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arXiv · 2209.07054

Lie symmetry approach to the time-dependent Karmarkar condition

Andronikos Paliathanasis·Robert S. Bogadi·Megandhren Govender
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Abstract

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.

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Andronikos Paliathanasis, Robert S. Bogadi, Megandhren Govender. 2022-09-15. Lie symmetry approach to the time-dependent Karmarkar condition. https://doi.org/10.1140/epjc/s10052-022-10929-2

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