Hyperplane-Symmetric Static Einstein-Dirac Spacetime

TL;DR

This paper derives exact solutions for Einstein-Dirac equations in static, hyperplane-symmetric spacetimes across arbitrary dimensions, revealing how mass and constraints influence the coupling and spacetime structure.

Contribution

It provides the first general solutions to Einstein-Dirac equations in this setting, including explicit curvature invariants and geodesic equations, with analysis of mass effects and singularities.

Findings

Only massive Dirac fields couple to spacetime via Einstein equations.

Massless Dirac fields require constraints to eliminate off-diagonal energy-momentum components.

Explicit expressions for Ricci and Kretschmann scalars reveal physical singularities.

Abstract

We derive the general solution to the coupled Einstein and Dirac field equations in static and hyperplane-symmetric spacetime of arbitrary dimension including a cosmological constant of either sign. As a result, only a massful Dirac field couples via the Einstein equations to spacetime, and in the massless case the Dirac field is required to fulfill appropriate constraints in order to eliminate off-diagonal components of the energy-momentum tensor. We also give explicit expressions for curvature invariants including the Ricci scalar and the Kretschmann scalar, indicating physical singularities. Moreover, we reduce the general solution of the geodesic equation to quadratures.