Nonlinear statistical spline smoothers for critical spherical black hole solutions in 4-dimension

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