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Geometrostatics: The Geometry of Static Space-Times

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

Abstract

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.

Keywords

Test Particle Weighted Sobolev Space Equipotential Surface Newtonian Potential Constant Mean Curvature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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