General relativity
${\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}$
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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

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