mathematical physics Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...

, Kundt spacetimes are

Lorentzian manifold In differential geometry, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian manifold in which the ...

s admitting a geodesic null congruence with vanishing

optical scalars In general relativity, optical scalars refer to a set of three scalar functions \ describing the propagation of a geodesic null congruence.Eric Poisson. ''A Relativist's Toolkit: The Mathematics of Black-Hole Mechanics''. Cambridge: Cambridge Univ ...

(expansion, twist and shear). A well known member of Kundt class is pp-wave.

Ricci-flat In the mathematical field of differential geometry, Ricci-flatness is a condition on the curvature of a Riemannian manifold. Ricci-flat manifolds are a special kind of Einstein manifold. In theoretical physics, Ricci-flat Lorentzian manifolds are o ...

Kundt spacetimes in arbitrary dimension are

algebraically special In differential geometry and theoretical physics, the Petrov classification (also known as Petrov–Pirani–Penrose classification) describes the possible algebraic symmetries of the Weyl tensor at each event in a Lorentzian manifold. It is mos ...

. In four dimensions Ricci-flat Kundt metrics of

Petrov type In differential geometry and theoretical physics, the Petrov classification (also known as Petrov–Pirani–Penrose classification) describes the possible algebraic symmetries of the Weyl tensor at each event in a Lorentzian manifold. It is mos ...

III and N are completely known. All

VSI spacetime In mathematical physics, vanishing scalar invariant (VSI) spacetimes are Lorentzian manifolds with all polynomial curvature invariants of all orders vanishing. Although the only Riemannian manifold with VSI property is flat space, the Lorentzian ca ...

s belong to a subset of the Kundt spacetimes..

References

Lorentzian manifolds {{math-physics-stub