Pure Lovelock Kasner metrics

Understand

We study pure Lovelock vacuum and perfect fluid equations for Kasner-type metrics.

• These equations correspond to a single $N$th order Lovelock term in the action in $d=2N+1,\,2N+2$ 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, $d=2N+1$, is kinematic; i.e.
• we may define an analogue Lovelock-Riemann tensor that vanishes in vacuum for $d=2N+1$, yet the Riemann curvature is non-zero.