Particlelike solutions of the Einstein-Dirac equations - art. no. 104020

The coupled Einstein-Dirac equations for a static, spherically symmetric sy stem 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 ( i.e., small rest mass of the fermions), all the solutions are linearly stab le (with respect to spherically symmetric perturbations), whereas for stron ger coupling, both stable and unstable solutions exist. For the physical in terpretation, 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 re gular and well behaved even for strong coupling. [S0556-2821(99)00708-0].