Editing Pp-wave spacetime (section)

==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 formalism|Newman–Penrose complex null tetrad]] such that the [[Newman–Penrose formalism#Weyl-NP and Ricci-NP scalars|Ricci-NP scalars]] <math>\Phi_{ij}</math> (describing any matter or nongravitational fields which may be present in a spacetime) and the [[Newman–Penrose formalism#Weyl-NP and Ricci-NP scalars|Weyl-NP scalars]] <math>\Psi_i</math> (describing any gravitational field which may be present) each have only one nonvanishing component.
Specifically, with respect to the NP tetrad
:<math> \vec{\ell} = \partial_u - H/2 \, \partial_v</math>
:<math> \vec{n} = \partial_v</math>
:<math> \vec{m} = \frac{1}{\sqrt2} \, \left( \partial_x + i \, \partial_y\right)</math>
the only nonvanishing component of the Ricci spinor is
:<math> \Phi_{00} = \frac{1}{4} \, \left( H_{xx} + H_{yy} \right)</math>
and the only nonvanishing component of the Weyl spinor is
:<math> \Psi_0 = \frac{1}{4} \, \left( \left( H_{xx}-H_{yy} \right) + 2i \, H_{xy} \right).</math>
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 classification|Petrov type]] '''N''' as may be verified by using the [[Petrov classification#Bel criteria|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, Weyl fermions, or some hypothetical kind of massless radiation other than these three, or any combination of these.  All this radiation is traveling in the same direction, and the null vector <math>k = \partial_v</math> plays the role of a [[wave vector]].