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Exact gravitational-wave solution to Einstein's field equations
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
[
edit
]
- ^
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
.
- ^
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
.
- ^
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
.
- ^
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
.
- ^
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
.
- ^
Kennefick, Daniel (2005).
"Einstein Versus the
Physical Review
"
.
Physics Today
.
58
(9): 43?48.
Bibcode
:
2005PhT....58i..43K
.
doi
:
10.1063/1.2117822
.