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

TL;DR

This paper applies nonlinear statistical models to estimate key functions in black hole physics within the Einstein-axion-dilaton system, achieving accurate and differentiable solutions for the metric and equations of motion.

Contribution

It introduces the use of parametric, nonparametric, and semi-parametric statistical models to estimate functions in black hole solutions, providing new tools for gravitational physics analysis.

Findings

Achieved accurate estimates of functions in black hole metrics.

Produced closed-form, differentiable solutions for equations of motion.

Validated models through numerical studies.

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.