Black hole thermodynamics in Hor̆ava Lifshitz gravity and the related geometry
Recently, Hor̆ava proposed a non-relativistic renormalizable theory of gravity which is essentially a field theoretic model for a UV complete theory of gravity and reduces to Einstein gravity with a non-vanishing cosmological constant in IR. Also the theory admits a Lifshitz scale-invariance in time and space with broken Lorentz symmetry at short scale. On the other hand, at large distances higher derivative terms do not contribute and the theory coincides with general relativity. Subsequently, Cai and his collaborators and then Catiuo et al. have obtained black hole solutions in this gravity theory and studied the thermodynamic properties of the black hole solution. In the present paper, we have investigated the black hole thermodynamic for two choices of the entropy function—a classical and a topological in nature. Finally, it is examined whether a phase transition is possible or not.

title: Energy Conditions, Cosmological Solutions and Cosmic No-Hair Conjecture in Gauss-Bonnet Theory
abstract: A detailed investigation of Gauss-Bonnet theory has been done from a different perspective. At first, the standard energy conditions are discussed and modified forms have been presented. Then some cosmological solutions have been obtained in 5D for perfect fluid assuming that the extra dimensional metric coefficient decreases with time. For some particular choice of the parameters, exponential solutions are obtained and finally, Cosmic No-Hair Conjecture has been proved for Gauss-Bonnet dilatonic scalar coupled to Einstein gravity with coupling parameter growing linearly in time.

title: NAKED SINGULARITIES IN HIGHER DIMENSIONAL GRAVITATIONAL COLLAPSE
abstract: Spherically symmetric inhomogeneous dust collapse has been studied in higher dimensional space–time and the factors responsible for the appearance of a naked singularity are analyzed in the region close to the centre for the marginally bound case. It is clearly demonstrated that in the former case naked singularities do not appear in the space–time having more than five dimension, which appears to a strong result. The non-marginally bound collapse is also examined in five dimensions and the role of shear in developing naked singularities in this space–time is discussed in details. The five-dimensional space–time is chosen in the later case because we have exact solution in closed form only in five dimension and not in any other case.

title: Exact solutions of the field equations for Charap’s chiral invariant model of the pion dynamics
abstract: The field equations for the chiral invariant model of pion dynamics developed by Charap have been revisited. Two new types of solutions of these equations have been obtained. Each type allows infinite number of solutions. It has also been shown that the chiral invariant field equations admit invariance for a transformation of the dependent variables.

title: Emergent universe in brane world scenario with Schwarzschild–de Sitter bulk
abstract: A model of an emergent universe is obtained in brane world. Here the bulk energy is in the form of cosmological constant, while the brane consists of a fluid satisfying an equation of state of the form $${p_{b}=\frac{1}{3}\rho_{b}}$$ , which is effectively a radiation equation of state at high energies. It is shown that with the positive bulk cosmological constant, one of our models represents an emergent universe.

title: Interacting Holographic Dark Energy at the Ricci scale and Dynamical system
abstract: In this work, we consider homogeneous and isotropic FRW model of the universe, filled with interacting dark matter and dark energy. The dark matter is chosen as usual in the form of dust while dark energy is holographic in nature with IR cut off at the Ricci's length and it is in the form of a perfect fluid with variable equation of state. We have chosen the interaction term of the following two types: (i) a linear combination of the matter density of the two fluids, (ii) a product of the two matter densities. For both the choices the evolution equations are transformed to an autonomous system and the corresponding critical points are analyzed. Finally, for the first choice of the interaction term the evolution of the ratio of the energy densities has been studied from the point of view of the present coincidence problem.

title: Calculating the jet quenching parameter in the plasma of NCYM theory from gauge/gravity duality
abstract: A particular decoupling limit of the nonextremal (D1, D3) brane bound state system of type IIB string theory is known to give the gravity dual of space-space noncommutative Yang-Mills theory at finite temperature. We use a string probe in this background to compute the jet quenching parameter in a strongly coupled plasma of hot noncommutative Yang-Mills theory in ($3+1$) dimensions from gauge/gravity duality. We give expressions for the jet quenching parameter for both small and large noncommutativity. For small noncommutativity, we find that the value of the jet quenching parameter gets reduced from its commutative value. The reduction is enhanced with temperature as ${T}^{7}$ for fixed noncommutativity and fixed 't Hooft coupling. We also give an estimate of the correction due to noncommutativity at the present collider energies like in RHIC or in LHC and find it too small to be detected. We further generalize the results for noncommutative Yang-Mills theories in diverse dimensions.

title: Collective flavor oscillations of supernova neutrinos and r-process nucleosynthesis
abstract: Neutrino-neutrino interactions inside core-collapse supernovae may give rise to collective flavor oscillations resulting in swap between flavors. These oscillations depend on the initial energy spectra, and relative fluxes or relative luminosities of the neutrinos. It has been observed that departure from energy equipartition among different flavors can give rise to one or more sharp spectral swap over energy, termed as splits. We study the occurrence of splits in the neutrino and antineutrino spectra, varying the initial relative fluxes for different models of initial energy spectrum, in both normal and inverted hierarchy. These initial relative flux variations give rise to several possible split patterns whereas variation over different models of energy spectra give similar results. We explore the effect of these spectral splits on the electron fraction, Ye, that governs r-process nucleosynthesis inside supernovae. Since spectral splits modify the electron neutrino and antineutrino spectra in the region where r-process is postulated to happen, and since the pattern of spectral splits depends on the initial conditions of the spectra and the neutrino mass hierarchy, we show that the condition Ye < 0.5 required for successful r-process nucleosynthesis will lead to constraints on the initial spectral conditions, for a given neutrino mass hierarchy.

title: Turbulence patterns and neutrino flavor transitions in high-resolution supernova models
abstract: During the shock-wave propagation in a core-collapse supernova (SN), matter turbulence may affect neutrino flavor conversion probabilities. Such effects have been usually studied by adding parametrized small-scale random fluctuations (with arbitrary amplitude) on top of coarse, spherically symmetric matter density profiles. Recently, however, two-dimensional (2D) SN models have reached a space resolution high enough to directly trace anisotropic density profiles, down to scales smaller than the typical neutrino oscillation length. In this context, we analyze the statistical properties of a large set of SN matter density profiles obtained in a high-resolution 2D simulation, focusing on a post-bounce time (2 s) suited to study shock-wave effects on neutrino propagation on scales as small as O(100) km and possibly below. We clearly find the imprint of a broken (Kolmogorov-Kraichnan) power-law structure, as generically expected in 2D turbulence spectra. We then compute the flavor evolution of SN neutrinos along representative realizations of the turbulent matter density profiles, and observe no or modest damping of the neutrino crossing probabilities on their way through the shock wave. In order to check the effect of possibly unresolved fluctuations at scales below O(100) km, we also apply a randomization procedure anchored to the power spectrum calculated frommore » the simulation, and find consistent results within ± 1σ fluctuations. These results show the importance of anchoring turbulence effects on SN neutrinos to realistic, fine-grained SN models.« less

title: Wess-Zumino-Witten Model for Galilean Conformal Algebra
abstract: In this note, we construct a Wess–Zumino–Witten model based on the Galilean conformal algebra in two-spacetime dimensions, which is a nonrelativistic analogue of the relativistic conformal algebra. We obtain exact background corresponding to σ-models in six dimensions (the dimension of the group manifold) and a central charge c = 6. We carry out a Sugawara type construction to verify the conformal invariance of the model. Further, we discuss the feasibility of the background obtained as a physical spacetime metric.

title: Probing the neutrino mass hierarchy with the rise time of a supernova burst
abstract: The rise time of a Galactic supernova (SN) bar-nue lightcurve, observable at a high-statistics experiment such as the IceCube Cherenkov detector, can provide a diagnostic tool for the neutrino mass hierarchy at "large" 1-3 leptonic mixing angle theta_13. Thanks to the combination of matter suppression of collective effects at early postbounce times on one hand and the presence of the ordinary Mikheyev-Smirnov-Wolfenstein effect in the outer layers of the SN on the other hand, a sufficiently fast rise time on O(100) ms scale is indicative of an inverted mass hierarchy. We investigate results from an extensive set of stellar core-collapse simulations, providing a first exploration of the astrophysical robustness of these features. We find that for all the models analyzed (sharing the same weak interaction microphysics) the rise times for the same hierarchy are similar not only qualitatively, but also quantitatively, with the signals for the two classes of hierarchies significantly separated. We show via Monte Carlo simulations that the two cases should be distinguishable at IceCube for SNe at a typical Galactic distance 99% of the times. Finally, a preliminary survey seems to show that the faster rise time for inverted hierarchy as compared to normal hierarchy is a qualitatively robust feature predicted by several simulation groups. Since the viability of this signature ultimately depends on the quantitative assessment of theoretical/numerical uncertainties, our results motivate an extensive campaign of comparison of different code predictions at early accretion times with implementation of microphysics of comparable sophistication, including effects such like nucleon recoils in weak interactions.