Geometrostatics: The Geometry of Static Space-Times

  • Carla CederbaumEmail author
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 157)


We present a new geometric approach to the study of static isolated general relativistic systems for which we suggest the name geometrostatics. After describing the setup, we introduce localized formulas for the ADM-mass and ADM/CMC-center of mass of geometrostatic systems. We then explain the pseudo-Newtonian character of these formulas and show that they converge to Newtonian mass and center of mass in the Newtonian limit, respectively, using Ehlers’ frame theory. Moreover, we present a novel physical interpretation of the level sets of the canonical lapse function and apply it to prove uniqueness results. Finally, we suggest a notion of force on test particles in geometrostatic space-times.


Test Particle Weighted Sobolev Space Equipotential Surface Newtonian Potential Constant Mean Curvature 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsEberhard Karls Universität TübingenTübingenGermany

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