Existence and Newtonian limit of nonlinear bound states in the Einstein-Dirac system

TL;DR

This paper proves the existence of nonlinear bound states in the Einstein-Dirac system in the Newtonian limit and shows they can be approximated by solutions of the Newton-Schrödinger system, bridging relativistic and non-relativistic quantum models.

Contribution

It establishes the existence of particlelike bound states in the Einstein-Dirac system near the Newtonian limit and connects these states to Newton-Schrödinger solutions, a novel analytical result.

Findings

Bound states exist in the almost Newtonian regime.

These states can be approximated by Newton-Schrödinger solutions.

The analysis bridges Einstein-Dirac and Newtonian quantum models.

Abstract

An analysis is given of particlelike nonlinear bound states in the Newtonian limit of the coupled Einstein-Dirac system introduced by Finster, Smoller and Yau. A proof is given of existence of these bound states in the almost Newtonianian regime, and it is proved that they may be approximated by the energy minimizing solution of the Newton-Schr\"odinger system obtained by Lieb.