Editing Pp-wave spacetime (section)

==Overview==
The pp-waves solutions model [[radiation]] moving at the [[speed of light]]. This radiation may consist of:

* [[electromagnetic radiation]], 
* [[gravitational radiation]],
* massless radiation associated with [[Weyl spinor|Weyl fermions]],
* ''massless'' radiation associated with some hypothetical distinct type relativistic classical field,

or any combination of these, so long as the radiation is all moving in the ''same'' direction.

A special type of pp-wave spacetime, the [[plane wave spacetimes]], provide the most general analogue in general relativity of the [[plane waves]] familiar to students of [[electromagnetism]].
In particular, in general relativity, we must take into account the gravitational effects of the energy density of the [[electromagnetic field]] itself.  When we do this, ''purely electromagnetic plane waves'' provide the direct generalization of ordinary plane wave solutions in [[Maxwell's theory]].

Furthermore, in general relativity, disturbances in the gravitational field itself can propagate, at the speed of light, as "wrinkles" in the curvature of spacetime.  Such ''gravitational radiation'' is the gravitational field analogue of electromagnetic radiation.
In general relativity, the gravitational analogue of electromagnetic plane waves are precisely the [[Vacuum solution (general relativity)|vacuum solutions]] among the plane wave spacetimes.
They are called [[gravitational plane wave]]s.

There are physically important examples of pp-wave spacetimes which are ''not'' plane wave spacetimes.
In particular, the physical experience of an observer who whizzes by a gravitating object (such as a star or a black hole) at nearly the speed of light can be modelled by an ''impulsive'' pp-wave spacetime called the [[Aichelburg–Sexl ultraboost]].
The gravitational field of a beam of light is modelled, in general relativity, by a certain [[axi-symmetric]] pp-wave.

An example of pp-wave given when gravity is in presence of matter is the gravitational field surrounding a neutral Weyl fermion: the system consists in a gravitational field that is a pp-wave, no electrodynamic radiation, and a massless spinor exhibiting axial symmetry. In the [[Weyl-Lewis-Papapetrou]] spacetime, there exists a complete set of exact solutions for both gravity and matter.<ref>Cianci, R.; Fabbri, L.; Vignolo S., Exact solutions for Weyl fermions with gravity</ref>

Pp-waves were introduced by [[Hans Brinkmann]] in 1925 and have been rediscovered many times since, most notably by [[Albert Einstein]] and [[Nathan Rosen]] in 1937. More research is indeed on its way.