2011/02/28 by Jörg Frauendiener, László B Szabados · 3 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Energy (signal processing) #Expression (computer science) #Field (mathematics) #Infinity #Limit (mathematics) #Newtonian fluid #Newtonian limit #Noncommutative and Quantum Gravity Theories #Term (time) #gr-qc
paper · pdf · doi:10.1088/0264-9381/28/23/235009
published in Classical and Quantum Gravity 28(23), 235009 (IOP Publishing) · final version, 12 pages, The last sentence of subsection 2.2, giving the quasi-local energy in the relativistically corrected Newtonian theory, is corrected
openalex publication_date 2011/11/16 · arxiv created 2012/02/28 · arxiv updated 2015/05/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
An 'effective' quasi-local energy expression, motivated by the (relativistically corrected) Newtonian theory, is introduced in exact general relativity as the volume integral of all the source terms in the field equation for the Newtonian potential in static spacetimes. In particular, we exhibit a new post-Newtonian correction in the source term in the field equation for the Newtonian gravitational potential. In asymptotically flat spacetimes, this expression tends to the Arnowitt–Deser–Misner energy at spatial infinity as a monotonically decreasing set function. We prove its positivity in spherically symmetric spacetimes under certain energy conditions, and that its vanishing characterizes flatness. We argue that any physically acceptable quasi-local energy expression should behave qualitatively like this 'effective' energy expression in this limit.