth

This paper investigates the population growth of a certain species in which every generation reproduces twice. First we probe the cases of 100% regeneration. We find that the population stabilizes for all the case although the stable values are different and exhibit interesting patterns. Then we study the survival period of a species by randomizing the reproduction probabilities within a window at same predefined ages. Now the population meets three different possibilities when left over for long periods  -Dies, Stabilizes, Shoots up. We carry out a detail study for these outcomes in the parameter space defined by the reproduction probabilities.&nbsp

Effects of charge on the interior volume of BTZ black holes

In this article we extend the variational technique for maximal volume estimation of a black hole developed by Christodoulou and Rovelli (CR) to the case of a charged BTZ black hole in 2+1 dimensions. The technique involves a study of the equation of motion of a hypothetical particle moving in an auxiliary manifold defined by spacetime variables. We then compare this estimation with the volume computed using maximization method and extrinsic curvature method. The charge Q of the black hole appears as a log term in the metric and hence an analytical solution for the volume does not exist. So first we compute the steady state radius and the volume for limiting case when the charge Q is very small i.e. Q << 1 and then carry out a numerical analysis to solve for the volume for more generic values of the charge. We find that the volume grows monotonically with the advance time. We further investigate the functional behaviour of the entropy of a massless scalar field living on the maximal hypersurface of a near extremal black hole. We show that this volume entropy exhibits a very different functional form compared to the horizon entropy.Comment: 11 pages, 5 figure

Evolution of the maximal hypersurface in a D-dimensional dynamical spacetime

In this article we set up a variational problem to arrive at the equation of a maximal hypersurface inside a spherically symmetric evolving trapped region. In the first part of the article, we present the Lagrangian and the corresponding Euler Lagrange equations that maximize the interior volume of a trapped region that is formed dynamically due to infalling matter in D-dimensions, with and without the cosmological constant. We explore the properties of special points in these maximal hypersurfaces at which the Kodama vector becomes tangential to the hypersurface. These points which we call steady state points, are shown to play a crucial role in approximating the maximal interior volume of a black hole. We derive a formula to locate these points on the maximal hypersurface in terms of coordinate invariants like area radius, principle values of energy momentum tensor, Misner Sharp mass and cosmological constant. Based on this formula, we estimate the location of these steady state points in various scenarios: (a) the case of static BTZ black holes in 2+1 dimensions and for the Schwarzschild, Schwarzschild-deSitter and Schwarzschild-Anti-deSitter black holes in D-dimensions. We plot the location of the steady state points in relation to the event horizon and cosmological horizon in a static D-dimensional scenario, (b) cosmological case: we prove that these steady state points do not exist for homogeneous evolving dust for the zero and negative cosmological constant but exist in the presence of positive cosmological constant when the scale factor is greater than a critical value.Comment: 13 pages, 12 figure

Noncritical-topological correspondence: disc amplitudes and noncompact branes

We examine the duality between type 0 noncritical strings and topological B-model strings, with special emphasis on the flux dependence. The former theory is known to exhibit holomorphic factorisation upto a subtle flux-dependent disc term. We give a precise definition of the B-model dual and propose that it includes both compact and noncompact B-branes. The former give the factorised part of the free energy, while the latter violate holomorphic factorisation and contribute the desired disc term. These observations are generalised to rational radii, for which we derive a nonperturbatively exact result. We also show that our picture extends to a proposed alternative topological-anti-topological picture of the correspondence for type 0 strings