Particle-Like Solutions of the Einstein-Dirac-Maxwell Equations
Felix Finster, Joel Smoller, and Shing-Tung Yau
TL;DR
This paper constructs and analyzes regular, soliton-like solutions to the coupled Einstein-Dirac-Maxwell equations for two fermions, revealing stable configurations even under strong electromagnetic repulsion.
Contribution
It introduces numerical solutions for the Einstein-Dirac-Maxwell system, demonstrating the existence of stable, regular configurations with strong electromagnetic interactions.
Findings
Solutions exist with strong electromagnetic repulsion
Solutions are regular and well-behaved
Ground state properties vary with electromagnetic coupling
Abstract
We consider the coupled Einstein-Dirac-Maxwell equations for a static, spherically symmetric system of two fermions in a singlet spinor state. Soliton-like solutions are constructed numerically. The stability and the properties of the ground state solutions are discussed for different values of the electromagnetic coupling constant. We find solutions even when the electromagnetic coupling is so strong that the total interaction is repulsive in the Newtonian limit. Our solutions are regular and well-behaved; this shows that the combined electromagnetic and gravitational self-interaction of the Dirac particles is finite.
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