Pp-wave Spacetime - Examples

Examples

There are many noteworthy explicit examples of pp-waves. ("Explicit" means that the metric functions can be written down in terms of elementary functions or perhaps well-known special functions such as Mathieu functions.)

Explicit examples of axisymmetric pp-waves include

• The Aichelburg-Sexl ultraboost is an impulsive plane wave which models the physical experience of an observer who whizzes by a spherically symmetric gravitating object at nearly the speed of light,

• The Bonnor beam is an axisymmetric plane wave which models the gravitational field of an infinitely long beam of incoherent electromagnetic radiation.

Explicit examples of plane wave spacetimes include

• exact monochromatic gravitational plane wave and monochromatic electromagnetic plane wave solutions, which generalize solutions which are well-known from weak-field approximation,

• the Schwarzschild generating plane wave, a gravitational plane wave which, should it collide head-on with a twin, will produce in the interaction zone of the resulting colliding plane wave solution a region which is locally isometric to part of the interior of a Schwarzschild black hole, thereby permitting a classical peek at the local geometry inside the event horizon,

• the uniform electromagnetic plane wave; this spacetime is foliated by spacelike hyperslices which are isometric to ,

• the wave of death is a gravitational plane wave exhibiting a strong nonscalar null curvature singularity, which propagates through an initially flat spacetime, progressively destroying the universe,

• homogeneous plane waves, or SG11 plane waves (type 11 in the Sippel and Gönner symmetry classification), which exhibit a weak nonscalar null curvature singularity and which arise as the Penrose limits of an appropriate null geodesic approaching the curvature singularity which is present in many physically important solutions, including the Schwarzschild black holes and FRW cosmological models.