Abstract
The solutions of the Einstein field equations of general relativity (GR) are prone to rendering systems which are physically non-viable as shown by Delgaty and Lake (1998). This does not detract from the success of general relativity but rather suggests the possibility for implementing new solution methods while being cautious that the resulting systems are indeed physically viable. This emphasizes the importance of applying appropriate criteria in closing the system of non-linear, coupled differential equations of GR. In the case of static systems describing massive compact bodies, an intrinsic property is the vanishing of the radial pressure at the surface boundary of the object which is embedded in an empty Schwarzschild exterior spacetime. In attempting to complete the gravitational description, we first assume a standard, physically plausible metric potential such as that of Finch and Skea. We then attempt to solve for the other metric component by imposing an ansatz which assists in extrapolating from the vanishing pressure boundary condition. Our model is guided by the physicality of the sound speed profiles and associated stability conditions.
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