We present a new family of spherically symmetric, static solutions of the Einstein field equations in isotropic, comoving coordinates. The radial pressure at each interior point of these models vanishes yet equilibrium is still possible. The constant density Florides solution which describes the gravitational field inside an Einstein cluster is obtained as a special case of our solution-generating method. We show that our solutions can be utilized to model strange star candidates such as Her. X-1, SAX J1808.4-3658(SS2), SAX J1808.4-3658(SS1) and PSR J1614-2230.
In this paper, we investigate the effect of anisotropic stresses (radial and tangential pressures being unequal) for a collapsing fluid sphere dissipating energy in the form of radial flux. The collapse starts from an initial static sphere described by the Bowers and Liang solution and proceeds until the time of formation of the horizon. We find that the surface redshift increases as the stellar fluid moves away from isotropy. We explicitly show that the formation of the horizon is delayed in the presence of anisotropy. The evolution of the temperature profiles is investigated by employing a causal heat transport equation of the Maxwell–Cattaneo form. Both the Eckart and causal temperatures are enhanced by anisotropy at each interior point of the stellar configuration.
We investigate the role of symmetries for charged perfect fluids by assuming that spacetime admits a conformal Killing vector. The existence of a conformal symmetry places restrictions on the model. It is possible to find a general relationship for the Lie derivative of the electromagnetic field along the integral curves of the conformal vector. The electromagnetic field is mapped conformally under particular conditions. The Maxwell equations place restrictions on the form of the proper charge density.
We investigate the propagation equations for the expansion, vorticity and shear for perfect fluid space-times which are geodesic. It is assumed that space-time admits a conformal Killing vector which is inheriting so that fluid flow lines are mapped conformally. Simple constraints on the electric and magnetic parts of the Weyl tensor are found for conformal symmetry. For homothetic vectors the vorticity and shear are free; they vanish for nonhomothetic vectors. We prove a conjecture for conformal symmetries in the special case of inheriting geodesic flows: there exist no proper conformal Killing vectors ( ¼ ) for perfect fluids except for Robertson-Walker space-times. For a nonhomothetic vector field the propagation of the quantity ÐÒ´Ê Ù Ù µ along the integral curves of the symmetry vector is homogeneous.
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