Eur. Phys. J. Plus (2021) 136: 331
https://doi.org/10.1140/epjp/s13360-021-01324-z

Regular Article

New exact even-dimensional pure Lovelock interior metrics

Astrophysics Research Centre, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X54001, 4000, Durban, South Africa

^a hansrajs@ukzn.ac.za

Received: 14 December 2020
Accepted: 13 March 2021
Published online: 22 March 2021

Abstract

While it is well known that Nth-order pure Lovelock spacetimes of dimension $d=2N+1$ do not admit bounded compact objects, this is not the case for the $d=2N+2$ case. In the $N=2$, pure Gauss–Bonnet gravity exact models for the Vaidya–Tikekar superdense star ansatz are investigated and new classes of metrics are discovered in terms of elementary functions. An astrophysical model of a stellar distribution that is consistent with the physical expectations extrapolated from four-dimensional gravity is exhibited. The isothermal sphere is re-considered and found to be inconsistent in pure Lovelock theory. Finally, we briefly consider the case of the third-order Lovelock polynomial term and several classes of exact solutions emerge.