In mathematical physics

Mathematical physics

Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...

, VSI spacetimes are Lorentzian manifolds with all polynomial curvature invariant

Curvature invariant

In Riemannian geometry and pseudo-Riemannian geometry, curvature invariants are scalar quantities constructed from tensors that represent curvature...

s of all orders vanishing. An example with this property in four dimensions is a pp-wave

Pp-wave spacetime

In general relativity, the pp-wave spacetimes, or pp-waves for short, are an important family of exact solutions of Einstein's field equation. These solutions model radiation moving at the speed of light...

. VSI spacetimes however also contain some other four-dimensional Kundt spacetime

Kundt spacetime

In mathematical physics, Kundt spacetimes are Lorentzian manifolds admitting a geodesic null congruence with vanishing optical scalars . A well known member of Kundt class is pp-wave. Ricci-flat Kundt spacetimes in arbitrary dimension are algebraically special. In four dimensions Ricci-flat ...

s of Petrov type N and III. VSI spacetimes in higher dimensions have similar properties as in the four-dimensional case.

The only Riemannian manifold

Riemannian manifold

In Riemannian geometry and the differential geometry of surfaces, a Riemannian manifold or Riemannian space is a real differentiable manifold M in which each tangent space is equipped with an inner product g, a Riemannian metric, which varies smoothly from point to point...

with VSI property is flat space.