Trajectory around a spherically symmetric non- rotating black hole
The trajectory of a test particle or a photon around a general spherical black hole is studied, and bending of the light trajectory is investigated. A pseudo-Newtonian gravitational potential describing the gravitational field of the black hole is determined and is compared with the related effective potential for test particle motion. As an example, results are presented for a Reissner-Nordstrom black hole.

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: 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: 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: 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: The mass-hierarchy and CP-violation discovery reach of the LBNO long-baseline neutrino experiment
abstract: A bstractThe next generation neutrino observatory proposed by the LBNO collaboration will address fundamental questions in particle and astroparticle physics. The experiment consists of a far detector, in its first stage a 20 kt LAr double phase TPC and a magnetised iron calorimeter, situated at 2300 km from CERN and a near detector based on a highpressure argon gas TPC. The long baseline provides a unique opportunity to study neutrino flavour oscillations over their 1st and 2nd oscillation maxima exploring the L/E behaviour, and distinguishing effects arising from δCP and matter.In this paper we have reevaluated the physics potential of this setup for determining the mass hierarchy (MH) and discovering CP-violation (CPV), using a conventional neutrino beam from the CERN SPS with a power of 750 kW. We use conservative assumptions on the knowledge of oscillation parameter priors and systematic uncertainties. The impact of each systematic error and the precision of oscillation prior is shown. We demonstrate that the first stage of LBNO can determine unambiguously the MH to > 5σ C.L. over the whole phase space. We show that the statistical treatment of the experiment is of very high importance, resulting in the conclusion that LBNO has ~ 100% probability to determine the MH in at most 4-5 years of running. Since the knowledge of MH is indispensable to extract δCP from the data, the first LBNO phase can convincingly give evidence for CPV on the 3σ C.L. using today’s knowledge on oscillation parameters and realistic assumptions on the systematic uncertainties.

title: Observing supernova neutrino light curve in future dark matter detectors
abstract: The possibility of observing supernova (SN) neutrinos through the process of coherent elastic neutrino-nucleus scattering (CENNS) in future ton scale detectors designed primarily for direct detection of dark matter is investigated. In particular, we focus on the possibility of distinguishing the various phases of the SN neutrino emission. The neutrino emission rates from the recent long term Basel/Darmstadt simulations are used to calculate the expected event rates. The recent state-of-the-art SN simulations predict closer fluxes among different neutrino flavors and lower average energies compared to the earlier simulation models. We find that our estimated total event rates are typically a factor of two lower than those predicted using older simulation models. We further find that, with optimistic assumptions on the detector's time resolution (~ 10 ms) and energy threshold (~ 0.1 keV), the neutrinos associated with the accretion phase of the SN can in principle be demarcated out with, for example, a 10-ton Xe detector, although distinguishing the neutrinos associated with the neutronization burst phase of the explosion would typically require several tens of ton detectors. We also comment on the possibility of studying the properties of non-electron flavor neutrinos from the CENNS of SN neutrinos.

title: Wilson loops in noncommutative Yang–Mills theory using gauge/gravity duality
abstract: By using the gauge/gravity duality and the Maldacena prescription we compute the expectation values of the Wilson loops in hot, noncommutative Yang–Mills (NCYM) theory in ( 3 + 1 ) dimensions. We consider both the time-like and the light-like Wilson loops. The gravity dual background is given by a particular decoupling limit of non-extremal (D1, D3) bound state of type IIB string theory. We obtain the velocity dependent quark–antiquark potential and numerically study how the dipole length and the potential change with velocity (for 0 v 1 , i.e., the Wilson loop is time-like) of the dipole as well as noncommutativity. We discuss and compare the results with the known commutative results. We also obtain an analytic expression for the screening length when the rapidity is large and the noncommutativity parameter is small with the product remaining small. When v → 1 , the time-like Wilson loop becomes light-like and in that case we obtain the form of the jet quenching parameter for the strongly coupled noncommutative Yang–Mills plasma which matches with our earlier results obtained using different approach.

title: The effect of collective flavor oscillations on the diffuse supernova neutrino background
abstract: Collective flavor oscillations driven by neutrino-neutrino interactions inside core-collapse supernovae have now been shown to drastically alter the resultant neutrino fluxes. This would in turn significantly affect the diffuse supernova neutrino background (DSNB), created by all core-collapse supernovae that have exploded in the past. In view of these collective effects, we re-analyze the potential for detecting the DSNB in currently running and planned large scale detectors meant for detecting both {nu}-bar{sub e} and . We find that the event rate can be different from previous estimates by up to 50%, depending on the value of {theta}{sub 13}. The next generation detectors should be able to observe DSNB fluxes. Under certain conducive conditions, one could learn about neutrino parameters. For instance, it might be possible to determine the neutrino mass hierarchy, even if

title: An eigenvalue problem in two dimensions for an irregular boundary
abstract: An analytical perturbative method is suggested for solving the Helmholtz equation (∇2 + k2)ψ = 0 in two dimensions where ψ vanishes on an irregular closed curve. We can thus find the energy levels of a quantum mechanical particle confined in an infinitely deep potential well in two dimensions having an irregular boundary or the vibration frequencies of a membrane whose edge is an irregular closed curve. The method is tested by calculating the energy levels for an elliptical and a supercircular boundary and comparing with the results obtained numerically. Further, the phenomenon of level crossing due to shape variation is also discussed.