SMuK 2021 – wissenschaftliches Programm
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GR: Fachverband Gravitation und Relativitätstheorie
GR 6: Numerical relativity
GR 6.1: Vortrag
Mittwoch, 1. September 2021, 16:30–16:45, H6
The rotating mass shell in general relativity — •Florian Atteneder1, Tobias Benjamin Russ2, Reinhard Alkofer3, and Helios Sanchis-Alepuz3 — 1Theoretical Physics Institute, University of Jena, Jena, Germany — 2Theoretical Physics, Ludwig Maxmillians University, Munich, Germany — 3Institute of Physics, University of Graz, Graz, Austria
The model of a rotating mass shell (RMS) was initially introduced to judge if rotation has only relative meaning. It comprises a description of a spacetime with an energy-matter content that is assembled in a statically rotating quasi-spherical shell with zero radial extension. Latest perturbation theory (PT) calculations have shown that relativity of rotation is indeed realized in such a spacetime. However, because this conclusion was based on PT, its validity is limited to slowly RMSs. This work pursues a numerical treatment of the problem, where the mathematical formulation involves a splitting of the spacetime into a region that is flat and one that is asymptotically flat. The latter is used as a reference to define relative rotation. The RMS forms at the common boundary of these two regions. On the basis of previous work, we formulate Einstein's equations as a free-boundary value problem and solve them numerically using a pseudo-spectral method. As a result we obtain a three-parameter solution that is characterized by the shell's polar radius, its gravitational mass and angular momentum. The existence of the solution is enough to positively answer the question if Mach's idea of relativity of rotation can be extended for rapidly RMSs.