Pp-wave Spacetime - Physical Interpretation

Physical Interpretation

It is a purely mathematical fact that the characteristic polynomial of the Einstein tensor of any pp-wave spacetime vanishes identically. Equivalently, we can find a Newman-Penrose complex null tetrad such that the Ricci-NP scalars (describing any matter or nongravitational fields which may be present in a spacetime) and the Weyl-NP scalars (describing any gravitational field which may be present) each have only one nonvanishing component. Specifically, with respect to the NP tetrad

the only nonvanishing component of the Ricci spinor is

and the only nonvanishing component of the Weyl spinor is

This means that any pp-wave spacetime can be interpreted, in the context of general relativity, as a null dust solution. Also, the Weyl tensor always has Petrov type N as may be verified by using the Bel criteria.

In other words, pp-waves model various kinds of classical and massless radiation traveling at the local speed of light. This radiation can be gravitational, electromagnetic, some hypothetical kind of massless radiation other than these two, or any combination of these. All this radiation is traveling in the same direction, and the null vector plays the role of a wave vector.