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

Abstract

We introduce a physically important object, called the horizon function, in the study of geodesic collapse. It is closely related to the stellar characteristics and satisfies a simple Riccati equation. This equation is integrated and all of its solutions are found in terms of some generating function. Previous solutions are regained and further investigated.

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

“…Eq (34) has already been found [20] from the equation for the Z function [18]. Eq (31) transforms intoḊ…”

“…This results in generalized traveling waves and self-similar solutions. Finally, all solutions of the equation were found with the help of two generating functions, based on the approach discussed in the present paper [20]. All previous solutions were obtained by choosing the generating functions in a proper way.…”

Riccati equations for bounded radiating systems

“…Equation (8) has been integrated for geodesic motion by Ivanov [14], and in particular cases with nongeodesic motion and shear in [13].…”

“…It should be noted that (14) can be transformed into an equation with constant coefficients by making use of the change of independent variable y = log(C(t)).…”

Properties of expansion-free dynamical stars

“…Models of radiating stars in general relativity are important to describe astrophysical processes and to study gravitational collapse. Some recent examples of exact models which are physically reasonable were obtained by Tewari and Charan [1], Tewari [2], and Ivanov [3][4][5]. Anisotrophy and dissipative effects have been shown to influence the collapse rate and temperature profiles in radiating stars by Reddy et al [6].…”