2020/09/01 by Bjoern S. Schmekel, Schmekel, Bjoern S.
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2009.00264
openalex publication_date 2020/09/01 · openalex created_date 2023/10/14 · openalex updated_date 2026/07/28
It is shown that under proper conditions in an appropriate coordinate system\nwith a suitable time slicing the Hamiltonian and the Einstein-Hilbert action\nincluding all necessary boundary terms can be written on shell in terms of the\nBrown-York quasi-local energy in the absence of matter. If matter is present\nthe non-vanishing bulk term only consists of stress-energy. It is argued that\nthe dynamical content of general relativity is stored in the quasi-local energy\nterm. The results underscore the interpretation of the Brown-York quasi-local\nenergy as the field energy of the gravitational field plus stress-energy. As an\napplication we derive uncertainty relations of the time-energy kind which may\nbe useful in the understanding of gravity induced quantum state reduction and\nthe more conventional kind for conjugate variables. The latter is computed for\na modified Vaidya metric which may be used in the investigation of black hole\nradiance. The boundary terms expressed as quasi-local energy cancel second\nderivatives in the action leaving only a square of a first derivative term in\nthe chosen gauge which is desirable for a quantization of the action.\n