Nonlinear statistical spline smoothers for critical spherical black hole solutions in 4dimension
Abstract
This paper focuses on selfsimilar gravitational collapse solutions of the Einsteinaxiondilaton 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 Einsteinaxiondilaton literature, we apply the nonlinear statistical spline regression methods to estimate the critical spherical black hole solutions in four dimensions. These spline methods include truncated power basis, natural cubic spline and penalized Bspline. 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.
 Publication:

Annals of Physics
 Pub Date:
 November 2022
 DOI:
 10.1016/j.aop.2022.169112
 arXiv:
 arXiv:2201.00949
 Bibcode:
 2022AnPhy.44669112H
 Keywords:

 Mathematical physics;
 Gravity;
 Theoretical physics;
 Black holes;
 Statistical physics;
 General Relativity and Quantum Cosmology;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory;
 Physics  Computational Physics;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 V2: Minor revision, 34 pages, 12 figures, and 9 tables. Accepted version to be published in Annals of Physics