General Relativity and Gravitation

, Volume 43, Issue 6, pp 1685–1696

New shear-free relativistic models with heat flow

Research Article

DOI: 10.1007/s10714-011-1150-5

Cite this article as:
Msomi, A.M., Govinder, K.S. & Maharaj, S.D. Gen Relativ Gravit (2011) 43: 1685. doi:10.1007/s10714-011-1150-5


We study shear-free spherically symmetric relativistic models with heat flow. Our analysis is based on Lie’s theory of extended groups applied to the governing field equations. In particular, we generate a five-parameter family of transformations which enables us to map existing solutions to new solutions. All known solutions of Einstein equations with heat flow can therefore produce infinite families of new solutions. In addition, we provide two new classes of solutions utilising the Lie infinitesimal generators. These solutions generate an infinite class of solutions given any one of the two unknown metric functions.


Gravitating fluidsExact solutionsLie symmetries

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • A. M. Msomi
    • 1
    • 2
  • K. S. Govinder
    • 1
  • S. D. Maharaj
    • 1
  1. 1.Astrophysics and Cosmology Research Unit, School of Mathematical SciencesUniversity of KwaZulu-NatalDurbanSouth Africa
  2. 2.Department of Mathematical SciencesMangosuthu University of TechnologyJacobsSouth Africa