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

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.

V2: Minor revision, 34 pages, 12 figures, and 9 tables. Accepted version to be published in Annals of Physics

References in corpus (3)

• Critical formation of trapped surfaces in the collision of gravitational shock waves
• Scaling Phenomena in Gravity from QCD
• Critical gravitational collapse: towards a holographic understanding of the Regge region