Einstein–Rosen metric explained

In general relativity, the Einstein–Rosen metric is an exact solution to the Einstein field equations derived in 1937 by Albert Einstein and Nathan Rosen.^[1] It is the first exact solution to describe 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 and References

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