Stellar structure and accretion in gravitating systems.
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Date
2012
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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.
Description
Thesis (Ph.D.)-University of KwaZulu-Natal, Westville, 2012.
Keywords
Unified field theories., Gravitation., Theses--Mathematics.