Einstein-Dirac system in semiclassical gravity

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.

17 pages, 2 figures

References in corpus (11)

• Asymptotically flat scalar, Dirac and Proca stars: discrete vs. continuous families of solutions
• Cylindrical wormholes
• Dirac star in the presence of Maxwell and Proca fields
• Critical Behavior in the Gravitational Collapse of a Scalar Field with Angular Momentum in Spherical Symmetry
• Constructing spherically symmetric Einstein-Dirac systems with multiple spinors: Ansatz, wormholes and other analytical solutions
• Dirac star with SU(2) Yang-Mills and Proca fields
• Stealth spontaneous spinorization of relativistic stars
• Non-Abelian Proca-Dirac-Higgs theory: particle-like solutions and their energy spectrum
• Perturbing the ground state of Dirac stars
• Nonlinear effects in the excited states of many-fermion Einstein-Dirac solitons
• Conservative discretization of the Einstein-Dirac equations in spherically symmetric spacetime