Estimation of Critical Collapse Solutions to Black Holes with Nonlinear Statistical Models

Abstract

The self-similar gravitational collapse solutions to the Einstein-axion-dilaton system have already been found out. Those solutions become invariants after combining the spacetime dilation with the transformations of internal SL(2, R). We apply nonlinear statistical models to estimate the functions that appear in the physics of Black Holes of the axion-dilaton system in four dimensions. These statistical models include parametric polynomial regression, nonparametric kernel regression and semi-parametric local polynomial regression models. Through various numerical studies, we reached accurate numerical and closed-form continuously differentiable estimates for the functions appearing in the metric and equations of motion.

arXiv commentV2:38 pages, 12 Figures. Various clarifications are added. Published version in Journal of Mathematics

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Cited by in corpus (4)

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• Sequential Monte Carlo with Cross-validated Neural Networks for Complexity of Hyperbolic Black Hole Solutions in 4D
• Modeling the complexity of Elliptic Black Hole Solution In 4D Using Hamiltonian Monte Carlo with Stacked Neural Networks
• Neural Networks Assisted Metropolis-Hastings for Bayesian Estimation of Critical Exponent on Elliptic Black Hole Solution in 4D Using Quantum Perturbation Theory