On Critical Exponents for Self-Similar Collapse

Abstract

We explore systematically perturbations of self-similar solutions to the Einstein-axion-dilaton system, whose dynamics are invariant under spacetime dilations combined with internal $SL(2,R)$ transformations. The self-similar solutions capture the enticing behavior critical systems on the verge of gravitational collapse, in arbitrary spacetime dimensions. Our methods rest on a combination of analytical and numerical tools, apply to all three conjugacy classes of $SL(2,R)$ transformations and allow accurate estimates of the corresponding Choptuik exponents. It is well known that these exponents depend on the spacetime dimension and on the matter content. Our main result is that they also attain different values, even within a given conjugacy class, for the distinct types of critical solutions that we recently identified in the Einstein-axion-dilaton system.

arXiv commentV3: 29 pages, 4 figures and published version in JHEP

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• On Perturbation Theory and Critical Exponents for Self-Similar Systems
• On Higher Dimensional Self-Similar Axion-Dilaton Solutions
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• Analysis of Black Hole Solutions in Parabolic Class Using Neural Networks
• Estimation of Critical Collapse Solutions to Black Holes with Nonlinear Statistical Models
• Sequential Monte Carlo with Cross-validated Neural Networks for Complexity of Hyperbolic Black Hole Solutions in 4D
• Neural Networks Assisted Metropolis-Hastings for Bayesian Estimation of Critical Exponent on Elliptic Black Hole Solution in 4D Using Quantum Perturbation Theory