In [1] we formulated and derived the three universal laws governing Near Horizon Extremal Geometries (NHEG). In this work we focus on the Entropy Perturbation Law (EPL) which, similarly to the first law of black hole thermodynamics, relates perturbations of the charges labeling perturbations around a given NHEG to the corresponding entropy perturbation. We show that field perturbations governed...

Entropy for two dimensional extremal black holes is computed explicitly in a finite-space formulation of the black hole thermodynamics and is shown to be zero locally. Our results are in conformity with the recent one by Hawking et al in four dimensions. It is known that black holes have temperature and entropy and are therefore amenable to a thermodynamic description. For an asymptotic observe...

We construct new non-extremal rotating black hole solutions in SO(6) gauged fivedimensional supergravity. Our solutions are the first such examples in which the two rotation parameters are independently specifiable, rather than being set equal. The black holes carry charges for all three of the gauge fields in the U(1) subgroup of SO(6), albeit with only one independent charge parameter. We dis...

A class of solutions to Supergravity in 10 or 11 dimensions is presented which extends the non-standard or semi-local intersections of Dp-branes to the case of non-extremal p-branes. The type of non-extremal solutions involved in the intersection is free and we provide two examples involving black-branes and/or D−D̄ systems. After a rotation among the time coordinate and a relatively transverse ...

where λ, μ > 0 are parameters and Ω is a smoothly bounded domain of R , N ≥ 1. As shown by M. Montenegro (see [6]), there exists a limiting curve Υ in the first quadrant of the (λ, μ)-plane serving as borderline for existence of classical solutions of (1). He also proved the existence of a weak solution u∗ for every (λ∗, μ∗) on the curve Υ and left open the question of its regularity. Following...

Stochastic local search algorithms are proved to be one of the most effective approach for computing approximate solutions of hard combinatorial problems. Most of them are based on a typical randomness related to some uniform distributions for generating initial solutions. Particularly, Extremal Optimization is a recent meta-heuristic proposed for finding high quality solutions to hard optimiza...

In this paper, by using a monotone iterative technique in the presence of lower and upper solutions, we discuss the existence of solutions for a new system of nonlinear mixed type implicit impulsive integro-differential equations in Banach spaces. Under wide monotonicity conditions and the noncompactness measure conditions, we also obtain the existence of extremal solutions and a unique solutio...

the present note is devoted to establish some extremal results for the zeroth-order general randi'{c} index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.

The present note is devoted to establish some extremal results for the zeroth-order general Randi'{c} index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.

We investigate the existence of Taub-NUT/bolt solutions in Gauss-Bonnet gravity and obtain the general form of these solutions in d dimensions. We find that for all nonextremal NUT solutions of Einstein gravity having no curvature singularity at r = N , there exist NUT solutions in Gauss-Bonnet gravity that contain these solutions in the limit that the Gauss-Bonnet parameter α goes to zero. Fur...