Perfect fluid filled universe in odd dimensional pure Lovelock gravity

Abstract

It is well known that d = 2 N + 1 dimensional pure Lovelock metrics do not describe bounded distributions neither do they admit nontrivial vacuum solutions. On this basis it has been variously claimed that matter fields should be nondynamical. However, from earlier work it has long been demonstrated fairly generally that 2 N + 1 pure Lovelock solutions are not kinematic. In this work we find perfect fluid filled universes with d = 2 N + 1 that exhibit curvature of spacetime. New classes of exact solutions for pure Gauss–Bonnet gravity ( N = 2 ) are generated by integrating the pressure isotropy condition with suitable metric potential choices for the critical spacetime dimension 5. Amongst the physically important cases we study are the Vaidya–Tikekar superdense star ansatz, the Finch–Skea model as well as isothermal fluids. The physical properties are analysed with the aid of graphical plots and the model is found to be causal and stable in the sense of Chandrasekhar and satisfies the energy conditions. Finally we examine the most general Lovelock polynomials for all N and d = 2 N + 1 . In particular the special case N = 3 , d = 7 has not been considered previously in the literature and we discover a number of classes of exact solutions for this case.