Particle-Like Solutions of the Einstein-Dirac Equations

Abstract

The coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state are derived. Using numerical methods, we construct an infinite number of soliton-like solutions of these equations. The stability of the solutions is analyzed. For weak coupling (i.e., small rest mass of the fermions), all the solutions are linearly stable (with respect to spherically symmetric perturbations), whereas for stronger coupling, both stable and unstable solutions exist. For the physical interpretation, we discuss how the energy of the fermions and the (ADM) mass behave as functions of the rest mass of the fermions. Although gravitation is not renormalizable, our solutions of the Einstein-Dirac equations are regular and well-behaved even for strong coupling.

31 pages, LaTeX, 21 PostScript figures, some references added

Cited by in corpus (72)

• Traversable wormholes in Einstein-Dirac-Maxwell theory
• The Schrödinger-Newton equation as non-relativistic limit of self-gravitating Klein-Gordon and Dirac fields
• Asymptotically flat scalar, Dirac and Proca stars: discrete vs. continuous families of solutions
• Asymptotically flat spinning scalar, Dirac and Proca stars
• Non-Existence of Time-Periodic Solutions of the Dirac Equation in a Reissner-Nordstrom Black Hole Background
• Stability Analysis and Area Spectrum of 3-Dimensional Lifshitz Black Holes
• Fermions without Vierbeins in Curved Space-Time
• Dirac quasinormal frequencies in Schwarzschild-AdS space-time
• Fermions in gravity with local spin-base invariance
• Multipolar boson stars: macroscopic Bose-Einstein condensates akin to hydrogen orbitals
• The Penrose process, superradiance and ergoregion instabilities
• Tideless Traversable Wormholes surrounded by cloud of strings in $f(R)$ gravity
• Fermion soliton stars
• Dirac star in the presence of Maxwell and Proca fields
• Constructing spherically symmetric Einstein-Dirac systems with multiple spinors: Ansatz, wormholes and other analytical solutions
• Dirac stars supported by nonlinear spinor fields
• Existence and Newtonian limit of nonlinear bound states in the Einstein-Dirac system
• Einstein-Dirac-Maxwell wormholes: ansatz, construction and properties of symmetric solutions
• Global surpluses of spin-base invariant fermions
• Supersymmetric Multi-trace Boundary Conditions in AdS
• Spontaneous growth of spinor fields in gravity
• Spin-base invariance of Fermions in arbitrary dimensions
• Maximum mass of relativistic self-gravitating Bose-Einstein condensates with repulsive or attractive $|\phi {|}^4$ self-interaction
• Dirac star with SU(2) Yang-Mills and Proca fields
• Virial identities in relativistic gravity: 1D effective actions and the role of boundary terms
• The Interaction of Dirac Particles with Non-Abelian Gauge Fields and Gravity - Bound States
• Tidal Love numbers and approximate universal relations for fermion soliton stars
• Critical Phenomena in the Einstein-Massless-Dirac System
• The normalized energy eigenspinors of the Dirac field on anti-de Sitter spacetime
• Boson and Dirac stars in $D\ge 4$ dimensions
• Spinning gauged boson and Dirac stars: a comparative study
• Lightlike limit of the boosted Kerr black holes in higher-dimensional spacetimes
• Dirac-boson stars
• Deconstructing scaling virial identities in General Relativity: spherical symmetry and beyond
• Structure of the confining solutions for SU(3)-Yang-Mills equations and confinement mechanism
• Perturbing the ground state of Dirac stars
• Axially symmetric Proca-Higgs boson stars
• Nonlinear effects in the excited states of many-fermion Einstein-Dirac solitons
• Einstein-Dirac system in semiclassical gravity
• Probing the connection between entangled particles and wormholes in general relativity
• Are Einstein-Dirac-Maxwell wormholes traversable?
• Fermion self-trapping in the optical geometry of Einstein-Dirac solitons
• Infinite-redshift localized states of Dirac fermions under Einsteinian gravity
• The repulsive nature of naked singularities from the point of view of Quantum Mechanics
• Einstein-Dirac-Maxwell wormholes in quantum field theory
• Spinor Walls in Five-Dimensional Warped Spacetime
• Polarons as stable solitary wave solutions to the Dirac-Coulomb system
• Quantum Oscillations Can Prevent the Big Bang Singularity in an Einstein-Dirac Cosmology
• Some properties of Dirac-Einstein bubbles
• Spinor domain wall and test fermions on an arbitrary domain wall
• Conservative discretization of the Einstein-Dirac equations in spherically symmetric spacetime
• Some Recent Progress in Classical General Relativity
• Gravitationally localized states of two neutral fermions interacting with a Higgs field
• Time-dependent Spinor field in a static cylindrically-symmetric space-time
• Spinor field solutions in $F\left(B^2\right)$ modified Weyl gravity
• Polar form of Dirac fields: implementing symmetries via Lie derivative
• The Spacetime of a Dirac Fermion
• Rapidly rotating Dirac stars
• A Mechanism for Dark Matter and Dark Energy in the Theory of Causal Fermion Systems
• Dirac stars with wormhole topology
• Boson Stars in Bumblebee Gravity and Their Gravitational Waveforms from Extreme-Mass-Ratio Inspirals
• The Interaction of Gravity with Other Fields
• A Spatially Homogeneous and Isotropic Einstein-Dirac Cosmology
• Static and collapsing configurations supported by the spinor fluid
• Super-Symmetric Coupling: Existence and Multiplicity
• Rotating wormholes in Einstein-Dirac-Maxwell theory
• 'Stealth' singularities from self-gravitating fermions
• Tidal Love numbers and the dynamical instability of AdS bubbles
• Self-gravitating nonlinear Dirac fields
• Phase transition of spacetime: particles as black holes in anti-de Sitter space
• Model of a spin-$1/2$ electric charge in $F\left(B^2\right)$ modified Weyl gravity
• Integrability of Dirac equations in static spherical space-times