We present a class of anisotropic brane configurations which shows BKL oscillations near their cosmological singularities. Near horizon limits of these solutions represent Kasner space embedded in AdS background. Dynamical probe branes in these geome
tries inherit anisotropies from the background. Amusingly, for a probe M5 brane, we find that there exists a parameter region where three of its world-volume directions expand while the rest contract.
For charged black hole, within the grand canonical ensemble, the decay rate from thermal AdS to the black hole at a fixed high temperature increases with the chemical potential. We check that this feature is well captured by a phenomenological matrix
model expected to describe its strongly coupled dual. This comparison is made by explicitly constructing the kink and bounce solutions around the de-confinement transition and evaluating the matrix model effective potential on the solutions.
We provide an explicit solution representing an anisotropic power law inflation within the framework of rolling tachyon model. This is generated by allowing a non-minimal coupling between the tachyon and the world-volume gauge field on non-BPS D3 bra
ne. We also show that this solution is perturbatively stable.
We argue that a convenient way to analyze instabilities of black holes in AdS space is via Bragg-Williams construction of a free energy function. Starting with a pedagogical review of this construction in condensed matter systems and also its impleme
ntation to Hawking-Page transition, we study instabilities associated with hairy black holes and also with the $R$-charged black holes. For the hairy black holes, an analysis of thermal quench is presented.
Assuming gauge theory realization at the boundary, we show that the viscosity to entropy ratio is 1/(4 pi) where the bulk is represented by a large class of extremal black holes in anti-de Sitter space. In particular, this class includes multiple R-charged black holes in various dimensions.
We propose an effective model of strongly coupled gauge theory at finite temperature on $R^3$ in the presence of an infrared cutoff. It is constructed by considering the theory on $S^3$ with an infrared cutoff and then taking the size of the $S^3$ to
infinity while keeping the cutoff fixed. This model reproduces various qualitative features expected from its gravity dual.
After reviewing the thermodynamics and critical phenomena associated with AdS black holes carrying multiple R-charges in various dimensions, we do a Bragg-Williams like analysis of the systems around its critical points. This leads us to propose an e
ffective potential governing the equilibrium properties of the boundary gauge theory. We also study certain non-equilibrium phenomena associated with these gauge theories. In particular, we compute the conductivities and diffusion coefficients for theories with multiple R-charges in four, three and six dimensions.
We show the existence of some bouncing cosmological solutions in the braneworld scenario. More specifically, we consider a dynamical three-brane in the background of Born-Infeld and electrically charged Gauss-Bonnet black hole. We find that, in certa
in range of parameter space, the brane universe, at least classically, never shrinks to a zero size, resulting in a singularity-free cosmology within the classical domain.
This is a continuation of our earlier work where we constructed a phenomenologically motivated effective action of the boundary gauge theory at finite temperature and finite gauge coupling on $S^3 times S^1$. In this paper, we argue that this effecti
ve action qualitatively reproduces the gauge theory representing various bulk phases of R-charged black hole with Gauss-Bonnet correction. We analyze the system both in canonical and grand canonical ensemble.
