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Particlelike solutions of the Einstein-Dirac equations

Felix Finster Joel Smoller Shing-Tung Yau

Theoretical Physics mathscidoc:1912.43529

Physical Review D, 59, (10), 104020, 1999.4
The coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state are derived. Using numerical methods, we construct an infinite number of solitonlike solutions of these equations. The stability of the solutions is analyzed. For weak coupling (ie, small rest mass of the fermions), all the solutions are linearly stable (with respect to spherically symmetric perturbations), whereas for stronger coupling, both stable and unstable solutions exist. For the physical interpretation, we discuss how the energy of the fermions and the (ADM) mass behave as functions of the rest mass of the fermions. Although gravitation is not renormalizable, our solutions of the Einstein-Dirac equations are regular and well behaved even for strong coupling.
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@inproceedings{felix1999particlelike,
  title={Particlelike solutions of the Einstein-Dirac equations},
  author={Felix Finster, Joel Smoller, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203833481402093},
  booktitle={Physical Review D},
  volume={59},
  number={10},
  pages={104020},
  year={1999},
}
Felix Finster, Joel Smoller, and Shing-Tung Yau. Particlelike solutions of the Einstein-Dirac equations. 1999. Vol. 59. In Physical Review D. pp.104020. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203833481402093.
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