Particle-Like Solutions of the Einstein-Dirac Equations

Details Particle-Like Solutions of the Einstein-Dirac Equations Particle-Like Solutions of the Einstein-Dirac Equations

1998-01-22

arxiv.org/abs/gr-qc/9801079v3

Phys.Rev.D59:104020,1999

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

31 pages, LaTeX, 21 PostScript figures, some references added

Scientific paper

10.1103/PhysRevD.59.104020

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 soliton-like solutions of these equations. The stability of the solutions is analyzed. For weak coupling (i.e., 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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