Stellar structure and accretion in gravitating systems.

Abstract

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.