Critical Behavior in a Massless Scalar Field Collapse with Self-interaction Potential

Abstract

We examine a one-parameter family of analytical solutions representing spherically symmetric collapse of a nonlinear massless scalar field with self-interaction in an asymptotically flat spacetime. The time evolution exhibits a type of critical behavior. Depending on the scalar charge parameter $q$ as compared to a critical value $q^{\ast }$, the incoming scalar wave collapses either to a globally naked central singularity if $q<q^{\ast }$ (weak field) or to a scalar-hairy black hole if $q>q^{\ast }$ (strong field), both having finite asymptotic masses. Near the critical evolution, the black hole mass follows a product-logarithmic scaling law: $-M^2\ln M\sim q-q^{\ast }$ with $0<M\ll 1$ and $q>q^{\ast }$. The solution admits no self-similarity and satisfies the null and the strong energy conditions.

arXiv comment19 pages, 6 figures

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• Examples of naked singularity formation in higher-dimensional Einstein-vacuum spacetimes
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• AdS and Lifshitz Scalar Hairy Black Holes in Gauss-Bonnet Gravity
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• Holographic equation of state in fluid/gravity duality
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• Multiple critical gravitational collapse of charged scalar with reflecting wall
• Self-similar solutions and critical behavior in Einstein-Maxwell-dilaton theory sourced by charged null fluids
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