Higher dimensional generalization of the Buchdahl-Vaidya-Tikekar model for a supercompact star

We obtain higher-dimensional solutions for a supercompact 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 a density gradient. It turns out that the key pressure isotropy equation continues to have the same Gauss form and, hence, four-dimensional solutions can be taken over to higher dimensions with K satisfying the relation, K-n = (K-4 - n + 4)/(n-3), where the subscript refers to the dimension of spacetime. Further, K >= 0 is required (otherwise, the density would have the undesirable feature of increasing with radius), and the equality indicates a constant density star described by the Schwarzschild interior solution. This means that, for a given K-4, the maximum dimension could only be n = K-4 + 4. Otherwise, K-n will turn negative.