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

Author

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  • Ehsan Hatefi

    (GRAM Research Group, Department of Signal Theory and Communications, University of Alcala, 28805 Alcala de Henares, Spain
    Scuola Normale Superiore and I.N.F.N, Piazza dei Cavalieri 7, 56126 Pisa, Italy)

  • Armin Hatefi

    (Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Canada)

Abstract

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.

Suggested Citation

  • Ehsan Hatefi & Armin Hatefi, 2022. "Estimation of Critical Collapse Solutions to Black Holes with Nonlinear Statistical Models," Mathematics, MDPI, vol. 10(23), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4537-:d:989718
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    Cited by:

    1. Alena Vagaská, 2023. "Mathematical–Statistical Nonlinear Model of Zincing Process and Strategy for Determining the Optimal Process Conditions," Mathematics, MDPI, vol. 11(3), pages 1-21, February.

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