Gravitational radiation of systems and the role of their force field
A.I. Nikishov,
V.I. Ritus
Lebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp. 53, Moscow, 119991, Russian Federation
Gravitational radiation (GR) from compact relativistic systems with a known energy-momentum tensor (EMT) and
GR from two masses elliptically orbiting their common center
of inertia are considered. In the ultrarelativistic limit, the GR
spectrum of a charge rotating in a uniform magnetic field, a
Coulomb field, a magnetic moment field, and a combination of
the last two fields differs by a factor of 4πGm2Γ2 / e2 (Γ being
of the order of the charge Lorentz factor) from its electromagnetic radiation (EMR) spectrum. This factor is independent of
the radiation frequency but does depend on the wave vector
direction and the way the field behaves outside of the orbit.
For a plane wave external field, the proportionality between
the gravitational and electromagnetic radiation spectra is exact, whatever the velocity of the charge. Qualitative estimates
of Γ are given for a charge moving ultrarelativistically in an
arbitrary field, showing that it is of the order of the ratio of the
nonlocal and local source contributions to the GR. The localization of external forces near the orbit violates the proportionality
of the spectra and reduces GR by about the Lorentz factor
squared. The GR spectrum of a rotating relativistic string with
masses at the ends is given, and it is shown that the contributions
by the masses and string are of the same order of magnitude. In
the nonrelativistic limit, the harmonics of GR spectra behave
universally for all the rotating systems considered. A trajectory
method is developed for calculating the GR spectrum. In this
method, the spatial (and hence polarization) components of the
conserved EMT are calculated in the long wavelength approximation from the time component of the EMTs of the constituent masses of the system. Using this method, the GR spectrum
of two masses moving in elliptic orbits about their common
center of inertia is calculated, as are the relativistic corrections
to it.
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