
Physics 2011
A note on the postNewtonian limit of quasilocal energy expressionsDOI: 10.1088/02649381/28/23/235009 Abstract: An `effective' quasilocal 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 postNewtonian 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 quasilocal energy expression should behave qualitatively like this `effective' energy expression in this limit.
