New analytical stellar models in general relativity.
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Date
2009
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Abstract
We present new exact solutions to the Einstein and Einstein-Maxwell field equations that model the interior of neutral, charged and radiating stars. Several new classes of solutions in static spherically symmetric interior spacetimes are found in the presence of charge. These correspond to isotropic matter with a specified electric field intensity. Our solutions are found by choosing different rational forms for one of the gravitational potentials and a particular form for the electric field. The models generated contain results found previously including Finch and Skea (1989) neutron stars, Durgapal and Bannerji (1983) dense stars, Tikekar (1990) superdense stars in the limit of vanishing charge. Then we study the general situation of a compact relativistic object with anisotropic pressures in the presence of the electromagnetic field. We assume the equation of state is linear so that the model may be applied to strange stars with quark matter and dark energy stars. Several new classes of exact solutions are found, and we show that the densities and masses are consistent with real stars. We regain as special cases the Lobo (2006) dark energy stars, the Sharma and Maharaj (2007) strange stars and the realistic isothermal universes of Saslaw et al (1996). In addition, we consider relativistic radiating stars undergoing gravitational collapse when the fluid particles are in geodesic motion. We transform the governing equation into Bernoulli, Riccati and confluent hypergeometric equations. These admit an infinite family of solutions in terms of simple elementary functions and special functions. Particular models contain the Minkowski spacetime and the Friedmann dust spacetime as limiting cases. Finally, we model the radiating star with shear, acceleration and expansion in the presence of anisotropic pressures. We obtain several classes of new solutions in terms of arbitrary functions in temporal and radial coordinates by rewriting the junction condition in the form of a Riccati equation. A brief physical analysis indicates that these models are physically reasonable.
Description
Thesis (Ph.D.)-University of KwaZulu-Natal, Westville, 2009.
Keywords
Stars., Relativity (Physics), Einstein field equations., Theses--Mathematics.