Abstract
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, , 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 satisfying the relation, , where the subscript refers to the dimension of spacetime. Further, 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 , the maximum dimension could only be . Otherwise, will turn negative.
- Received 29 March 2016
DOI:https://doi.org/10.1103/PhysRevD.94.064065
© 2016 American Physical Society