Buchdahl–Vaidya–Tikekar model for stellar interior in pure Lovelock gravity

Abstract

In the paper (Khugaev et al. in Phys Rev D94:064065. arXiv: 1603.07118, 2016), we have shown that for perfect fluid spheres the pressure isotropy equation for Buchdahl–Vaidya–Tikekar metric ansatz continues to have the same Gauss form in higher dimensions, and hence higher dimensional solutions could be obtained by redefining the space geometry characterizing Vaidya–Tikekar parameter K. In this paper we extend this analysis to pure Lovelock gravity; i.e. a $(2N+2)$-dimensional solution with a given $K_{2N+2}$ can be taken over to higher n-dimensional pure Lovelock solution with $K_n=(K_{2N+2}-n+2N+2)/(n-2N-1)$ where N is degree of Lovelock action. This ansatz includes the uniform density Schwarzshild and the Finch–Skea models, and it is interesting that the two define the two ends of compactness, the former being the densest and while the latter rarest. All other models with this ansatz lie in between these two limiting distributions.