Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-02-09
Class. Quantum Grav. vol 28 (2011) 235009, Corrigendum: Class. Quantum Grav. vol 29 (2012) 069501
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
final version, 12 pages, The last sentence of subsection 2.2, giving the quasi-local energy in the relativistically corrected
Scientific paper
An `effective' quasi-local energy expression, motivated by the (relativistically corrected) Newtonian theory, is introduced in exact GR 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 ADM energy at the spatial infinity as a {\em 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.
Frauendiener Jörg
Szabados Laszlo B.
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