Abstract
If we ask what characterizes radiation, our answers might include the transmission of energy and information through space, or the existence of a wave equation which some quantity satisfies. These aspects are, of course, related, in that there is a characteristic speed of transmission which is determined by the wave equation. In Newtonian gravitational theory energy (and information) is transmitted via the gravitational field which is determined by the gravitational potential V. In empty space V satisfies ∇2V = 0, which is not a wave equation, but might be regarded as the limit of a wave equation in which the characteristic speed of transmission tends to infinity. Put another way, gravitational effects are, according to Newton’s theory, transmitted instantaneously, which is thoroughly unsatisfactory from the relativistic point of view. Moreover, with an infinite speed of transmission it is impossible to associate a wavelength with a given frequency of oscillation.
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This expressive means of showing the effect of the polarization mode on a cloud of test particles is borrowed from Misner, Thorne, and Wheeler. See Misner, Thorne, and Wheeler, 1973, §35.6.
See, for example, Landau and Lifshitz, 1980, §§62, 63.
See, for example, Landau and Lifshitz, 1980, §§66, 67. Note that the assumption of small speeds is equivalent to the dimensions of the source being small compared with the wavelength. If it were not made, then equation (5.41) would contain extra terms indicating radiation from moments higher than the quadrupole, and for this reason the assumption is sometimes referred to as the quadrupole assumption.
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© 2006 Springer Science+Business Media, Inc.
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Foster, J., Nightingale, J.D. (2006). Gravitational radiation. In: A Short Course in General Relativity. Springer, New York, NY. https://doi.org/10.1007/978-0-387-27583-3_6
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DOI: https://doi.org/10.1007/978-0-387-27583-3_6
Publisher Name: Springer, New York, NY
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