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Doctoral Degrees (Applied Mathematics)

Permanent URI for this collectionhttps://hdl.handle.net/10413/7094

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Browsing Doctoral Degrees (Applied Mathematics) by Author "Brassel, Byron Perry."

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    Dynamics of radiating stars in the strong gravity regime.
    (2017) Brassel, Byron Perry.; Maharaj, Sunil Dutt.; Goswami, Rituparno.
    We model the dynamics of a spherically symmetric radiating dynamical star, emitting outgoing null radiation, with three spacetime regions. The local internal atmosphere is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the Schwarzschild exterior. A large family of solutions to the field equations are presented for various realistic equations of state. A comparison of our solutions with earlier well known results is undertaken and we show that all these solutions, including those of Husain, are contained in our family. We then generalise our class of solutions to higher dimensions and consider the effects of diffusive transport We also study the gravitational collapse in the context of the cosmic censorship conjecture. We outline the general mathematical framework to study the conditions on the mass function so that future directed nonspacelike geodesics can terminate at the singularity in the past. Mass functions for several equations of state are analysed using this framework and it is shown that the collapse in each case terminates at a locally naked central singularity. These singularities are strong curvature singularities which implies that no extension of spacetime through them is possible. These results are then extended to modified gravity. We establish the result that the standard Boulware-Deser spacetime can radiate. This allows us to model the dynamics of a spherically symmetric radiating dynamical star in ve-dimensional Einstein-Gauss-Bonnet gravity with three spacetime regions. Finally, the junction conditions are derived entirely in five dimensional Einstein-Gauss-Bonnet gravity via the matching of two spacetime region leading to a model for a radiating star in higher order gravity.