Higher dimensional generalization of the Buchdahl-Vaidya-Tikekar model for a supercompact star
Annotatsiya
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, ${K}_{n}=({K}_{4}\ensuremath{-}n+4)/(n\ensuremath{-}3)$, where the subscript refers to the dimension of spacetime. Further, $K\ensuremath{\ge}0$ 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.