Critical phenomena in the gravitational collapse of electromagnetic waves

Abstract

We numerically investigate the threshold of black-hole formation in the gravitational collapse of electromagnetic waves in axisymmetry. We find approximate power-law scaling ${\rho }_{\max }\sim ({\eta }_{\ast }-\eta {)}^{-2\gamma }$ of the maximum density in the time evolution of near-subcritical data with $\gamma \simeq 0.145$, where $\eta$ is the amplitude of the initial data. We directly observe approximate discrete self-similarity in near-critical time evolutions with a log-scale echoing period of $\Delta \simeq 0.55$. The critical solution is approximately the same for two families of initial data, providing some evidence of universality. Neither the discrete self-similarity nor the universality, however, are exact. We speculate that the absence of an exactly discrete self-similarity might be caused by the interplay of electromagnetic and gravitational wave degrees of freedom, or by the presence of higher-order angular multipoles, or both, and discuss implications of our findings for the critical collapse of vacuum gravitational waves.

arXiv comment5 pages, 3 figures; version accepted for publication in PRL

References in corpus (36)

• On the Numerical Integration of Einstein's Field Equations
• Gauge conditions for long-term numerical black hole evolutions without excision
• New Formalism for Numerical Relativity
• Observation of critical phenomena and self-similarity in the gravitational collapse of radiation fluid
• Critical phenomena in gravitational collapse
• Critical behaviour in gravitational collapse of radiation fluid --- A renormalization group (linear perturbation) analysis ---
• Critical phenomena in gravitational collapse (Physics Reports)
• A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
• Numerical relativity simulations of binary neutron stars
• Understanding critical collapse of a scalar field
• Non-Universality of Critical Behaviour in Spherically Symmetric Gravitational Collapse
• Covariant formulations of BSSN and the standard gauge
• The Choptuik spacetime as an eigenvalue problem
• Numerical Relativity in Spherical Polar Coordinates: Evolution Calculations with the BSSN Formulation
• Deriving formulations for numerical computation of binary neutron stars in quasicircular orbits
• Scaling of curvature in sub-critical gravitational collapse
• BSSN equations in spherical coordinates without regularization: vacuum and non-vacuum spherically symmetric spacetimes
• SENR/NRPy+: Numerical Relativity in Singular Curvilinear Coordinate Systems
• Critical Behaviour and Universality in Gravitational Collapse of a Charged Scalar Field
• Gravitational Collapse of Gravitational Waves in 3D Numerical Relativity
• Numerical evolution of Brill waves
• Global structure of Choptuik's critical solution in scalar field collapse
• The Einstein constraints: uniqueness and non-uniqueness in the conformal thin sandwich approach
• Collapse of Nonlinear Gravitational Waves in Moving-Puncture Coordinates
• Constrained evolution in axisymmetry and the gravitational collapse of prolate Brill waves
• On critical collapse of gravitational waves
• Numerical Relativity in Spherical Polar Coordinates: Off-center Simulations
• Evolutions of centered Brill waves with a pseudospectral method
• Critical collapse of rotating radiation fluids
• Aspherical deformations of the Choptuik spacetime
• Critical phenomena in the aspherical gravitational collapse of radiation fluids
• Multi-oscillating Boson Stars
• Slicing conditions for axisymmetric gravitational collapse of Brill waves
• Critical gravitational collapse with angular momentum II: soft equations of state
• Critical gravitational collapse with angular momentum
• Critical collapse of ultra-relativistic fluids: damping or growth of aspherical deformations

Cited by in corpus (16)

• Universality of curvature invariants in critical vacuum gravitational collapse
• Critical phenomena in the collapse of gravitational waves
• Evolution of Brill waves with an adaptive pseudospectral method
• Critical phenomena in the gravitational collapse of electromagnetic dipole and quadrupole waves
• Critical phenomena in the collapse of quadrupolar and hexadecapolar gravitational waves
• A semi-linear wave model for critical collapse
• Formulation Improvements for Critical Collapse Simulations
• Relativistic radiation hydrodynamics in a reference-metric formulation
• Dynamics of gravitational collapse in the axisymmetric Einstein-Vlasov system
• Critical phenomena in gravitational collapse with competing scalar field and gravitational waves, in 4+1 dimensions
• New results on the dynamics of critical collapse
• Energy in critical collapse
• Twist and higher modes of a complex scalar field at the threshold of collapse
• Gravitational collapse in the vicinity of the extremal black hole critical point
• Comparison of linear Brill and Teukolsky waves
• Pseudospectral implementation of the Einstein-Maxwell system