Abstract
Einstein field equations for a static and spherically symmetric perfect fluid are considered. A formulation given by Patiño and Rago is used to obtain a class of nine solutions, two of them are Tolman solutions I, IV and the remaining seven are new. The solutions are the correct ones corresponding to expressions derived by Patiño and Rago which have been shown by Knutsen to be incorrect. Similar to Tolman solution IV each of the new solutions satisfies energy conditions inside a sphere in some range of two independent parameters. Besides, each solution could be matched to the exterior Schwarzschild solution at a boundary where the pressure vanishes and thus the solutions constitute a class of new physically reasonable stellar models.
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Haggag, S. A new class of relativistic stellar models. Astrophys Space Sci 225, 137–149 (1995). https://doi.org/10.1007/BF00657851
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DOI: https://doi.org/10.1007/BF00657851