The Singularity Threshold of the Nonlinear Sigma Model Using 3D Adaptive Mesh Refinement
arXiv:gr-qc/0202093 · doi:10.1103/PhysRevD.66.041703
Abstract
Numerical solutions to the nonlinear sigma model (NLSM), a wave map from 3+1 Minkowski space to S^3, are computed in three spatial dimensions (3D) using adaptive mesh refinement (AMR). For initial data with compact support the model is known to have two regimes, one in which regular initial data forms a singularity and another in which the energy is dispersed to infinity. The transition between these regimes has been shown in spherical symmetry to demonstrate threshold behavior similar to that between black hole formation and dispersal in gravitating theories. Here, I generalize the result by removing the assumption of spherical symmetry. The evolutions suggest that the spherically symmetric critical solution remains an intermediate attractor separating the two end states.
5 pages, 5 figures, 1 table; To be published in Phys. Rev. D.; Added discussion of initial data; Added figure and references
Cited by in corpus (48)
- Evolutions in 3D numerical relativity using fixed mesh refinement
- Echoes of ECOs: gravitational-wave signatures of exotic compact objects and of quantum corrections at the horizon scale
- Critical phenomena in gravitational collapse
- Neutron-star mergers in scalar-tensor theories of gravity
- Effects of the microphysical Equation of State in the mergers of magnetized Neutron Stars With Neutrino Cooling
- Magnetized Neutron Star Mergers and Gravitational Wave Signals
- The Large-Misalignment Mechanism for the Formation of Compact Axion Structures: Signatures from the QCD Axion to Fuzzy Dark Matter
- Critical phenomena in gravitational collapse (Physics Reports)
- Gravitational Wave Signatures of Highly Compact Boson Star Binaries
- Simulating binary neutron stars: dynamics and gravitational waves
- Magnetospheres of Black Hole Systems in Force-Free Plasma
- On the final fate of compact boson star mergers
- Characteristic extraction in numerical relativity: binary black hole merger waveforms at null infinity
- Critical Collapse of the Massless Scalar Field in Axisymmetry
- Intense Electromagnetic Outbursts from Collapsing Hypermassive Neutron Stars
- Mergers of Magnetized Neutron Stars with Spinning Black Holes: Disruption, Accretion and Fallback
- Relativistic MHD with Adaptive Mesh Refinement
- Black Hole Dynamics in Einstein-Maxwell-Dilaton Theory
- Binary black holes' effects on electromagnetic fields
- Understanding possible electromagnetic counterparts to loud gravitational wave events: Binary black hole effects on electromagnetic fields
- Neutron star mergers as a probe of modifications of general relativity with finite-range scalar forces
- Modeling magnetized neutron stars using resistive MHD
- The Current Status of Binary Black Hole Simulations in Numerical Relativity
- Electromagnetic Luminosity of the Coalescence of Charged Black Hole Binaries
- Perturbed disks get shocked. Binary black hole merger effects on accretion disks
- Black Hole Excision with Multiple Grid Patches
- Linking electromagnetic and gravitational radiation in coalescing binary neutron stars
- The instability \& gravitational wave signal in binary neutron star mergers
- Massively Parallel Simulations of Binary Black Hole Intermediate-Mass-Ratio Inspirals
- Boosting jet power in black hole spacetimes
- Gravitational wave signatures of dark matter cores in binary neutron star mergers by using numerical simulations
- A Simflowny-based finite-difference code for high-performance computing in Relativity
- Adaptive Mesh Refinement for Coupled Elliptic-Hyperbolic Systems
- Interaction of misaligned magnetospheres in the coalescence of binary neutron stars
- Critical Behavior in the Gravitational Collapse of a Scalar Field with Angular Momentum in Spherical Symmetry
- The role of the ergosphere in the Blandford-Znajek process
- Magnetosphere of a Kerr black hole immersed in magnetized plasma and its perturbative mode structure
- Adaptive hp-Refinement for Spectral Elements in Numerical Relativity
- Adaptive Mesh Refinement for Characteristic Grids
- Towards fidelity and scalability in non-vacuum mergers
- A semi-linear wave model for critical collapse
- A Numerical Method for Studying Super-Eddington Mass Transfer in Double White Dwarf Binaries
- The Nonlinear Sigma Model With Distributed Adaptive Mesh Refinement
- Threshold of Singularity Formation in the Semilinear Wave Equation
- Adaptive Event Horizon Tracking and Critical Phenomena in Binary Black Hole Coalescence
- Maxwell-dilaton dynamics
- A User-Friendly Python Interface for the Numerical Relativity Code AMSS-NCKU
- Gamma-radiation sky maps from compact binaries