Editing Pp-wave spacetime (section)

==Relation to other theories==
Since they constitute a very simple and natural class of Lorentzian manifolds, defined in terms of a null congruence, it is not very surprising that they are also important in other [[theory of relativity|relativistic]] [[classical field theories]] of [[gravitation]].  In particular, pp-waves are exact solutions in the [[Brans–Dicke theory]],
various [[higher curvature theories]] and [[Kaluza–Klein theory|Kaluza–Klein theories]], and certain gravitation theories of [[J. W. Moffat]].
Indeed, [[B. O. J. Tupper]] has shown that the ''common'' vacuum solutions in general relativity and in the Brans/Dicke theory are precisely the vacuum pp-waves (but the Brans/Dicke theory admits further wavelike solutions). [[Hans-Jürgen Schmidt]] has reformulated the theory of (four-dimensional) pp-waves in terms of a ''two-dimensional'' '''metric-dilaton''' theory of gravity.

Pp-waves also play an important role in the search for [[quantum gravity]], because as [[Gary Gibbons]] has pointed out, all [[loop term]] quantum corrections vanish identically for any pp-wave spacetime.  This means that studying [[Feynman diagram#Loop order|tree-level]] quantizations of pp-wave spacetimes offers a glimpse into the yet unknown world of quantum gravity.

It is natural to generalize pp-waves to higher dimensions, where they enjoy similar properties to those we have discussed.  [[C. M. Hull]] has shown that such ''higher-dimensional pp-waves'' are essential building blocks for [[eleven-dimensional supergravity]].