2020
DOI: 10.3390/sym12081372
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Shapovalov Wave-Like Spacetimes

Abstract: A complete classification of space-time models is presented, which admit the privileged coordinate systems, where the Hamilton–Jacobi equation for a test particle is integrated by the method of complete separation of variables with separation of the isotropic (wave) variable, on which the metric depends (wave-like Shapovalov spaces). For all types of Shapovalov spaces, exact solutions of the Einstein equations with a cosmological constant in vacuum are found. Complete integrals are presented for the eikonal eq… Show more

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Cited by 28 publications
(36 citation statements)
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“…Wave-like Shapovalov spaces [22] arise as a subset of the Stäckel spaces [23][24][25], admitting the existence of privileged coordinate systems, where the equation of the motion of test particles in the Hamilton-Jacobi formalism,…”
Section: Wave-like Shapovalov Spacesmentioning
confidence: 99%
See 3 more Smart Citations
“…Wave-like Shapovalov spaces [22] arise as a subset of the Stäckel spaces [23][24][25], admitting the existence of privileged coordinate systems, where the equation of the motion of test particles in the Hamilton-Jacobi formalism,…”
Section: Wave-like Shapovalov Spacesmentioning
confidence: 99%
“…Here, g ij is the space-time metric, S is the test particle action function, m is the test particle mass. Shapovalov spaces, by definition [22], allow the separation of non-ignored "wave" variables (on which the metric depends) along which the space-time interval is equal to zero. The ability to separate the wave variables on which the metric depends allows us to consider these space-time models as "wave-like".…”
Section: Wave-like Shapovalov Spacesmentioning
confidence: 99%
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“…For example, the problem of complete separation of variables in the Klein-Gordon-Fock equation has been solved for the Einstein spaces and for vacuum solutions of the Einstein equations (see [14][15][16][17]). In the papers [18][19][20] intersections of sets of homogeneous spaces and the Stackel spaces have been considered. Due to the high level of symmetry of the Stackel spaces, they remain interesting objects for research in various branches of theoretical and mathematical physics.…”
Section: Introductionmentioning
confidence: 99%