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Tetrad formalism and reference frames in general relativity

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Abstract

This review is devoted to problems of defining the reference frames in the tetrad formalism of General Relativity. Tetrads are the expansion coefficients of components of an orthogonal basis over the differentials of a coordinate space. The Hamiltonian cosmological perturbation theory is presented in terms of these invariant differential forms. This theory does not contain the double counting of the spatial metric determinant in contrast to the conventional Lifshits-Bardeen perturbation theory. We explicitly write out the Lorentz transformations of the orthogonal-basis components from the cosmic microwave background (CMB) reference frame to the laboratory frame, moving with a constant velocity relative to the CMB frame. Possible observational consequences of the Hamiltonian cosmological perturbation theory are discussed, in particular, the quantum anomaly of geometric interval and the shift of the origin, as a source of the CMB anisotropy, in the course of the universe evolution.

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Authors and Affiliations

  1. National Astronomical Observatories, Chinese Academy of Sciences, Beijing, 100012, People’s Republic of China

    A. F. Zakharov

  2. Institute of Theoretical and Experimental Physics, ul. B. Cheremushkinskaya 25, Moscow, 117259, Russia

    A. F. Zakharov

  3. Astro Space Center, Lebedev Physical Institute, ul. Profsoyuznaya 84/12, Moscow, 117810, Russia

    A. F. Zakharov

  4. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980, Russia

    A. F. Zakharov, V. A. Zinchuk & V. N. Pervushin

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  1. A. F. Zakharov
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  2. V. A. Zinchuk
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  3. V. N. Pervushin
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Original Russian Text © A.F. Zakharov, V.A. Zinchuk, V.N. Pervushin, 2006, published in Fizika Elementarnykh Chastits i Atomnogo Yadra, 2006, Vol. 37, No. 1.

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Zakharov, A.F., Zinchuk, V.A. & Pervushin, V.N. Tetrad formalism and reference frames in general relativity. Phys. Part. Nuclei 37, 104–134 (2006). https://doi.org/10.1134/S1063779606010035

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