Nonlinear Statistical Spline Smoothers for Critical Spherical Black Hole Solutions in 4-dimension

TL;DR

This paper introduces nonlinear statistical spline regression methods to estimate critical spherical black hole solutions in four-dimensional Einstein--axion-dilaton gravity, achieving high accuracy and smooth estimators for the collapse functions.

Contribution

It is the first application of spline regression techniques to critical black hole solutions in Einstein--axion-dilaton theory, providing unbiased, smooth estimators with low prediction errors.

Findings

Prediction errors less than 0.01 on average

Derived closed-form, differentiable estimators for collapse functions

Spline models are effective unbiased estimators

Abstract

This paper focuses on self-similar gravitational collapse solutions of the Einstein--axion-dilaton configuration for two conjugacy classes of SL(2, R) transformations. These solutions are invariant under spacetime dilation, combined with internal transformations. For the first time in Einstein--axion-dilaton literature, we apply the nonlinear statistical spline regression methods to estimate the critical spherical black hole solutions in four dimension. These spline methods include truncated power basis, natural cubic spline and penalized B-spline. The prediction errors of the statistical models, on average, are almost less than $10^{-2}$, so all the developed models can be considered unbiased estimators for the critical collapse functions over their entire domains. In addition to this excellence, we derived closed forms and continuously differentiable estimators for all the critical collapse functions.