Abstract
Exploiting the use of curvature coordinates (also called Schwarzschild coordinates), new classes of exact solutions are discovered. By prescribing the timelike potential two new solutions are found one of which displays all the necessary qualitative features demanded of closed compact astrophysical objects. Since the analysis reduces to a single first order nonlinear differential equation, the single integration constant is obtained in terms of the mass and radius through matching of the interior and exterior metrics. Invoking the second matching condition results in constraining the value of the Gauss–Bonnet coupling constant in terms of the mass and radius of the star. Stability, causality and energy conditions are satisfied for a suitable choice of parameter space. In attempting to specify the radially oriented potential it was only possible to find a defective spacetime and to regain the interior Schwarzschild metric for an incompressible fluid sphere.
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