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arXiv · 2304.10627

Einstein-Dirac system in semiclassical gravity

Ben Kain
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Abstract

We study the Dirac equation minimally coupled to general relativity using quantum field theory and the semiclassical gravity approximation. Previous studies of the Einstein-Dirac system did not quantize the Dirac field and required multiple independent Dirac fields to preserve spherical symmetry. We canonically quantize a single Dirac field in a static spherically symmetric curved spacetime background. Using the semiclassical gravity approximation, in which the Einstein field equations are sourced by the expectation value of the stress-energy-momentum tensor, we derive a system of equations whose solutions describe static spherically symmetric self-gravitating configurations of identical quantum spin-1/2 particles. We self-consistently solve these equations and present example configurations. Although limiting cases of our semiclassical system of equations reproduce the multi-field system of equations found in the literature, our system of equations is derived from the excitations of a single quantum field.

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Ben Kain. 2023-04-20. Einstein-Dirac system in semiclassical gravity. https://doi.org/10.1103/physrevd.107.124001

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