Pure Lovelock Kasner metrics

Abstract

We study pure Lovelock vacuum and perfect fluid equations for Kasner-type metrics. These equations correspond to a single Nth order Lovelock term in the action in d N N 2 1, 2 2 = + + dimensions, and they capture the relevant gravitational dynamics when aproaching the big-bang singularity within the Lovelock family of theories. Pure Lovelock gravity also bears out the general feature that vacuum in the critical odd dimension, d N 2 1 = + , is kinematic, i.e. we may define an analogue Lovelock-Riemann tensor that vanishes in vacuum for d N 2 1 =