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arXiv · 2006.08396

Gauge-invariant quadratic approximation of quasi-local mass and its relation with Hamiltonian for gravitational field

Jacek Jezierski·Jerzy Kijowski·Piotr Waluk
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Abstract

Gauge invariant, Hamiltonian formulation of field dynamics within a compact region $Σ$ with boundary $\partial Σ$ is given for the gravitational field linearized over a Kottler metric. The boundary conditions which make the system autonomous are discussed and the corresponding Hamiltonian functional $\mathcal{H}_\text{Invariant}$ is calculated. It is shown that, under specific boundary conditions, the quasi-local Geroch--Hawking mass $\mathcal{H}_\text{Hawking}$ reduces to $\mathcal{H}_\text{Invariant}$ in the weak field approximation. This observation is a quasi-local version of the classical Brill--Deser result.

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Jacek Jezierski, Jerzy Kijowski, Piotr Waluk. 2020-07-31. Gauge-invariant quadratic approximation of quasi-local mass and its relation with Hamiltonian for gravitational field. https://doi.org/10.1088/1361-6382%2Fabdb4c

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