Wave resonance of light and gravitational waves (the Gertsenshtein effect)
M. E. Gertsenshtein
Summary and citation · read the original at the source
In one page
Two pages in a Soviet journal, and the whole modern subject of turning light into gravity starts here. Gertsenshtein’s argument is disarmingly simple. In general relativity, light and gravitational waves travel at the same speed along the same rays, so if the two are linearly coupled they stay in step — wave resonance, a phenomenon well known to radio engineers — and even a very weak coupling can transfer appreciable energy given enough distance. He sends light through a strong constant magnetising field, expands the energy-momentum tensor into three pieces, keeps the interference term that describes the resonance, and solves for the gravitational wave that grows out of it. The amplitude builds with the time the ray spends inside the field. He then works an interstellar case — a field of ten microgauss, correlated over ten light years, over ten million years — and gets a conversion ratio of about ten to the minus seventeen. The frequency of the gravitational wave, he notes, is set by the frequency of the light.
Why it matters hereChapters 4 and 11 both need one thing to be true — that an electromagnetic field and the metric are coupled strongly enough to move energy between them — and this is the paper that wrote the coupling down and put a number on it.
What it claims
01Light and gravitational waves propagate at the same speed and their rays coincide, so if the two are linearly related, wave resonance sets in — the same phenomenon radio physics has long used — and appreciable transfer of energy becomes possible even at low coupling.Opening paragraph, p. 84
Settled physics02For light propagating in a strong constant magnetising field, the energy-momentum tensor splits into three terms — the square of the constant field, the square of the light wave’s own field, and an interference term describing the wave resonance — and it is that interference term that sources the gravitational wave.Eqs. 1–4, p. 84
Published and peer-reviewed03For a constant external field with negligible absorption or scattering along the ray, the gravitational-wave amplitude grows with the travel time of the ray inside the field, so the effect accumulates over path length rather than saturating.Eqs. 5–6, p. 84
Published and peer-reviewed04For a turbulent, randomly varying field the excited waves add incoherently in energy rather than in amplitude, giving a conversion ratio proportional to the gravitational constant times the square of the background field times the correlation radius times the travel time. Putting in interstellar numbers — ten microgauss, a correlation radius of ten light years, ten million years of travel — gives a ratio of about ten to the minus seventeen, and the frequency of the excited gravitational wave is set by the frequency of the light.Eq. 7 and the paragraph following, pp. 84–85
Published and peer-reviewed05The same mechanism operates inside stars, where strong magnetic fields exist and the correlation length is set by the free path of the radiation. Gertsenshtein concludes that the gravitational-radiation spectrum of a star has maxima both at very low frequencies, those of planetary orbits, and up in the gamma-quantum range, with comparable energy in both portions.p. 85, discussion of stellar interiors
Published and peer-reviewed06General relativity equally permits the inverse conversion, gravitational waves back into light — a possibility Gertsenshtein set aside in one sentence as hardly of interest, and which is now the basis of a live search strategy for high-frequency gravitational waves using strong laboratory and astrophysical magnetic fields as the converter.Closing sentence, p. 85
What to watch
The way in
https://jetp.ras.ru/cgi-bin/dn/e_014_01_0084.pdfThe English translation is held by the journal, which serves the two-page scan free from its own archive at jetp.ras.ru; this page carries a summary and sends the reader straight to that scan.
How to cite it
M. E. Gertsenshtein (1962) Wave resonance of light and gravitational waves (the Gertsenshtein effect). https://jetp.ras.ru/cgi-bin/dn/e_014_01_0084.pdf
Where it sits in the curriculum
The metric, warp drives and wormholesGravity control and superconductors