Colliding Plane Gravitational Waves Research Articles

Singularities from colliding plane gravitational waves

A simple geometrical argument is given which shows that a collision between two plane gravitational waves must result in singularities. The argument suggests that these singularities are a peculiar feature of plane waves, because singularities are also a consequence of a collision between self-gravitating plane waves of other fields with arbitrarily small energy density.

Colliding plane gravitational waves

A method is given by which new solutions representing colliding plane gravitational waves can be generated from the ones given by Szekeres and Stoyanov. Some of the new solutions are singularity free like those of Stoyanov.

Collision of plane gravitational waves without singularities

Mathematical and physical causes of development of singularities in space-time representing the collision of two strong plane gravitational waves with collinear polarization are considered. The conclusion is drawn that emergence of any physical space-time singularity is not inevitable, provided that the incoming plane waves themselves have regular wave fronts. The new exact solutions are given which provide sufficient bases for such conclusion.

Colliding plane gravitational waves

New exact solutions of the vacuum Einstein field equations are constructed which describe the collision of plane gravitational waves. These solutions generalize those of Szekeres by relaxing the requirement of collinear polarization.

Colliding Impulsive Gravitational Waves

We formulate the problem of colliding plane gravitational waves with two polarizations as the harmonic mappings of Riemannian manifolds and construct an exact solution of the vacuum Einstein field equations describing the interaction of colliding impulsive gravitational waves which in the limit of collinear polarization reduces to the solution of Khan and Penrose.

Applications of Arnowitt-Deser-Misner quantization of some metrics with at-least-two-parameter isometry groups

The physical situations of spacetimes in general relativity with cylindrical symmetry, with plane symmetry, and the spacetime in the interaction regions of two colliding plane gravitational waves are mathematically related by the existence of an isometry group with at least two parameters in each case. We extend the work of Kucha\ifmmode \check{r}\else \v{r}\fi{}, Berger, and Gowdy to include the Arnowitt-Deser-Misner (ADM) quantization of cylindrical spacetimes with a quantized scalar field source, plane spacetimes with a quantized scalar field source, and the interaction region of two colliding gravitational plane waves with noncompact invariant hypersurfaces. The inhomogeneous nonvacuum metrics are interesting because they provide the first example of the quantization of arbitrarily strong interacting gravitational and quantum matter fields in the usual framework of a quantum field theory. Tentative conclusions are drawn concerning the "Landau conjecture" of a "gravitational renormalization" of the usual special-relativistic quantum field-theoretic divergences, and conclusions concerning the effect of quantum gravity on the classically predicted general-relativistic singularities are also presented. Finally, the extremely simple model of plane symmetry with scalar field source is closely related to the spherically symmetric situation, and represents an analogous physical mechanism to the particle production by Hawking's "exploding black holes." A program involving ADM quantization that can extend the "exploding black hole" calculations to include back reaction and quantum-gravity effects is presented.