Convergence to a self-similar solution in general relativistic gravitational collapse

Abstract

We study the spherical collapse of a perfect fluid with an equation of state $P=k\rho$ by full general relativistic numerical simulations. For $0<k\alt 0.036$, it has been known that there exists a general relativistic counterpart of the Larson-Penston self-similar Newtonian solution. The numerical simulations strongly suggest that, in the neighborhood of the center, generic collapse converges to this solution in an approach to a singularity and that self-similar solutions other than this solution, including a ``critical solution'' in the black hole critical behavior, are relevant only when the parameters which parametrize initial data are fine-tuned. This result is supported by a mode analysis on the pertinent self-similar solutions. Since a naked singularity forms in the general relativistic Larson-Penston solution for $0<k\alt0.0105$, this will be the most serious known counterexample against cosmic censorship. It also provides strong evidence for the self-similarity hypothesis in general relativistic gravitational collapse. The direct consequence is that critical phenomena will be observed in the collapse of isothermal gas in Newton gravity, and the critical exponent $\gamma$ will be given by $\gamma \approx 0.11$, though the order parameter cannot be the black hole mass.

22 pages, 15 figures, accepted for publication in Physical Review D, reference added, typos corrected

Cited by in corpus (60)

• Critical phenomena in gravitational collapse
• Critical phenomena in gravitational collapse (Physics Reports)
• Why do naked singularities form in gravitational collapse?
• Equilibrium configurations from gravitational collapse
• Non-singular quantum-inspired gravitational collapse
• Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity
• Spherical gravitational collapse in N-dimensions
• Effects of Gauss-Bonnet term on the final fate of gravitational collapse
• Self-similar cosmological solutions with dark energy. II: black holes, naked singularities and wormholes
• The Similarity Hypothesis in General Relativity
• Gravitational collapse of an isentropic perfect fluid with a linear equation of state
• Can a primordial black hole or wormhole grow as fast as the universe?
• Effects of Lovelock terms on the final fate of gravitational collapse: analysis in dimensionally continued gravity
• Stability criterion for self-similar solutions with a scalar field and those with a stiff fluid in general relativity
• Time Delay between Relativistic Images as a probe of Cosmic Censorship
• No Go Theorem for Kinematic Self-Similarity with A Polytropic Equation of State
• Self-similar cosmological solutions with dark energy. I: formulation and asymptotic analysis
• Stability criterion for self-similar solutions with perfect fluids in general relativity
• Genericity aspects in gravitational collapse to black holes and naked singularities
• Critical gravitational collapse: towards a holographic understanding of the Regge region
• Dimensional Dependence of Black Hole Formation in Self-Similar Collapse of Scalar Field
• Role of initial data in spherical collapse
• Border of Spacetime
• Einstein-Cartan gravitational collapse of a homogeneous Weyssenhoff fluid
• The role of anisotropy and inhomogeneity in Lemaitre-Tolman-Bondi collapse
• Cauchy horizon stability in self-similar collapse: scalar radiation
• Three parameter metrics in the presence of a scalar field in four and higher dimensions
• Critical phenomena in Newtonian gravity
• On the global visibility of a singularity in spherically symmetric gravitational collapse
• Trapped surfaces and nature of singularities in Lyra's geometry
• Curvature driven diffusion, Rayleigh-Plateau, and Gregory-Laflamme
• Gravitational collapse with tachyon field and barotropic fluid
• Einstein-Rosen waves and the self-similarity hypothesis in cylindrical symmetry
• Instability of black hole formation under small pressure perturbations
• Criticality and convergence in Newtonian collapse
• Formation of regular black hole from baryonic matter
• All black holes in Lemaitre-Tolman-Bondi inhomogeneous dust collapse
• Semiclassical Instability of the Cauchy Horizon in Self-Similar Collapse
• Odd-parity perturbations of self-similar Vaidya spacetime
• Inside charged black holes I. Baryons
• Black hole formation from the gravitational collapse of a non-spherical network of structures
• Critical Collapse of an Ultrarelativistic Fluid in the $\Gamma \to 1$ Limit
• Odd Parity Perturbations of the Self-Similar LTB Spacetime
• Kinematics of discretely self-similar spherically symmetric spacetimes
• Spherically symmetric perfect fluid in area-radial coordinates
• High-Speed Collapse of a Hollow Sphere of Type I Matter
• Bounds for scalar waves on self-similar naked-singularity backgrounds
• Non-Singular Collapse Scenario From Matter-Curvature Coupling
• Asymptotically Friedmann self-similar scalar field solutions with potential
• Renormalization group approach to Einstein-Rosen waves
• Energy emission from high curvature region and its backreation
• Self-similar motion of a Nambu-Goto string
• Electromagnetic radiation due to naked singularity formation in self-similar gravitational collapse
• Gravitational Collapse of an Imperfect Non Adiabatic Fluid
• Accelerating FJNW Metric
• Stability analysis of self-similar behaviors in perfect fluid gravitational collapse
• The Modification of the Oppenheimer and Snyder Collapsing Dust Ball to a Static Ball in Discrete Space-time
• Dynamics of Rarefaction Waves in General-Relativistic Collapsing Clouds
• Breakdown of self-similar evolution in homogeneous perfect fluid collapse
• Gravitational shocks as a key ingredient of Gamma-Ray Bursts