Gravitational radiation in quantum gravity

The effective field theory of quantum gravity generically predicts non-locality to be present in the effective action, which results from the low-energy propagation of gravitons and massless matter. Working to second order in gravitational curvature, we reconsider the effects of quantum gravity on the gravitational radiation emitted from a binary system. In particular, we calculate for the first time the leading order quantum gravitational correction to the classical quadrupole radiation formula which appears at second order in Newton’s constant.     

Gravitational radiation of isolated systems

The gravitational radiation of isolated systems is studied by introducing a class of reference systems that is the analog of the class of inertial systems in flat space. Expressions for the total energy of these systems and the flux of gravitational radiation are obtained. The fundamental role of the Bondi-Metzner-Sachs asymptotic symmetry groups in the general theory of relativity is explained; transformations of the group characterize transitions from one reference system of a given class to another.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 47–54, November, 1973.     

Gravitational radiation from n-body systems

An expression for the quadrupole moment of any two-body system with structure is derived from a “paralel axes” theorem. Within the weak-field limit of the theory of general relativity, expressions for the gravitational radiation flux of energy and angular momentum from two particles or two spherically symmetric bodies in arbitrary plane motion arising from any type of forces are consequently obtained in terms of time derivatives of the relative coordinates of the system. An estimate of the gravitational flux from any plane motion follows. In particular, the flux from systems with Keplerian and straight-line motion are deduced as special cases. For the general problem of a two-body system with intrinsic quadrupole moment (due to deviation from spherical symmetry), it is found that in addition to the flux from the orbital and the spin motion there is another source of flux—the interaction flux. This is shown explicitly in two special cases—the system of a particle moving in the plane of symmetry of a Jacobi ellipsoid, and that of two spinning rigid rods in plane circular motion with parallel spin and orbital angular momentum. The interaction flux is regarded as the result of interaction of the bodies with gravitational waves. An outline of the method for the calculation of gravitational radiation flux from an n-body system is given. For a three-body system—an astrophysically interesting situation—this is worked out in detail. It is seen that the presence of an unsuspected third body can, by virtue of the interaction power term, increase the generation of gravitational waves significantly.     

Gravitational radiation of Island systems with an electromagnetic field

A study is made of the gravitational radiation of a system of bounded sources in the presence of an electromagnetic field. A class of frames of reference-analogs of inertial frames in flat space-is introduced on the basis of the criterion proposed by Dozmorov. Expressions are obtained for the total energy of such systems and the flux of gravitational radiation.     

Gravitational radiation and neutrinos

A class of neutrino-gravitational fields with zero energy-momentum tensor is defined. These space-times may also be interpreted as describing gravitational waves and are of Petrov typeD orN. A wave-like example of the latter is given.     

Gravitational effects in quantum mechanics

To date, both quantum theory and Einstein’s theory of general relativity have passed every experimental test in their respective regimes. Nevertheless, almost since their inception, there has been debate surrounding whether they should be unified, and by now, there exists strong theoretical arguments pointing to the necessity of quantising the gravitational field. In recent years, a number of experiments have been proposed which, if successful, should give insight into features at the Planck scale. Here, we review some of the motivations, from the perspective of semi-classical arguments, to expect new physical effects at the overlap of quantum theory and general relativity. We conclude with a short introduction to some of the proposals being made to facilitate empirical verification.     

Gravitational radiation from Coulomb collisions

The problem is considered of gravitational bremsstrahlung radiation from collisions between nonrelativistic charged particles at arbitrary values of the Born parameter ¦e₁e₂¦/hv (with exact Coulomb wave functions). It is shown that the existing estimates of this type of radiation from the solar plasma are far too high as they are based on equations for the cross section which are not applicable at the given temperature. A new estimate is derived.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 12, pp. 94–99, December, 1974.     

Gravitational scattering of electromagnetic radiation

The scattering of electromagnetic radiation by linearized gravitational fields is studied to second order in a perturbation expansion. The incoming electromagnetic radiation can be of arbitrary multipole structure, and the gravitational fields are also taken to be advanced fields of arbitrary multipole structure. All electromagnetic multipole radiation is found to be scattered by gravitational monopole and time-varying dipole fields. No case has been found, however, in which any electromagnetic multipole radiation is scattered by gravitational fields of quadrupole or higher-order multipole structure. This lack of scattering is established for infinite classes of special cases, and is conjectured to hold in general. The results of the scattering analysis are applied to the case of electromagnetic radiation scattered by a moving mass. It is shown how the mass and velocity may be determined by a knowledge of the incident and scattered radiation.This work was supported in part by the National Aeronautics and Space Administration and the National Science Foundation. It incorporates some of the results of the first author's doctoral dissertation at the University of Pittsburgh.     

Gravitational radiation in spherical coordinates

The law of gravitation is taken in the formR ₄₄=0, whereR ₄₄ is the time curvature component of the Ricci tensor. Space-time separable equations are developed in spherical coordinates for the nonlinear wave equation determined byR ₄₄=0. One exact solution is examined in detail.     

Gravitational radiation reaction in quasistatic,axially symmetric systems with possibly strong fields

The leading radiation reaction in quasistatic, axially symmetric systems is calculated by matched asymptotic expansions. Earlier results on inductive transfer of near-zone energy are combined via matching with a wave-zone expansion in the Regge-Wheeler gauge. Two independent measures of the damping are computed: (1) the change of the 1/Rcoefficient in a Weyl-Levi-Cività type of multipole expansion in the near zone and (2) the change in Bondi energy at future null infinity. When an averaging process is justified, such as in (nearly) periodic systems, both quantities yield a generalized version of the usual quadrupole formula, provided the radiation is outgoing at future null infinity. It is also shown that terms nonanalytic in the slow-motion parameter make a time-even contribution to the near-zone monopole coefficient. The principal advantage of this calculation over previous work is that the sources are permitted to have strong gravitational fields. Moreover, no specific model for the sources is assumed.     

Gravitational radiation generated by the gravitational scattering of two stars

Within the framework of general relativity, the gravitational scattering of two stars is considered with regard to the gravitational radiation effects. The angular and frequency dependence of the generated gravitational radiation is investigated by Fourier's analysis of the gravitational field in the radiation zone. The results of the numerical calculations show a strong directional dependence of the radiation in the plane of movement of the stars.     

Gravitational radiation recoil on anN-body system

The main purpose of this paper is to present a formula of gravitational radiation recoil of an N-body material system.