https://doi.org/10.1140/epjc/s10052-022-10929-2
Regular Article - Theoretical Physics
Lie symmetry approach to the time-dependent Karmarkar condition
1
Institute of Systems Science, Durban University of Technology, 4000, Durban, South Africa
2
Departamento de Matemáticas, Universidad Católica del Norte, Casilla 1280, Avda. Angamos 0610, Antofagasta, Chile
3
Department of Mathematics, Faculty of Applied Sciences, Durban University of Technology, 4000, Durban, South Africa
Received:
6
September
2022
Accepted:
14
October
2022
Published online:
3
November
2022
We obtain solutions of the time-dependent Einstein Field Equations which satisfy the Karmarkar condition via the method of Lie symmetries. Spherically symmetric spacetime metrics are used with metric functions set to impose conformal flatness, Weyl-free collapse and shear-free collapse. In particular, a solution was found which satisfies the heat-flux boundary condition of Santos, and a radiating stellar model was then obtained and investigated. Solutions obtained which do not allow for the application of the junction conditions at a boundary surface may lend themselves to cosmological models. This is a first attempt in generating solutions satisfying the Karmarkar condition via the method of Lie symmetries and our example of a radiating model highlights the viability of this method.
© The Author(s) 2022
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