Regular Article - Theoretical Physics
Stellar modelling of isotropic Einstein–Maxwell perfect fluid spheres of embedding class one
Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X54001, Durban, 4000, South Africa
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Accepted: 21 May 2020
Published online: 3 June 2020
It is indeed remarkable that while charged anisotropic models with the embedding class one property are abundant, there are no reports of the physically important isotropic case despite its simplicity. In fact, the Karmarkar condition turns out to be the only avenue to generate all such stellar models algorithmically. The process of determining exact solutions is almost trivial: either specify the spatial potential and perform a single integration to obtain the temporal potential or simply select any temporal potential and get the space potential without any integrations. Then the model is completely determined and all dynamical quantities may be calculated. The difficulty lies in ascertaining whether such models satisfy elementary physical requisites. A number of physically relevant models are considered though not exhaustively. We prove that conformally flat charged isotropic stars of embedding class one do not exist. If spacetime admits conformal symmetries then the space potential must be of the Finch–Skea type in this context. A general metric ansatz is stated which contains interesting special cases. The Finch–Skea special case is shown to be consistent with the expectations of a stellar model while the Vaidya–Tikekar special case generates a physically viable cosmological fluid. The case of an isothermal sphere with charge and the Karmarkar property is examined and is shown to be defective. When the Karmarkar property is abandoned for isothermal charged fluids, the spacetimes are necessarily flat.
© The Author(s), 2020