Perturbation method for particlelike solutions of Einstein-Dirac equations
Simona Rota Nodari (CEREMADE)
TL;DR
This paper demonstrates the existence of static, spherically symmetric solutions to the Einstein-Dirac equations for two fermions using a perturbation approach, linking them to solutions of the nonlinear Choquard equation.
Contribution
It introduces a perturbation method to prove solutions of Einstein-Dirac equations and connects these solutions to the nonlinear Choquard equation.
Findings
Solutions exist for the Einstein-Dirac system under specified conditions.
Nondegenerate solutions of the Choquard equation generate Einstein-Dirac solutions.
The method provides a new approach to analyze coupled Einstein-Dirac systems.
Abstract
The aim of this work is to prove by a perturbation method the existence of solutions of the coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state. We relate the solutions of our equations to those of the nonlinear Choquard equation and we show that the nondegenerate solution of Choquard's equation generates solutions for Einstein-Dirac equations.
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