Generalised Kerr-Schild space-times

If V is a space-time with metric tensor g_μν admitting a null, geodesic shear free vector field l_μ, then one may determine a function H so that the spacetime $\text{V}\text{?}$ with metric g_μν = g_μν + 2Hl_μl_ν satisfies the Einstein field equations for various material sources, and for no sources. When V is Minkowski space, $\text{V}\text{?}$ is a Kerr-Schild space-time. In case V is a vacuum space-time, one may choose H so that the source is a null fluid with no pressure. In case V is a Robertson-Walker universe H may be chosen so that the source has a stress-energy tensor with one timelike proper vector and three spacelike ones. There are two equal proper values associated with the latter vectors and one which differs from these. The stress-energy tensor describing this source may be interpreted as representing a perfect fluid with anisotropic pressures or as one describing the sum of a perfect fluid with isotropic pressures and a presureless null fluid. Vaidya's Kerr metric in a cosmological background [Pramana8 (1977) 512–517] is discussed as is the metric representing an accelerating point mass in an expanding universe.     

Curvature collineations in certain gravitational space-times

It has been shown that the space-times formed from the product of two surfaces and from a thick gravitational plane wave sandwiched between two flat spacetimes admit proper curvature collineation in general. The curvature collineation vectors have been determined explicitly. For the space-time formed from the product of two surfaces conditions are obtained for it to admit motion. It has also been pointed out that the spacetime formed from a thick plane gravitational wave belongs to the class (III_b) of pure gravitational radiation and admits five- and six-parameter groups of motion in the two possible cases. Conservation laws given by Sachs and Katzin-Levine-Davis in terms of curvature collineation vectors are satisfied identically in the case of the plane gravitational wave solution, and Sachs' conservation law can be deduced in this case as a consequence of the theorem given by Katzin and others.     

The energy-momentum gravitational pseudotensor and Kerr-Schild metrics

It is shown that the Landau-Lifshitz pseudotensor vanishes for any Kerr-Schild metricg =n + 2Hl l satisfying the conditionS l =0. Some solutions verifying this condition are indicated.     

Low frequency antenna for gravitational radiation

We report on a resonant antenna for gravitational radiation at $\text{ω}\text{2π}\text{= 44}\text{Hz}$. The 14 kg aluminum antenna works in a torsional vibration mode and has a decay time τ = 1.4 × 10⁵s , namely, a quality factor Q = 4.0 × 10⁷, at 4 K.     

Progressing wave gravitational perturbations of Robertson-Walker space-times

In a series of papers Janis and coworkers found a family of Robertson-Walker space-times whose most general radiative purely gravitational perturbations could be expressed as progressing waves. In this paper we significantly generalize, simplify, and extend, their results.     

Linearization stability of coupled gravitational and scalar fields in asymptotically flat space-times

Using the methods of Choquet-Bruhat, Fischer and Marsden and using weighted Sobolev spaces developed recently by Christodoulou and Choquet-Bruhat, it is proved that the Einstein field equations coupled with self-gravitating scalar fields are linearization stable in asymptotically flat space-times.     

Advances in gravitational radiation detection

New experiments are reported which improve our estimates of the bandwidth and energy flux of the observed radiation. These include search for coincident, sudden increases in power of newly instrumented detectors at 1661 Hertz and 1581 Hertz, at opposite ends of a 1000 kilometer baseline, and search for coincidences between outputs of detectors at 1661 Hertz and 5000 Hertz. Coincidences are observed for the detectors separated by 80 Hertz, implying a radiation bandwidth exceeding 80 Hertz.The new instrumentation is a modification of the earlier technique for bonding ferroelectric crystals to aluminium cylinders. Three detectors are fully operational with sensitivity one order better than earlier ones.Progress has been made in data retrieval employing a computer and magnetic tape. Earlier results on the coincidence rates and time delay experiments have been confirmed.A 1661 Hertz detector has been developed for operation at liquid helium temperatures. It is now undergoing tests at the Argonne National Laboratory.An experiment has been approved by NASA to employ the moon as a gravitational radiation detector. Equipment has been designed by Bendix and the University of Maryland for emplacement by the Apollo 17 astronauts.Supported in part by the U.S. National Science Foundation.Presented at the International Conference on Gravitation and Relativity, Copenhagen, 5–10 July, 1971.     

Neutrino radiation in gravitational fields

A differential equation representing radiation solutions of the general relativistic Weyl equation is derived. Their optical properties and the group of motion of the corresponding energy-momentum tensor are studied. If there exists neutrino radiation the Riemann space must be algebraically special and the propagation of the neutrinos occurs only along one of the principal null directions. Gravitational- and neutrinopp-waves taken together, represent an exact solution of the Weyl-Einstein system of field equations.     

Electromagnetically induced gravitational radiation

Using a general relativistic treatment we have analyzed the coupled emission of gravitational and electromagnetic radiation in the simplest possible radiation process: a massive charged particle falling radially into a Reissner-Nordstrøm geometry. Particular attention is given to a detailed analysis of the “feedback” terms between gravitational and electromagnetic radiation.     

Spherically symmetric lightlike radiation and conformally flat space-times

The problem of the coexistence of spherical symmetry of a 3-space, tracelessness of the energy-momentum tensor, conformally flat 4-metrics, and the validity of the Einstein equations is investigated. The assertion is proved that when spherical symmetry is present nonequilibrium lightlike radiation with the energymomentum tensor T_µv = l _µ l _v (l v = 0) cannot serve as the source of the gravitational field corresponding to a conformally flat space-time (type 0 according to the algebraic classification). An exact spherically symmetric solution with a conformally flat metric is obtained which describes dust and equilibrium isotropic radiation without energy exchange between them. This solution is rewritten for a synchronous reference frame in which it is evident that it describes a homogeneous and isotropic universe. In the limit of the absence of radiation the solution changes into the well-known Friedmann solution for an open universe.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 32–35, July, 1984.In conclusion the authors express their gratitude to all the participants in the seminar of the gravitation section of the Scientific and Technical Council of Minvuz of the USSR (the physics faculty of Moscow State University) for a useful discussion of the results of this paper.     

High density current drive by high frequency radiation

A self-consistent theory is developed for current drive by intense radiation in the presence of the ion-acoustic instability. The spectrum of ion-acoustic turbulent noise generated by the driven current and concentrated in a limited cone of angles along the propagation direction of the wave is found. Excitation of the instability is accompanied by the establishment of an electron drift that is excited by the electromagnetic wave and has a velocity on the order of the ion acoustic speed. This current drive regime is realized over a wide range of intensities, as long as the region of turbulence in the angles of the acoustic wave vector is expanding. At yet higher intensities, the driven current increases in proportion to the intensity of the fundamental wave. Similar behavior is found for driven heat fluxes. Zh. éksp. Teor. Fiz. 111, 107–119 (January 1997)     

The thermodynamics of gravitational radiation

I conjecture, and show for a large class of cases, that given a spacelike hypersurface on which is an arbitrary distribution of linearized gravitons and matter, the latter satisfying the positive energy condition, the expectation value of the number of events in which a graviton is absorbed by or scattered inelastically from the matter within any future time,t, is always less then the expectation value of the number of gravitons in the initial state (except for a set of initial configurations of measure zero). Consequences of this result are: (1) the impossibility of any system containing gravitational radiation reaching thermal equilibrium in a finite time, (2) the absence of an ultraviolet catastrophe for gravitational radiation, (3) the impossibility of measuring accurately the quantum state of the linearized gravitational field, and (4) the impossibility of constructing a gravitational wave laser.This essay received the second award from the Gravity Research Foundation for the year 1983 [Ed.].     

Does gravitational radiation exist?

An attempt is made to extend the Wheeler and Feynman absorber theory of electromagnetic radiation to the case of the gravitational field (described by the Einstein linear weak-field equations) on the assumption that the source is at the center of a sphere of matter having a density equal to the average density in the universe and a radius equal to the reciprocal of the Hubble constant. It is found that near the source the field of the matter is negligible compared to that of the source, so that one can conclude that the gravitational field generated by the source is time-symmetric (one-half advanced plus one-half retarded). One can conclude that a physical system does not lose energy as gravitational radiation, although a gravitational wave detector may record signals. It appears that there are no periodic running waves in nature, and hence no gravitons. These considerations hold also in the bimetric gravitation theory.