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

The self-similar gravitational collapse solutions to the Einstein-axion-dilaton system have already been discovered. 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.

Automated summary

The self-similar gravitational collapse solutions have been discovered as invariants after combining spacetime dilation with internal transformations. Nonlinear statistical models are applied to estimate the functions of axion-dilaton system in black hole physics. Accurate numerical and closed-form continuously differentiable estimates for the functions in the metric and equations of motion are obtained through various numerical studies.