AR_final file_2018-19

Laxman. N. Katkar Non-static conformally flat spherically symmetric spacetimes in EinsteinCartan theory By exploiting the null tetrad formalism of Jogia and Griffiths, and the technique of differential forms on a non-Riemannian spacetime, non-static con- formally flat, Petrov-type D, spherically symmet- ric solutions of the EinsteinCartan field equations; when Weyssenhoff fluid is the source of curva- ture and spin, are obtained. In general, the solu- tion is expanding, accelerating, rotating and non- shearing. However, the dynamic solution is ex- panding and rotating with zero acceleration and shear; whereas the static solution is accelerating and rotating with expansion free and shear free “congruences”. This solution has been obbained in collaboration with D. R. Phadarate. A static spherically symmetric solution in Einstein- Cartan theory of gravitation A static spherically symmetric solution of Einstein- Cartan field equations is obtained by using the techniques of differential forms. The solution is proved to be expansion free, shear free and rotat- ing with non zero acceleration. The pressure and density have been influenced by the spin. The so- lution is algebraically special Petrov-type D. In the absence of spin, the solution reduces to the solution of Prasanna (Phys Rev D 11 :2076 1975). This so- lution has been obtained in collaboration with D. R. Phadarate. Ram Kishor Normalization of Hamiltonian and non-linear sta- bility of triangular equilibrium points in the pho- togravitational restricted three body problem with P- R drag in non-resonance case Normal forms of Hamiltonian are very important to analyze the nonlinear stability of a dynamical sys- tem in the vicinity of invariant objects. The Hamil- tonian of the system is normalized up to fourth order through Lie transform method, and then to apply the Arnold-Moser theorem, Birkhoff normal form of the Hamiltonian is computed followed by nonlinear stability of the equilibrium points is ex- amined. Similar to the case of classical problem, we have found that in the presence of assumed per- turbations, there always exists one value of mass parameter within the stability range at which the discriminant D 4 vanishes, consequently, Arnold- Moser theorem fails, which infer that triangular equilibrium points are unstable in non linear sense within the stability range. Present analysis is lim- ited up to linear effect of the perturbations, which will be helpful to study the more generalized prob- lem. This work has been done in collaboration with M. Xavir James Raj, and Bhola Ishwar. Nagendra Kumar Fluid dynamical instabilities in magnetized par- tially ionized dense dusty plasma We study fluid dynamical instabilities in magne- tized partially ionized dense dusty plasma by tak- ing into account relative flow between dust and neutral gas. We consider a magnetized partially ionized dense dusty plasmas whose dynamics are governed by dust and neutral gas components. The electrons dynamics is not considered, as the elec- trons have no significant influence on the overall be- haviour of dusty plasma. The plasma is considered quasi neutral. Following Hurwitz criterion, the on- set criteria for instabilities are derived for different densities of the neutral gas, and dust components across the interface. It is found that in case of no significant magnetic field, stabilization occurs not only due to dust neutral gas collisions but due to relative flow also. Our results might be useful in many situations of astrophysical magnetized dusty plasma namely comets and circumsteller dusty disk e.g., T-Tauri stars. This work has been done in col- laboration with Anil Kumar, and Vinod Kumar. Suresh Kumar Cosmological bounds on dark matter-photon cou- pling We investigate an extension of the CDM model, where the dark matter (DM) is coupled to pho- tons, inducing a non conservation of the numbers of particles for both species, where the DM particles are allowed to dilute throughout the cosmic history with a small deviation from the standard evolution decaying into photons, while the associated scat- tering processes are assumed to be negligible. In addition, we consider the presence of massive neu- trinos with the effective number of species N eff as a free parameter. The effects of the DM-photon cou- pling on the cosmic microwave background (CMB) and matter power spectra are analyzed. We derive ( 196 )