Critical exact solutions for self-gravitating Dirac fields

Abstract

We consider the Einstein-Dirac field equations describing a self-gravitating massive neutrino, looking for axially-symmetric exact solutions; in the search of general solutions, we find some that are specific and which have critical features, such as the fact that the space-time curvature turns out to be flat and the spinor field gives rise to a vanishing bi-linear scalar $\overline{\psi }\psi =0$ with non-vanishing bi-linear pseudo-scalar $i\overline{\psi }{\gamma }^5\psi \ne 0$: because in quantum field theory general computational methods are built on plane-wave solutions, for which bi-linear pseudo-scalar vanishes while the bi-linear scalar does not vanish, then the solutions we found cannot be treated with the usual machinery of quantum field theory. This means that for the Einstein-Dirac system there exist admissible solutions which nevertheless cannot be quantized with the common prescriptions; we regard this situation as yet another issue of tension between Einstein gravity and quantum principles. Possible ways to quench this tension can be seen either in enlarging the validity of quantum field theory or by restricting the space of the solutions of the Einstein-Dirac system of field equations.

12 pages

References in corpus (1)

• Palatini Approach to Modified Gravity: f(R) Theories and Beyond

Cited by in corpus (9)

• MGD Dirac stars
• Singularity-free spinors in gravity with propagating torsion
• Fundamental Theory of Torsion Gravity
• Spinor Fields, Singular Structures, Charge Conjugation, ELKO and Neutrino Masses
• Exotic fermionic fields and minimal length
• Axially-Symmetric Exact Solutions for Flagpole Fermions with Gravity
• Spinor solutions of a Chern-Simons model for the superconformal algebra
• Angular-Radial Integrability of Coulomb-like Potentials in Dirac Equations
• Integrability of Dirac equations in static spherical space-times