Integrability and Symmetry Algebra Associated with N=2 KP Flows

We show the complete integrability of N=2 nonstandard KP flows establishing the biHamiltonian structures. One of Hamiltonian structures is shown to be isomorphic to the nonlinear N=2 $\hat W_{\infty}$ algebra with the bosonic sector having $\hat W_{1+\infty}\oplus \hat W_{\infty}$ structure. A consistent free field representation of the super conformal algebra is obtained. The bosonic generators are found to be an admixture of free fermions and free complex bosons, unlike the linear one. The fermionic generators become exponential in free fields, in general.Comment: Latex file, 38 pages, no figure

Axially symmetric, asymptotically flat vacuum metric with a naked singularity and closed timelike curves

We present an axially symmetric, asymptotically flat empty space solution of the Einstein field equations containing a naked singularity. The spacetime is regular everywhere except on the symmetry axis where it possess a true curvature singularity. The spacetime is of type D in the Petrov classification scheme and is locally isometric to the metrics of case IV in the Kinnersley classification of type D vacuum metrics. Additionally, the spacetime also shows the evolution of closed timelike curves (CTCs) from an initial hypersurface free from CTCs.Comment: 8 pages, no figure

Generalized form of exponential wormhole metric

In this work we have formulated a general exponential wormhole metric. Here initially we have considered a exponential wormhole metric in which the temporal component is an exponential function of $r$ but the spatial components of the metrics are fixed as a particular function $e^{\frac{2m}{r}+2\alpha r}$. Following that, we have constructed a generalised exponential wormhole metric in which the spatial component is an exponential function of $r$ but the temporal component is fixed as a particular function given by $e^{-\frac{2m}{r}-2\alpha r}$. Finally we have considered exponential metric in which both the temporal and spatial components are generalised exponential function of $r$. We have also studied some of their properties including throat radius, energy conditions, the metric in curvature coordinates, effective refractive index, ISCO and photon sphere, Regge-Wheeler potential and determined the curvature tensor. The radius of the throat is found to be consistent with the properties of wormholes, which are given by $r=m$, $r = \frac{-1+\sqrt{1+4\alpha m}}{2\alpha}$, $r=\frac{-1+\sqrt{1+8\alpha m}}{4\alpha}$...etc. Most interestingly, their throat radius is same for the same spatial component and the same range of values of $m$. In addition to these they also violate Null Energy Condition(NEC) near the throat

Study of exponential wormhole metric in f(R)f(R) gravity

In this work, we have studied an "exponential form" of spacetime metric: \begin{equation*} ds^2 = -e^{-\frac{2m}{r}}dt^2 +e^{\frac{2m}{r}}dr^2 + e^{\frac{2m}{r}}[r^2 d\theta^2 + r^2 \sin^2\theta d\phi^2] \end{equation*} in some of the viable $f(R)$ gravity models, viz. exponential gravity model, Starobinsky gravity model, Tsujikawa model and Gogoi-Goswami f(R) gravity model. Here we have calculated the parameters including energy density, tangential and radial pressure for these corresponding models of $f(R)$ gravity. Subsequently we have investigated the energy conditions viz. null energy condition(NEC), weak energy condition(WEC) and strong energy condition(SEC) for the considered models. We have also explained the suitable conditions of energy for these models by related plots

Axial symmetry cosmological constant vacuum solution of field equations with a curvature singularity, closed time-like curves and deviation of geodesics

In this paper, we present a type D, non-vanishing cosmological constant, vacuum solution of the Einstein's field equations, extension of an axially symmetric, asymptotically flat vacuum metric with a curvature singularity. The space-time admits closed time-like curves (CTCs) that appear after a certain instant of time from an initial spacelike hypersurface, indicating it represents a time-machine space-time. We wish to discuss the physical properties and show that this solution can be interpreted as gravitational waves of Coulomb-type propagate on anti-de Sitter space backgrounds. Our treatment focuses on the analysis of the equation of geodesic deviation.Comment: 17 pages, accepted for publication in Adv. High Energy Physics journa

Constructing a Supersymmetric Integrable System from the Hirota Method in Superspace

An N=1 supersymmetric system is constructed and its integrability is shown by obtaining three soliton solutions for it using the supersymmetric version of Hirota's direct method.Comment: 10 pages, no figure