Geodesic
Two-dimensional field reduction of the~general theory of relativity
Teoretičeskaâ i matematičeskaâ fizika, Tome 199 (2019) no. 1, pp. 142-153

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In the framework of general relativity theory, we consider a space–time whose metric depends on only one coordinate and time. We choose a gauge class such that all the constraint conditions of the theory of gravity as a gauge theory are explicitly solved and construct a Hamiltonian depending only on dynamical physical variables $($gravitons$)$. We show that such a Hamiltonian can be obtained from the Polyakov action for a string in an anti-de Sitter background space with a "string constant" depending on time.
Keywords: general relativity theory, gravitational wave, string, anti-de Sitter space, gauge theory. 
@article{TMF_2019_199_1_a8,
     author = {V. V. Losyakov and I. V. Tyutin},
     title = {Two-dimensional field reduction of the~general theory of relativity},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {142--153},
     publisher = {mathdoc},
     volume = {199},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_199_1_a8/}
}
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V. V. Losyakov; I. V. Tyutin. Two-dimensional field reduction of the~general theory of relativity. Teoretičeskaâ i matematičeskaâ fizika, Tome 199 (2019) no. 1, pp. 142-153. http://geodesic.mathdoc.fr/item/TMF_2019_199_1_a8/