Поле электромагнитного узла и метрика Спарлинга - Тода - page 7

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Поле электромагнитного узла и метрика Спарлинга – Тода
The field of the electromagnetic knot
and the Sparling—Tod metrics
© V.N. Trishin
Bauman Moscow State Technical University, Moscow, 105005, Russia
The article considers explicit anti-selfdual solutions of complex Einstein equations
constructed from null Maxwell fields. It is shown that the solution of source-free Maxwell
equations describing electromagnetic unit corresponds to well-known Sparling—Tod
metrics.
Keywords:
anti-selfdual solutions, Einstein equations, electromagnetic unit, null Maxwell
fields.
REFERENCES
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Journal of
Mathematical Physics
, 1982, vol. 23, pp. 1147–1148.
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Spinors and space-time. Vol. 2. Spinor and Twistor Methods
in Space-Time Geometry.
Cambridge etc., Cambridge University Press, 1986. IX,
501 p., ISBN 0 521 25267 9.
[3] Dunajski M.
Solitons, instantons, and twistors
. Oxford, OUP, 2010, 359 p.
[4] Plebanski J. Some solutions of complexEinstein equations.
Journal ofMathematical
Physics
, 1975, vol. 16, pp. 2395–2402.
[5] Robinson I. Null electromagnetic fields.
Journal of Mathematical Physics
, 1961,
vol. 2, pp. 290–291.
[6] Nagatomo K. On a construction of null electromagnetic fields. Osaka Journal of
Mathematics, 1983, vol. 20, pp. 285–301.
[7] Dalhuisen J. W., Bouwmeester D. Twistors and electromagnetic knots.
Journal of
Physics
, 2012, vol. A45, pp. 135201–135209.
[8] Sparling G.A.J., Tod K.P. An example of an H-space.
Journal of Mathematical
Physics
, 1981, vol. 22, pp. 331–332.
TrishinV.N.
(b. 1977) graduated from the Physics Department of LomonosovMoscowState
University. Ph.D, Assoc. Professor of the Computational Mathematics and Mathematical
Physics Department of Bauman Moscow State Technical University. Author of 7 scientific
papers in the field of mathematical methods in the general theory of relativity.
e-mail:
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