1201.5433 (Carla Cederbaum)

The Newtonian Limit of Geometrostatics    [PDF]

Carla Cederbaum

This thesis discusses the Newtonian limit of General Relativity for static
isolated systems with compactly supported matter. We call these systems
"geometrostatic" to underline their geometric nature. We introduce new
quasi-local notions of mass and center of mass that can be read off locally in
the vicinity of the matter/black holes. We prove that these notions
asymptotically coincide with ADM-mass and the Huisken-Yau CMC-center of mass.
Moreover, we prove that they converge to Newtonian mass and center of mass in
the Newtonian limit. The Newtonian limit is discussed in the language of
Ehlers' frame theory.
Furthermore, we prove several uniqueness claims in geometrostatics as well as
other geometric and physical properties of these systems. We analyze
equipotential sets, provide a pseudo-Newtonian reformulation of
geometrostatics, and prove uniqueness of static photon spheres.

View original: http://arxiv.org/abs/1201.5433