Regular Article - Theoretical Physics
Lie group analysis of the general Karmarkar condition
Astrophysics Research Centre, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X54001, 4000, Durban, South Africa
Accepted: 16 April 2023
Published online: 27 April 2023
The Karmarkar embedding condition in different spherically symmetrical metrics is studied in general using Lie symmetries. In this study, the Lie symmetries for conformally flat and shear-free metrics are studied which extend recent results. The Lie symmetries for geodesic metrics and general spherical spacetimes are also obtained for the first time. In all cases group invariant exact solutions to the Karmarkar embedding condition are obtained via a Lie group analysis. It is further demonstrated that the Karmarkar condition can be used to produce a model with interesting features: an embeddable relativistic radiating star with a barotropic equation of state via Lie symmetries.
© The Author(s) 2023
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