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.

V2:38 pages, 12 Figures. Various clarifications are added. Published version in Journal of Mathematics

References in corpus (4)

• $N^3$ entropy of M5 branes from dielectric effect
• Scaling Phenomena in Gravity from QCD
• On Perturbation Theory and Critical Exponents for Self-Similar Systems
• On Higher Dimensional Self-Similar Axion-Dilaton Solutions

Cited by in corpus (4)

• Analysis of Black Hole Solutions in Parabolic Class Using Neural Networks
• 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