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Applied Mathematics

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Browsing Applied Mathematics by Subject "Anisotropy."

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    New class of LRS spacetimes with simultaneous rotation and spatial twist.
    (2016) Singh, Sayuri.; Goswami, Rituparno.; Maharaj, Sunil Dutt.
    In this thesis we study Locally Rotationally Symmetric (LRS) spacetimes in which there exists a unique preferred spatial direction at each point. The conventional 1+3 decomposition of spacetime is extended to a 1+1+2 decomposition which is a natural setting in LRS models. We establish the existence and find the necessary and sufficient conditions for a new class of solutions of LRS spacetimes that have non-vanishing rotation and spatial twist simultaneously. In this study there are three key questions. By relaxing the condition of a perfect fluid, that is by introducing pressure anisotropy and heat flux, is it possible to have dynamical solutions with non-zero rotation and non-zero twist? If yes, can these solutions be physical? What are the local geometrical properties of such solutions? We investigate these questions in detail by using the semi-tetrad 1+1+2 covariant formalism. It is transparently shown that the existence of such solutions demand non-vanishing and bounded heat flux and these solutions are self-similar. We provide a brief algorithm indicating how to solve the system of field equations with the given Cauchy data on an initial spacelike Cauchy surface. We indicate that these solutions can be used as a first approximation from spherical symmetry to study rotating, inhomogeneous, dynamic and radiating astrophysical stars.
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    Thermal evolution of radiation spheres undergoing dissipative gravitational collapse.
    (2014) Reddy, Kevin Poobalan.; Govender, Megandren.; Maharaj, Sunil Dutt.
    In this study we investigate the physics of a relativistic radiating star undergoing dissipative collapse in the form of a radial heat flux. Our treatment clearly demonstrates how the presence of shear affects the collapse process; we are in a position to contrast the physical features of the collapsing sphere in the presence of shear with the shear-free case. We first consider a particular exact solution found by Thirukkanesh et al [1] which is expanding, accelerating and shearing. By employing a causal heat transport equation of the Maxwell-Cattaneo form we show that the shear leads to an enhancement of the core stellar temperature thus emphasizing that relaxational effects cannot be ignored when the star leaves hydrostatic equilibrium. We also employ a perturbative scheme to study the evolution of a spherically symmetric stellar body undergoing gravitational collapse. The Bowers and Liang [2] static model is perturbed, and its subsequent dynamical collapse is studied in the linear perturbative regime. We find that anisotropic effects brought about by the differences in the radial and tangential pressures enhance the perturbations to the temperature, and that causal and non–causal cases yield identical profiles.