A group theoretic approach to shear-free radiating stars

Abstract

A systematic analysis of the junction condition, relating the radial pressure with the heat flow in a shearfree relativistic radiating star, is undertaken. This is a highly nonlinear partial differential equation in general. We obtain the Lie point symmetries that leave the boundary condition invariant. Using a linear combination of the symmetries, we transform the junction condition into ordinary differential equations. We present several new exact solutions to the junction condition. In each case we can identify the exact solution with a Lie point generator. Some of the solutions obtained satisfy the linear barotropic equation of state. As a special case we regain the conformally flat models which were found previously. Our analysis highlights the interplay between Lie algebras, nonlinear differential equations and application to relativistic astrophysics.

Charged radiating stars with Lie symmetries

“…Recently Abebe et al [28] considered the junction condition of an accelerating, expanding and shearing stellar in the absence of charge. Note that a comprehensive analysis of shear-free stellar models has been made by Abebe et al [29] with the help of Lie point symmetries. Other recent treatments with shearing matter utilizing the Lie method include the works of Mohanlal et al [30], and also [31].…”

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

“…Another approach to the junction equation uses its Lie point symmetries and provides different classes of solutions. This procedure was applied to perfect fluid models [14] and to models with anisotropic pressures [15].…”

Radiating stars with exponential Lie symmetries

“…It should be noted that the shear-free solution (40) appears to be new. It is not contained in the family of solutions found by Abebe et al [21] as in their model a 3 = 0 in (10) with only two infinitesimal generators. In our case a 3 = 0 and there are three generators.…”

“…Hence this is an example of a radiating star which is shear-free with a barotropic equation of state. Note that this example is not contained in the shear-free models of Abebe et al [21] as the infinitesimal Lie generator (10) …”