The Lovelock gravity in the critical spacetime dimension
  It is well known that the vacuum in the Einstein gravity, which is linear in
the Riemann curvature, is trivial in the critical (2+1=3) dimension because
vacuum solution is flat. It turns out that this is true in general for any odd
critical $d=2n+1$ dimension where $n$ is the degree of homogeneous polynomial
in Riemann defining its higher order analogue whose trace is the nth order
Lovelock polynomial. This is the "curvature" for nth order pure Lovelock
gravity as the trace of its Bianchi derivative gives the corresponding analogue
of the Einstein tensor \cite{bianchi}. Thus the vacuum in the pure Lovelock
gravity is always trivial in the odd critical (2n+1) dimension which means it
is pure Lovelock flat but it is not Riemann flat unless $n=1$ and then it
describes a field of a global monopole. Further by adding Lambda we obtain the
Lovelock analogue of the BTZ black hole.
