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arXiv · 2009.00264

Extracting Dynamical Degrees of Freedom From the Quasi-Local Energy Term in the Gravitational Action

Bjoern S. Schmekel
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Abstract

It is shown that under proper conditions in an appropriate coordinate system with a suitable time slicing the Hamiltonian and the Einstein-Hilbert action including all necessary boundary terms can be written on shell in terms of the Brown-York quasi-local energy in the absence of matter. If matter is present the non-vanishing bulk term only consists of stress-energy. It is argued that the dynamical content of general relativity is stored in the quasi-local energy term. The results underscore the interpretation of the Brown-York quasi-local energy as the field energy of the gravitational field plus stress-energy. As an application we derive uncertainty relations of the time-energy kind which may be useful in the understanding of gravity induced quantum state reduction and the more conventional kind for conjugate variables. The latter is computed for a modified Vaidya metric which may be used in the investigation of black hole radiance. The boundary terms expressed as quasi-local energy cancel second derivatives in the action leaving only a square of a first derivative term in the chosen gauge which is desirable for a quantization of the action.

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Bjoern S. Schmekel. 2020-09-01. Extracting Dynamical Degrees of Freedom From the Quasi-Local Energy Term in the Gravitational Action. https://arxiv.org/abs/2009.00264

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