The Schr\"odinger-Newton equation as non-relativistic limit of self-gravitating Klein-Gordon and Dirac fields
Domenico Giulini (1,2), Andr\'e Gro{\ss}ardt (1,2) ((1) ZARM -, University of Bremen - Germany, (2) Institute for Theoretical Physics -, University of Hannover - Germany)
TL;DR
This paper derives the Schrödinger-Newton equation as a non-relativistic limit of the Einstein-Klein-Gordon and Einstein-Dirac systems using a WKB-like expansion, linking quantum mechanics and gravity.
Contribution
It demonstrates how the Schrödinger-Newton equation emerges from relativistic field equations in the non-relativistic limit, providing a theoretical bridge between quantum fields and gravity.
Findings
Schrödinger-Newton equation derived from Einstein-Klein-Gordon system
Schrödinger-Newton equation derived from Einstein-Dirac system
Establishes a non-relativistic limit connecting quantum fields and gravity
Abstract
In this paper we show that the Schr\"odinger-Newton equation for spherically symmetric gravitational fields can be derived in a WKB-like expansion in 1/c from the Einstein-Klein-Gordon and Einstein-Dirac system.
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