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, Kn=(K4−n+4)/(n−3) where subscript refers to dimension of spacetime. Further K≥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 K4, maximum dimension could only be n=K4+4, else Kn will turn negative.
@article{arxiv.1603.07118,
title = {Higher dimensional generalization of Buchdahl-Vaidya-Tikekar model for super compact star},
author = {Avas Khugaev and Naresh Dadhich and Alfred Molina},
journal= {arXiv preprint arXiv:1603.07118},
year = {2016}
}