Mixed potentials in radiative stellar collapse

Abstract

We study the behaviour of a radiating star when the interior expanding, shearing fluid particles are traveling in geodesic motion. We demonstrate that it is possible to obtain new classes of exact solutions in terms of elementary functions without assuming a separable form for the gravitational potentials or initially fixing the temporal evolution of the model unlike earlier treatments. A systematic approach enables us to write the junction condition as a Riccati equation which under particular conditions may be transformed into a separable equation. New classes of solutions are generated which allow for mixed spatial and temporal dependence in the metric functions. We regain particular models found previously from our general classes of solutions.Comment: 10 pages, To appear in J. Math. Phy

All solutions for geodesic anisotropic spherical collapse with shear and heat radiation

“…It and the following equations hold on the surface. This equation coincides with Eq (9) from (Thirukkanesh and Maharaj 2010) and determines the evolution of a radiating geodesic and anisotropic star with shear. It is a highly nonlinear differential equation in partial derivatives.…”

“…where the formula for l has been taken from (Thirukkanesh and Maharaj 2010). Similar formula holds for D.…”

“…In Sect. 3, modifying the method of (Thirukkanesh and Maharaj 2010), the junction equation is written as a Riccati equation for the horizon function with simple coefficients. This allows to derive all geodesic solutions from two generating functions.…”

A different approach to anisotropic spherical collapse with shear and heat radiation

“…The previous solution is regained when certain parameters are set to zero. Later, more general exact solutions, depending on arbitrary functions of the coordinate radius, were given [18]. They encompass the previous solutions.…”

“…Now it is possible to measure the heat flow q from Eq (23) and the energy density µ. Then the two luminosities and the temperature on the star surface are given by Eqs (18,19,20). The two pressures are found from the Einstein equations (5,6).…”