Browsing by Author "John, Anslyn James."

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Spherically symmetric solutions in relativistic astrophysics.
(2002) John, Anslyn James.; Maharaj, Sunil Dutt.
In this thesis we study classes of static spherically symmetric spacetimes admitting a perfect fluid source, electromagnetic fields and anisotropic pressures. Our intention is to generate exact solutions that model the interior of dense, relativistic stars. We find a sufficient condition for the existence of series solutions to the condition of pressure isotropy for neutral isolated spheres. The existence of a series solution is demonstrated by the method of Frobenius. With the help of MATHEMATICA (Wolfram 1991) we recovered the Tolman VII model for a quadratic gravitational potential, but failed to obtain other known classes of solution. This establishes the weakness, in certain instances, of symbolic manipulation software to extract series solutions from differential equations. For a cubic potential, we obtained a new series solution to the Einstein field equations describing neutral stars. The gravitational and thermodynamic variables are non-singular and continuous. This model also satisfies the important barotropic equation of state p = p(p). Two new exact solutions to the Einstein-Maxwell system, that generalise previous results for uncharged stars, were also found. The first of these generalises the solution of Maharaj and Mkhwanazi (1996), and has well-behaved matter and curvature variables. The second solution reduces to the Durgapal and Bannerji (1983) model in the uncharged limit; this new result may only serve as a toy model for quark stars because of negative energy densities. In both examples we observe that the solutions may be expressed in terms of hypergeometric and elementary functions; this indicates the possibility of unifying isolated solutions under the hypergeometric equation. We also briefly study compact stars with spheroidal geometry, that may be charged or admit anisotropic pressure distributions. The adapted forms of the pressure isotropy condition can be written as a harmonic oscillator equation. Two simple examples are presented.
Stellar structure and accretion in gravitating systems.
(2012) John, Anslyn James.; Maharaj, Sunil Dutt.; Govinder, Keshlan Sathasiva.
In this thesis we study classes of static spherically symmetric solutions to the Einstein and Einstein–Maxwell equations that may be used to model the interior of compact stars. We also study the spherical accretion of fluids on to bodies in both general relativity and the Newtonian theory of gravity. The condition for pressure isotropy is obtained upon specifying one of the gravitational potentials and the electric field intensity. A series solution was found after specifying a cubic form for the potential. The pressure and energy density appear to be non–singular and continuous inside the star. This solution admits an explicit equation of state that, in regions close to the stellar centre, may be approximated by a polytrope. Another class of exact solutions to the Einstein–Maxwell solutions was found with charge. These solutions are in the form of hypergeometric functions with two free parameters. For particular parameter values we recovered two previously known exact solutions that are reasonable models for the interior of compact stars. We demonstrated two new solutions for other choices of the parameters. One of these has well behaved pressure, energy density and electric field intensity variables within the star. The other was rejected as unphysical on the grounds that it has a negative energy density. This violates the energy conditions. We obtained the mass accretion rate and critical radius of a polytrope accreting onto a D– dimensional Schwarzschild black hole. The accretion rate, ˙M , is an explicit function of the black hole mass, M, as well as the gas boundary conditions and the dimensionality, D, of the spacetime. We also found the asymptotic compression ratios and temperature profiles below the accretion radius and at the event horizon. This generalises the Newtonian expressions of Giddings and Mangano (2008) which examined the accretion of TeV black holes. We obtained the critical radius and accretion rates of a generalised Chaplygin gas accreting on to body under a Newtonian potential. The accretion rate is about 2 - 4 times greater than that for neutral hydrogen. The Rankine–Hugoniot relations for shocked GCG flow were also found. We found general expressions for the pressure and density compression ratios. Some post shock states imply negative volumes. We suspect that these may be thermodynamically forbidden.