  Universal spacetimes are spacetimes for which all conserved symmetric rank-2
tensors, constructed as contractions of polynomials from the metric, the
Riemann tensor and its covariant derivatives of arbitrary order, are multiples
of the metric. Consequently, metrics of universal spacetimes solve vacuum
equations of all gravitational theories with Lagrangian being a polynomial
curvature invariant constructed from the metric, the Riemann tensor and its
derivatives of arbitrary order. In the literature, universal metrics are also
discussed as metrics with vanishing quantum corrections and as classical
solutions to string theory. Widely known examples of universal metrics are
certain Ricci-flat pp waves.
  In this paper, we start a general study of geometric properties of universal
metrics in arbitrary dimension and we arrive at a broader class of such
metrics. In contrast with pp waves, these universal metrics also admit
non-vanishing cosmological constant and in general do not have to possess a
covariantly constant or recurrent null vector field. First, we show that a
universal spacetime is necessarily a CSI spacetime, i.e. all curvature
invariants constructed from the Riemann tensor and its derivatives are
constant. Then we focus on type N spacetimes, where we arrive at a simple
necessary and sufficient condition: a type N spacetime is universal if and only
if it is an Einstein Kundt spacetime. A class of type III Kundt universal
metrics is also found. Several explicit examples of universal metrics are
presented.
