A Class of Collisions of Plane Impulsive Light--Like Signals in General Relativity

We present a systematic study of collisions of homogeneous, plane--fronted, impulsive light--like signals which do not interact after head--on collision. For the head--on collision of two such signals, six real parameters are involved, three from each of the incoming signals. We find two necessary conditions to be satisfied by these six parameters for the signals to be non--interacting after collision. We then solve the collision problem in general when these necessary conditions hold. After collision the two signals focus each other at Weyl curvature singularities on each others signal front. Our family of solutions contains some known collision solutions as special cases.Comment: 14 pages, late

Detection of Impulsive Light-Like Signals in General Relativity

The principal purpose of this paper is to study the effect of an impulsive light-like signal on neighbouring test particles. Such a signal can in general be unambiguously decomposed into a light-like shell of null matter and an impulsive gravitational wave. Our results are: (a) If there is anisotropic stress in the light-like shell then test particles initially moving in the signal front are displaced out of this 2-surface after encountering the signal; (b) For a light-like shell with no anisotropic stress accompanying a gravitational wave the effect of the signal on test particles moving in the signal front is to displace them relative to each other with the usual distortion due to the gravitational wave diminished by the presence of the light-like shell. An explicit example for a plane-fronted signal is worked out.Comment: 13 pages, accepted for publication in Int. J. Mod. Phys.

The Aichelburg-Sexl Boost of Domain-Walls and Cosmic Strings

We consider the application of the Aichelburg-Sexl boost to plane and line distributions of matter. Our analysis shows that for a domain wall the space-time after the boost is flat except on a null hypersurface which is the history of a null shell. For a cosmic string we study the influence of the boost on the conical singularity and give the new value of the conical deficit.Comment: Latex File, 12 pages, accepted for publication in Physical Review

Colliding Impulsive Gravitational Waves and a Cosmological Constant

We present a space--time model of the collision of two homogeneous, plane impulsive gravitational waves (each having a delta function profile) propagating in a vacuum before collision and for which the post collision space--time has constant curvature. The profiles of the incoming waves are $k\,\delta(u)$ and $l\,\delta(v)$ where $k, l$ are real constants and $u=0, v=0$ are intersecting null hypersurfaces. The cosmological constant $\Lambda$ in the post collision region of the space--time is given by $\Lambda=-6\,k\,l$.Comment: 12 pages, Latex file, published pape

Wave and Particle Scattering Properties of High Speed Black Holes

The light-like limit of the Kerr gravitational field relative to a distant observer moving rectilinearly in an arbitrary direction is an impulsive plane gravitational wave with a singular point on its wave front. By colliding particles with this wave we show that they have the same focussing properties as high speed particles scattered by the original black hole. By colliding photons with the gravitational wave we show that there is a circular disk, centered on the singular point on the wave front, having the property that photons colliding with the wave within this disk are reflected back and travel with the wave. This result is approximate in the sense that there are observers who can see a dim (as opposed to opaque) circular disk on their sky. By colliding plane electromagnetic waves with the gravitational wave we show that the reflected electromagnetic waves are the high frequency waves.Comment: Latex file, 22 pages, 1 figure, accepted for publication in Classical and Quantum Gravit

Scattering of High Speed Particles in the Kerr Gravitational Field

We calculate the angles of deflection of high speed particles projected in an arbitrary direction into the Kerr gravitational field. This is done by first calculating the light-like boost of the Kerr gravitational field in an arbitrary direction and then using this boosted gravitational field as an approximation to the gravitational field experienced by a high speed particle. In the rest frame of the Kerr source the angles of deflection experienced by the high speed test particle can then easily be evaluated.Comment: 10 pages, Latex file, accepted for publication in Phys. Rev.

On Generating Gravity Waves with Matter and Electromagnetic Waves

If a homogeneous plane light-like shell collides head-on with a homogeneous plane electromagnetic shock wave having a step-function profile then no backscattered gravitational waves are produced. We demonstrate, by explicit calculation, that if the matter is accompanied by a homogeneous plane electromagnetic shock wave with a step-function profile then backscattered gravitational waves appear after the collision.Comment: Latex file, 15 pages, accepted for publication in Physical Review

Light-like Signals in General relativity and Cosmology

The modelling of light-like signals in General Relativity taking the form of impulsive gravitational waves and light-like shells of matter is examined. Systematic deductions from the Bianchi identities are made. These are based upon Penrose's hierarchical classification of the geometry induced on the null hypersurface history of the surface by its imbedding in the space-times to the future and to the past of it. The signals are not confined to propagate in a vacuum and thus their interaction with matter (a burst of radiation propagating through a cosmic fluid, for example) is also studied. Results are accompanied by illustrative examples using cosmological models, vacuum space-times, the de sitter univers and Minkowskian space-time.Comment: 21 pages, latex, no figure

Matching LTB and FRW spacetimes through a null hypersurface

Matching of a LTB metric representing dust matter to a background FRW universe across a null hypersurface is studied. In general, an unrestricted matching is possible only if the background FRW is flat or open. There is in general no gravitational impulsive wave present on the null hypersurface which is shear-free and expanding. Special cases of the vanishing pressure or energy density on the hypersurface is discussed. In the case of vanishing energy momentum tensor of the null hypersurface, i.e. in the case of a null boundary, it turns out that all possible definitions of the Hubble parameter on the null hypersurface, being those of LTB or that of FRW, are equivalent, and that a flat FRW can only be joined smoothly to a flat LTB.Comment: 9 page

Implications of Spontaneous Glitches in the Mass and Angular Momentum in Kerr Space-Time

The outward-pointing principal null direction of the Schwarzschild Riemann tensor is null hypersurface-forming. If the Schwarzschild mass spontaneously jumps across one such hypersurface then the hypersurface is the history of an outgoing light-like shell. The outward-- pointing principal null direction of the Kerr Riemann tensor is asymptotically (in the neighbourhood of future null infinity) null hypersurface-forming. If the Kerr parameters of mass and angular momentum spontaneously jump across one such asymptotic hypersurface then the asymptotic hypersurface is shown to be the history of an outgoing light-like shell and a wire singularity-free spherical impulsive gravitational wave.Comment: 16 pages, TeX, no figures, accepted for publication in Phys. Rev.