A group theoretic approach to shear-free radiating stars

The European Physical Journal C

G. Z. Abebe¹  S. D. Maharaj¹  K. S. Govinder¹ 

[1] Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag 54001, 4000, Durban, South Africa;

关键词: Master Equation;    Junction Condition;    Anisotropic Pressure;    Relativistic Astrophysics;    Conformal Flatness;   

DOI  :  10.1140/epjc/s10052-015-3722-0

来源: Springer

【 摘 要 】

A systematic analysis of the junction condition, relating the radial pressure with the heat flow in a shear-free 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.

【 授权许可】

CC BY