New exact even-dimensional pure Lovelock interior metrics

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.