Higher dimensional generalization of Buchdahl-Vaidya-Tikekar model for super compact star

Abstract

We obtain higher dimensional solutions for super compact star for the Buchdahl-Vaidya-Tikekar metric ansatz. In particular, Vaidya and Tikekar characterized the $3$-geometry by a parameter, $K$ which is related to the sign of density gradient. It turns out that the key pressure isotropy equation continues to have the same Gauss form, and hence $4$-dimensional solutions can be taken over to higher dimensions with $K$ satisfying the relation, $K_n=(K_4-n+4)/(n-3)$ where subscript refers to dimension of spacetime. Further $K\ge 0$ is required else density would have undesirable feature of increasing with radius, and the equality indicates a constant density star described by the Schwarzschild interior solution. This means for a given $K_4$, maximum dimension could only be $n=K_4+4$, else $K_n$ will turn negative.

13 pages, 6 figures

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Cited by in corpus (5)

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• Relativistic charged spheres: Compact stars, compactness and stable configurations
• Revisiting Vaidya-Tikekar stellar model in the linear regime
• An electromagnetic extension of the Schwarzschild interior solution and the corresponding Buchdahl limit