We consider the general situation of a compact relativistic body with anisotropic pressures in the presence of the electromagnetic field. The equation of state for the matter distribution is linear and may be applied to strange stars with quark matter. Three classes of new exact solutions are found to the Einstein-Maxwell system. This is achieved by specifying a particular form for one of the gravitational potentials and the electric field intensity. We can regain anisotropic and isotropic models from our general class of solution. A physical analysis indicates that the charged solutions describe realistic compact spheres with anisotropic matter distribution. The equation of state is consistent with dark energy stars and charged quark matter distributions. The masses and central densities correspond to realistic stellar objects in the general case when anisotropy and charge are present.
We investigate the behaviour of a relativistic spherically symmetric
radiative star with an accelerating, expanding and shearing interior matter
distribution in the presence of anisotropic pressures. The junction condition
can be written in standard form in three cases: linear, Bernoulli and Riccati
equations. We can integrate the boundary condition in each case and three
classes of new solutions are generated. For particular choices of the metric we
investigate the physical properties and consider the limiting behaviour for
large values of time. The causal temperature can also be found explicitly.Comment: 16 pages, To appear in J. Math. Phy
We study the gravitational behaviour of a spherically symmetric radiating
star when the fluid particles are in geodesic motion. We transform the
governing equation into a simpler form which allows for a general analytic
treatment. We find that Bernoulli, Riccati and confluent hypergeometric
equations are possible. These admit solutions in terms of elementary functions
and special functions. Particular models contain the Minkowski spacetime and
the Friedmann dust spacetime as limiting cases. Our infinite family of
solutions contains specific models found previously. For a particular metric we
briefly investigate the physical features, derive the temperature profiles and
plot the behaviour of the casual and acasual temperatures.Comment: 15 pages, to appear in J. Math. Phy
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