Geodesic
Einstein's equations on a~$4$-manifold of conformal torsion-free connection
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 3, pp. 393-408.

Voir la notice de l'article provenant de la source Math-Net.Ru

The main defect of Einstein equations – non geometrical right part – is eliminated. The key concept of equidual tensor is introduced. It appeared to be in a close relation both with Einstein's equations, and with Yang–Mills equations. The criterion of equidual basic affinor of conformal connection manifold without torsion is received. Decomposition of the basic affinor into a sum of equidual, conformally invariant and irreducible summands is found. A. Z. Petrov's algebraic classification is generalized. Einstein equations are given a new variational foundation and their geometrical nature is found. Geometric sense of acceleration and dilatation gauge transformations is specified.
Keywords: Einstein equations, Yang–Mills equations, Hodge operator, Maxwell's equations, manifold of conformal connection with torsion and without torsion. 
@article{JSFU_2012_5_3_a11,
     author = {Leonid N. Krivonosov and Vyacheslav A. Luk'yanov},
     title = {Einstein's equations on a~$4$-manifold of conformal torsion-free connection},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {393--408},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2012_5_3_a11/}
}
TY  - JOUR
AU  - Leonid N. Krivonosov
AU  - Vyacheslav A. Luk'yanov
TI  - Einstein's equations on a~$4$-manifold of conformal torsion-free connection
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2012
SP  - 393
EP  - 408
VL  - 5
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2012_5_3_a11/
LA  - ru
ID  - JSFU_2012_5_3_a11
ER  - 
%0 Journal Article
%A Leonid N. Krivonosov
%A Vyacheslav A. Luk'yanov
%T Einstein's equations on a~$4$-manifold of conformal torsion-free connection
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2012
%P 393-408
%V 5
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2012_5_3_a11/
%G ru
%F JSFU_2012_5_3_a11
Leonid N. Krivonosov; Vyacheslav A. Luk'yanov. Einstein's equations on a~$4$-manifold of conformal torsion-free connection. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 3, pp. 393-408. http://geodesic.mathdoc.fr/item/JSFU_2012_5_3_a11/

[1] Yu. S. Vladimirov, Geometrofizika, BINOM, M., 2010

[2] L. N. Krivonosov, V. A. Lukyanov, “Svyaz uravnenii Yanga–Millsa s uravneniyami Einshteina i Maksvella”, Zhurnal SFU. Matematika i fizika, 2:4 (2009), 432–448

[3] C. N. Kozameh, E. T. Newman, K. P. Tod, “Conformal Einstein Spaces”, Gen. Rel. Grav., 17 (1985), 343 | DOI | MR | Zbl

[4] A. Besse, Mnogoobraziya Einshteina, v. I, Mir, M., 1990 | MR | Zbl

[5] A. Z. Petrov, Novye metody v obschei teorii otnositelnosti, Nauka, M., 1966 | MR

[6] E. Kartan, Prostranstva affinnoi, proektivnoi i konformnoi svyaznosti, Izdatelstvo Kazanskogo universiteta, 1962 | MR

[7] M. Korzynski, J. Lewandowski, “The Normal Conformal Cartan Connection and the Bach Tensor”, Class. Quant. Grav., 20 (2003), 3745–3764 | DOI | MR | Zbl

[8] V. A. Lukyanov, “Uravneniya Yanga–Millsa na 4-mernykh mnogoobraziyakh konformnoi svyaznosti”, Izv. vuzov. Matem., 2009, no. 3, 67–72 | MR | Zbl

[9] P. A. M. Dirak, K sozdaniyu kvantovoi teorii polya, Nauka, M., 1990 | MR

[10] A. P. Norden, Prostranstva affinnoi svyaznosti, M.-L., 1950 | MR