Exact models of pure radiation in \(R^2\) gravity for spatially homogeneous wave-like Shapovalov spacetimes type II. (English) Zbl 1500.83003
Summary: Presented are exactly integrable models with pure radiation in \(R^2\) gravity with a cosmological constant related to wave-like Shapovalov spacetimes type II. Spatially homogeneous models of Shapovalov spacetimes were considered. The obtained solutions belong to spaces of type III according to the Bianchi classification and of type N according to the Petrov classification. For the models under consideration, exact solutions for the equations of motion of test particles are obtained in the Hamilton-Jacobi formalism. For the obtained exact models, solutions of the geodesic deviation equations are obtained.
©2021 American Institute of Physics
©2021 American Institute of Physics
MSC:
| 83C10 | Equations of motion in general relativity and gravitational theory |
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 83F05 | Relativistic cosmology |
| 83C80 | Analogues of general relativity in lower dimensions |
| 53C30 | Differential geometry of homogeneous manifolds |
| 70H20 | Hamilton-Jacobi equations in mechanics |
| 53D25 | Geodesic flows in symplectic geometry and contact geometry |
References:
| [1] | Capozziello, S.; De Laurentis, M., Extended theories of gravity, Phys. Rep., 509, 167-321 (2011) · doi:10.1016/j.physrep.2011.09.003 |
| [2] | Nojiri, S.; Odintsov, S. D., Introduction to modified gravity and gravitational alternative for dark energy, Int. J. Geom. Methods Mod. Phys., 04, 115-145 (2007) · Zbl 1112.83047 · doi:10.1142/s0219887807001928 |
| [3] | Nojiri, S.; Odintsov, S. D., Unified cosmic history in modified gravity: From F(R) theory to Lorentz non-invariant models, Phys. Rep., 505, 59-144 (2011) · doi:10.1016/j.physrep.2011.04.001 |
| [4] | Nojiri, S.; Odintsov, S. D.; Oikonomou, V. K., Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution, Phys. Rep., 692, 1-104 (2017) · Zbl 1370.83084 · doi:10.1016/j.physrep.2017.06.001 |
| [5] | Shapovalov, V. N., Symmetry and separation of variables in Hamilton-Jacobi equation. I, Sov. Phys. J., 21, 1124-1129 (1978) · doi:10.1007/bf00894559 |
| [6] | Shapovalov, V. N., Symmetry and separation of variables in Hamilton-Jacobi equation. II, Sov. Phys. J., 21, 1130-1132 (1978) · doi:10.1007/bf00894560 |
| [7] | Shapovalov, V. N., Stäckel spaces, Sib. Math. J., 20, 790-800 (1979) · Zbl 0442.53024 · doi:10.1007/BF00971844 |
| [8] | Osetrin, K.; Osetrin, E., Shapovalov wave-like spacetimes, Symmetry, 12, 1372 (2020) · doi:10.3390/SYM12081372 |
| [9] | Bazański, S., Hamilton-Jacobi formalism for geodesics and geodesic deviations, J. Math. Phys., 30, 1018-1029 (1989) · Zbl 0682.70016 · doi:10.1063/1.528370 |
| [10] | Bagrov, V. G.; Obukhov, V. V., Classes of exact solutions of the Einstein-Maxwell equations, Ann. Phys., 495, 181-188 (1983) · Zbl 0556.35116 · doi:10.1002/andp.19834950402 |
| [11] | Bagrov, V. G.; Obukhov, V. V.; Shapovalov, A. V., Special Stäckel electrovac spacetimes, Pramana, 26, 93-108 (1986) · doi:10.1007/bf02847629 |
| [12] | Bagrov, V. G.; Obukhov, V. V.; Osetrin, K. E., Classification of null-Stäckel electrovac metrics with cosmological constant, Gen. Relativ. Gravitation, 20, 1141-1154 (1988) · Zbl 0652.53048 · doi:10.1007/bf00758935 |
| [13] | Obukhov, V., Separation of variables in Hamilton-Jacobi equation for a charged test particle in the Stackel spaces of type (2.1), Int. J. Geom. Methods Mod. Phys., 17, 2050186 (2020) · Zbl 07819413 · doi:10.1142/S0219887820501868 |
| [14] | Obukhov, V., Hamilton-Jacobi equation for a charged test particle in the Stäckel spaces of type (2.0), Symmetry, 12, 1289 (2020) · doi:10.3390/sym12081289 |
| [15] | Osetrin, K.; Filippov, A.; Osetrin, E., The spacetime models with dust matter that admit separation of variables in Hamilton-Jacobi equations of a test particle, Mod. Phys. Lett. A, 31, 1650027 (2016) · Zbl 1334.70032 · doi:10.1142/s0217732316500279 |
| [16] | Bagrov, V. G.; Istomin, A. D.; Obukhov, V. V.; Osetrin, K. E., Classification of conformal steckel spaces in the vaidya problem, Russ. Phys. J., 39, 744-749 (1996) · doi:10.1007/bf02437084 |
| [17] | Obukhov, V. V.; Osetrin, K. E.; Filippov, A. E.; Rybalov, Y. A., The Vaidya problem in conformally flat Stäckel spaces of type (1.1), Russ. Phys. J., 52, 11-14 (2009) · Zbl 1178.83076 · doi:10.1007/s11182-009-9198-3 |
| [18] | Osetrin, E.; Osetrin, K., Pure radiation in space-time models that admit integration of the eikonal equation by the separation of variables method, J. Math. Phys., 58, 112504 (2017) · Zbl 1386.83136 · doi:10.1063/1.5003854 |
| [19] | Osetrin, K.; Filippov, A.; Osetrin, E., Wave-like spatially homogeneous models of Stäckel spacetimes (2.1) type in the scalar-tensor theory of gravity, Mod. Phys. Lett. A, 35, 2050275 (2020) · Zbl 1448.83043 · doi:10.1142/s0217732320502752 |
| [20] | Osetrin, E.; Osetrin, K.; Filippov, A.; Kirnos, I., Wave-like spatially homogeneous models of Stackel spacetimes (3.1) type in the scalar-tensor theory of gravity, Int. J. Geom. Methods Mod. Phys., 17, 2050184 (2020) · Zbl 07807372 · doi:10.1142/s0219887820501844 |
| [21] | Osetrin, K. E.; Filippov, A. E.; Osetrin, E. K., Models of generalized scalar-tensor gravitation theories with radiation allowing the separation of variables in the eikonal equation, Russ. Phys. J., 61, 1383-1391 (2018) · Zbl 1418.83047 · doi:10.1007/s11182-018-1546-8 |
| [22] | Bagrov, V. G.; Obukhov, V. V., New method of integration for the Dirac equation on a curved space-time, J. Math. Phys., 33, 2279-2289 (1992) · Zbl 0765.53057 · doi:10.1063/1.529600 |
| [23] | Osetrin, K. E.; Rybalov, Y. A., Cosmological models with scalar and spinor fields, Russ. Phys. J., 55, 1416-1424 (2013) · Zbl 07876777 · doi:10.1007/s11182-013-9975-x |
| [24] | Obukhov, V. V.; Osetrin, K. E.; Filippov, A. E., Metrics of homogeneous spaces admitting (3.1)-type complete sets, Russ. Phys. J., 45, 42-48 (2002) · Zbl 1063.53073 · doi:10.1023/A:1016093620137 |
| [25] | Osetrin, K. E.; Obukhov, V. V.; Filippov, A. E., Homogeneous spacetimes and separation of variables in the Hamilton-Jacobi equation, J. Phys. A: Math. Gen., 39, 6641-6647 (2006) · Zbl 1101.83013 · doi:10.1088/0305-4470/39/21/s64 |
| [26] | Osetrin, E. K.; Osetrin, K. E.; Filippov, A. E., Spatially homogeneous conformally Stäckel spaces of type (3.1), Russ. Phys. J., 63, 403-409 (2020) · Zbl 1439.83008 · doi:10.1007/s11182-020-02050-2 |
| [27] | Osetrin, E. K.; Osetrin, K. E.; Filippov, A. E., Spatially homogeneous models Stäckel spaces of type (2.1), Russ. Phys. J., 63, 410-419 (2020) · Zbl 1439.83009 · doi:10.1007/s11182-020-02051-1 |
| [28] | Ivashchuk, V. D.; Kobtsev, A. A., On exponential cosmological type solutions in the model with Gauss-Bonnet term and variation of gravitational constant, Eur. Phys. J. C, 75, 177 (2015) · doi:10.1140/epjc/s10052-015-3394-9 |
| [29] | Ivashchuk, V. D., On stable exponential solutions in Einstein-Gauss-Bonnet cosmology with zero variation of G, Gravitation Cosmol., 22, 329-332 (2016) · Zbl 1380.83052 · doi:10.1134/s0202289316040095 |
| [30] | Osetrin, K.; Kirnos, I.; Osetrin, E.; Filippov, A., Wave-like exact models with symmetry of spatial homogeneity in the quadratic theory of gravity with a scalar field, Symmetry, 13, 1173 (2021) · doi:10.3390/sym13071173 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
