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Journal of Physical Studies 26(4), Article 4001 [6 pages] (2022)
DOI: https://doi.org/10.30970/jps.26.4001 KEPLER PROBLEM IN GENERAL RELATIVITY WITH LORENTZ-COVARIANT DEFORMED POISSON BRACKETS
K.-D. V. Kovach, M. I. Samar
Ivan Franko National University of Lviv, Professor Ivan Vakarchuk Department for Theoretical Physics,
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We consider a Lorentz-covariant deformed algebra, which in the nonrelativistic limit leads to an undeformed one. In the classical limit, this algebra leads to the Lorentz-covariant deformed Poisson brackets. Within covariant Hamiltonian mechanics, we consider a particle's motion in the Schwarzschild space-time with deformed Poisson brackets and obtain the precession angle of the orbit taking into account the deformation. As it turned out, the precession angle in the deformed case depends on the mass of the particle, which violates the weak equivalence principle. Assuming the mass-dependence of the deformation parameter, the equivalence principle can be recovered. Comparing our theoretical results with experimental data for Mercury's precession angle, we estimate the deformation parameter and the minimal length.
Key words: Kepler problem, Schwarzschild metric, precession of an orbit, Lorentz-covariant deformed algebra, minimal length.
