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arXiv · 1609.04426

Hamiltonian approach to GR - Part 1: covariant theory of classical gravity

Claudio Cremaschini·Massimo Tessarotto
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Abstract

A challenging issue in General Relativity concerns the determination of the manifestly-covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant Hamilton-Jacobi theory. The task is achieved by adopting a synchronous variational principle requiring distinction between the prescribed deterministic metric tensor $\widehat{g}(r)\equiv \left\{ \widehat{g}_{μν}(r)\right\} $ solution of the Einstein field equations which determines the geometry of the background space-time and suitable variational fields $x\equiv \left\{ g,π\right\} $ obeying an appropriate set of continuum Hamilton equations, referred to here as GR-Hamilton equations$.$ It is shown that a prerequisite for reaching such a goal is that of casting the same equations in evolutionary form by means of a Lagrangian parametrization for a suitably-reduced canonical state. As a result, the corresponding Hamilton-Jacobi theory is established in manifestly-covariant form. Physical implications of the theory are discussed. These include the investigation of the structural stability of the GR-Hamilton equations with respect to vacuum solutions of the Einstein equations, assuming that wave-like perturbations are governed by the canonical evolution equations.

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Claudio Cremaschini, Massimo Tessarotto. 2017-05-22. Hamiltonian approach to GR - Part 1: covariant theory of classical gravity. https://doi.org/10.1140/epjc%2Fs10052-017-4854-1

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