On the Hamilton approach for the metric GR

2015/09/28 by Alexei M. Frolov, Frolov, Alexei M.
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Physics (physics.gen-ph) #Pulsars and Gravitational Waves Research #physics.gen-ph

paper · pdf · doi:10.48550/arxiv.1509.08928

openalex publication_date 2015/09/28 · arxiv created 2016/01/14 · arxiv updated 2016/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Basic principles of the Hamilton approach developed for the metric General Relativity (Einstein`s GR) are discussed. In particular, we derive the Hamiltonian of the metric GR in the explicit form. This Hamiltonian is a quadratic function of the momenta π^mn conjugate to the spatial components g_mn of the metric tensor g_αβ. The Hamilton approach is used to analyze some problems of metric GR, including the internal structure of propagating gravitational waves and quantization of the metric GR. We also derive the Schrödinger equation for the free Gravitational field and show that actual gravitational field cannot propagate as pure harmonic oscillations, or harmonic gravitational waves. A number of inequalities useful in applications to the metric GR are derived.

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