On gravitational shock waves in curved spacetimes

Some years ago Dray and 't Hooft found the necessary and sufficient conditions to introduce a gravitational shock wave in a particular class of vacuum solutions to Einstein's equations. We extend this work to cover cases where non-vanishing matter fields and a cosmological constant are present. The sources of gravitational waves are massless particles moving along a null surface such as a horizon in the case of black holes. After we discuss the general case we give many explicit examples. Among them are the d-dimensional charged black hole (that includes the 4-dimensional Reissner-Nordström and the d-dimensional Schwarzschild solution as subcases), the 4-dimensional De Sitter and anti-De Sitter spaces (and the Schwarzschild-De Sitter black hole), the 3-dimensional anti-De Sitter black hole, as well as backgrounds with a covariantly constant null Killing vector. We also address the analogous problem for string-inspired gravitational solutions nd give a few examples.     

On electromagnetic and gravitational waves in general relativity. I

In this paper the external field of a bounded source emitting electromagnetic and gravitational radiation has been considered. The field has been assumed to be axially symmetric as well as reflexion symmetric and that it tends to flatness at infinity. The form of the electromagnetic tensor which is in accordance with the classical harmonic electric dipole radiation has been assumed. It has been shown that the whole set of field equations falls into seven main equations together with three supplementary conditions. These field equations have been solved by multipole expansion method and the corresponding Initial Value Problem has been discussed.     

Progressing waves on spherical spacetimes

A family of spherically symmetrical spacetimes that are transparent to minimally coupled scalar multipole waves is investigated. The concept of transparency is reformulated in terms of the established concept of progressing waves. The set of spherically symmetric spacetimes and the family of wave equations for which the transparency condition can be shown to hold is generalized.     

引力、引力波和引力波的探测

简要地回顾了引力和引力波概念的由来,以及人们为探测引力波所作的各种努力．     

Imploding-exploding gravitational waves

A solution of Einstein's vacuum field equations is constructed describing an imploding spherical impulsive gravitational wave followed by an exploding similar wave. The two waves propagate in Minkowskian spacetime and the history of the process is the past and future sheets of the null-cone of an event (taken as origin) in the spacetime. The solution is a superposition of two of Penrose's impulsive wave solutions and is described in a single coordinate system in which the metric tensor components are continuous across the histories of the wave fronts.     

Linear gravitational waves

The equations for a weak gravitational field are investigated without the usual simplifications; attention is paid to the difference between gravitational and electromagnetic waves.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 98–101, February, 1982.     

The frequency of light propagating in gravitational wave spacetimes

We study the propagation of light signals in two exact solutions of vacuum Einstein's equations, in the geometric optics approximation. The gravitational wave affects the frequency of light propagating in it (a known effect) even if the metric componentsg _tt andg _ti (i=1, 2, 3) are zero. Moreover we find that red-/blue-shift depends on the relative spatial position of the light source and the observer, even if the wavefront is perfectly uniform, leading to a characteristic redshift pattern.     

Toward the detection of gravitational waves under non-Gaussian noises I. Locally optimal statistic

After reviewing the standard hypothesis test and the matched filter technique to identify gravitational waves under Gaussian noises, we introduce two methods to deal with non-Gaussian stationary noises. We formulate the likelihood ratio function under weakly non-Gaussian noises through the Edgeworth expansion and strongly non-Gaussian noises in terms of a new method we call Gaussian mapping where the observed marginal distribution and the two-body correlation function are fully taken into account. We then apply these two approaches to Student’s t-distribution which has a larger tails than Gaussian. It is shown that while both methods work well in the case the non-Gaussianity is small, only the latter method works well for highly non-Gaussian case.     

Using gravitational lenses to detect gravitational waves

Gravitational lenses could be used to detect gravitational waves, because a gravitational wave affects the travel-time of a light ray. In a gravitational lens, this effect produces time-delays between the different images. Thus the bending of light, which was the first experimental confirmation of Einstein's theory, can be used to search for gravitational waves, which are the most poorly confirmed aspect of that same theory. Applying this method to the gravitational lens 0957+561 gives new upper bounds on the amplitude of low-frequency gravitational waves in the universe, and new limits on the energy-density during an early inflationary phase.This Essay received the First Award from the Gravity Research Foundation, 1990-Ed.     

The plane-fronted gravitational waves

This paper is a contribution to the theory of pure radiation in General Relativity. It gives a survey of the radiation fields which possess a twistfree and non-expanding null congruence, and characterizes their subclasses of different Petrov type by geometrical properties. The term “plane-fronted”, intuitive inMaxwell's theory, is generalized toEinstein's theory.     

Weak cylindrical gravitational waves

A study is made of the linearized Einstein equations without right-hand side on the background of a flat metric in cylindrical coordinates. General solutions are obtained by an expansion with respect to irreducible representations of the group of cylindrical symmetry. The solutions are investigated with allowance for additional conditions imposed on the physicogeometrical quantities, a monad choice being made of the frame of reference in the Chronometrie and kinemetric gauges.     

Generalized plane gravitational waves

The definition of plane gravitational waves is generalized to include the case in which rays are not orthogonal to the two-dimensional wave surfaces. All Einstein spaces and some new solutions of the Einstein-Maxwell equations of this type are given.     

On gravitational shock waves

The discontinuity planes of the Riemann curvature tensorR _klm ⁱ in the Einsteinian vacuumR _kl =0 are isotropic hypersurfaces. These surfaces are to be conceived as being constructed of lightlike geodesics, which form, in the eikonal approximation, gravitational radiation. The discontinuity planes themselves describe the wave fronts of disturbances of the metricg _ik , propagating with the velocity of light. By successively applying continuity conditions for the derivatives of theg _ik that follow from Einstein's equations, we obtain the universal expression of gravitational wave fields in space-time strips (or representations) of arbitrarily selected Einstein spaces.     

Smooth sandwich gravitational waves

Gravitational waves which are smooth and contain two asymptotically flat regions are constructed from the homogeneouspp wave vacuum solution. Motion of free test particles is calculated explicitly and the limit to an impulsive wave is also considered.     

Conformally invariant gravitational waves in a modified gravitational theory

International Journal of Theoretical Physics - An attempt is made to obtain a conformally invariant gravitational wave equation in an isotropic background universe by modifying the Einstein field...