Analysis of Black Hole Solutions in Parabolic Class Using Neural Networks

Abstract

In this paper, we introduce a numerical method based on Artificial Neural Networks (ANNs) for the analysis of black hole solutions to the Einstein-axion-dilaton system in a high dimensional parabolic class. Leveraging a profile root-finding technique based on General Relativity we describe an ANN solver to directly tackle the system of ordinary differential equations. Through our extensive numerical analysis, we demonstrate, for the first time, that there is no self-similar critical solution for the parabolic class in the high dimensions of space-time. Specifically, we develop $95\%$ ANN-based confidence intervals for all the solutions in their domains. At the $95\%$ confidence level, our ANN estimators confirm that there is no black hole solution in higher dimensions, hence the gravitational collapse does not occur. Results provide some doubts about the universality of the Choptuik phenomena. Therefore, we conclude that the fastest-growing mode of the perturbations that determine the critical exponent does not exist for the parabolic class in the high dimensions.

arXiv commentV4: 24 pages, 15 figures. Matched with Published version in The European Physical Journal C. All the codes related to different parts of the paper are added in this repository: \url{https://github.com/gramuah/ann4bh}

References in corpus (33)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Recent Advances and Applications of Deep Learning Methods in Materials Science
• Strong-Weak Coupling Duality in Four Dimensional String Theory
• Observation of critical phenomena and self-similarity in the gravitational collapse of radiation fluid
• Critical behaviour in gravitational collapse of radiation fluid --- A renormalization group (linear perturbation) analysis ---
• Choptuik Scaling and Quasinormal Modes in the AdS/CFT Correspondence
• The spherically symmetric collapse of a massless scalar field
• Non-Universality of Critical Behaviour in Spherically Symmetric Gravitational Collapse
• Critical formation of trapped surfaces in the collision of gravitational shock waves
• Universal Scaling and Echoing in Gravitational Collapse of a Complex Scalar Field
• On Choptuik's scaling in higher dimensions
• Stability, Tunneling and Flux Changing de Sitter Transitions in the Large Volume String Scenario
• Criticality and Bifurcation in the Gravitational Collapse of a Self-Coupled Scalar Field
• Evidence for Non-perturbative String Symmetries
• Critical Exponents and Stability at the Black Hole Threshold for a Complex Scalar Field
• Continuous Self-Similarity and $S$-Duality
• ADM reduction of IIB on $H^{p,q}$ and dS braneworld
• Universality and Scaling at the Onset of Quantum Black Hole Formation
• $N^3$ entropy of M5 branes from dielectric effect
• S-Duality at the Black Hole Threshold in Gravitational Collapse
• Scaling Phenomena in Gravity from QCD
• Dimension-Dependence of the Critical Exponent in Spherically Symmetric Gravitational Collapse
• Spherically symmetric scalar field collapse in any dimension
• Critical gravitational collapse: towards a holographic understanding of the Regge region
• Self-similarity in Einstein-Maxwell-dilaton theories and critical collapse
• Critical Collapse in the Axion-Dilaton System in Diverse Dimensions
• More On Critical Collapse of Axion-Dilaton System in Dimension Four
• On Perturbation Theory and Critical Exponents for Self-Similar Systems
• On Critical Exponents for Self-Similar Collapse
• On self-similar axion-dilaton configurations
• On Higher Dimensional Self-Similar Axion-Dilaton Solutions
• Estimation of Critical Collapse Solutions to Black Holes with Nonlinear Statistical Models

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