The Einstein–Rosen metric is an exact solution of Einstein's field equation. It was derived by Albert Einstein and Nathan Rosen in 1937.[1] It is the first exact solution of Einstein's equation that described the propagation of a gravitational wave.

This metric can be written in a form such that the Belinski–Zakharov transform applies, and thus has the form of a gravitational soliton.

In 1972 and 1973, J. R. Rao, A. R. Roy, and R. N. Tiwari published a class of exact solutions involving the Einstein-Rosen metric.[2][3]\[4]

In 2021 Robert F. Penna found an algebraic derivation of the Einstein-Rosen metric.[5]

In the history of science, one might consider as a footnote to the Einstein-Rosen metric that Einstein, for some time, believed that he had found a non-existence proof for gravitational waves.[6]

Notes

  1. ↑ Einstein, Albert & Rosen, Nathan (1937). "On Gravitational waves". Journal of the Franklin Institute. 223: 43–54. Bibcode:1937FrInJ.223...43E. doi:10.1016/S0016-0032(37)90583-0.
  2. ↑ Rao, J.R.; Roy, A.R.; Tiwari, R.N. (1972). "A class of exact solutions for coupled electromagnetic and scalar fields for einstein-rosen metric. I". Annals of Physics. 69 (2): 473–486. Bibcode:1972AnPhy..69..473R. doi:10.1016/0003-4916(72)90187-X.
  3. ↑ Rao, J.R; Tiwari, R.N; Roy, A.R (1973). "A class of exact solutions for coupled electromagnetic and scalar fields for Einstein-Rosen metric. Part IA". Annals of Physics. 78 (2): 553–560. Bibcode:1973AnPhy..78..553R. doi:10.1016/0003-4916(73)90272-8.
  4. ↑ Roy, A.R; Rao, J.R; Tiwari, R.N (1973). "A class of exact solutions for coupled electromagnetic and scalar fields for einstein-rosen metric. II". Annals of Physics. 79 (1): 276–283. Bibcode:1973AnPhy..79..276R. doi:10.1016/0003-4916(73)90293-5.
  5. ↑ Penna, Robert F. (2021). "Einstein–Rosen waves and the Geroch group". Journal of Mathematical Physics. 62 (8): 082503. arXiv:2106.13252. Bibcode:2021JMP....62h2503P. doi:10.1063/5.0061929. S2CID 235651978.
  6. ↑ Kennefick, Daniel (2005). "Einstein Versus the Physical Review". Physics Today. 58 (9): 43–48. Bibcode:2005PhT....58i..43K. doi:10.1063/1.2117822.
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