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 <i>SL</i>(2, <i>R</i>). We apply nonlinear statis...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-11-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/23/4537 |
| _version_ | 1797462702058110976 |
|---|---|
| author | Ehsan Hatefi Armin Hatefi |
| author_facet | Ehsan Hatefi Armin Hatefi |
| author_sort | Ehsan Hatefi |
| collection | DOAJ |
| description | 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 <i>SL</i>(2, <i>R</i>). 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. |
| first_indexed | 2024-03-09T17:40:23Z |
| format | Article |
| id | doaj.art-1907d2b4bb884c1e8c0de5806029f878 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T17:40:23Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-1907d2b4bb884c1e8c0de5806029f8782023-11-24T11:35:13ZengMDPI AGMathematics2227-73902022-11-011023453710.3390/math10234537Estimation of Critical Collapse Solutions to Black Holes with Nonlinear Statistical ModelsEhsan Hatefi0Armin Hatefi1GRAM Research Group, Department of Signal Theory and Communications, University of Alcala, 28805 Alcala de Henares, SpainDepartment of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, CanadaThe 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 <i>SL</i>(2, <i>R</i>). 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.https://www.mdpi.com/2227-7390/10/23/4537mathematical physicsblack holesstatistical analysis |
| spellingShingle | Ehsan Hatefi Armin Hatefi Estimation of Critical Collapse Solutions to Black Holes with Nonlinear Statistical Models Mathematics mathematical physics black holes statistical analysis |
| title | Estimation of Critical Collapse Solutions to Black Holes with Nonlinear Statistical Models |
| title_full | Estimation of Critical Collapse Solutions to Black Holes with Nonlinear Statistical Models |
| title_fullStr | Estimation of Critical Collapse Solutions to Black Holes with Nonlinear Statistical Models |
| title_full_unstemmed | Estimation of Critical Collapse Solutions to Black Holes with Nonlinear Statistical Models |
| title_short | Estimation of Critical Collapse Solutions to Black Holes with Nonlinear Statistical Models |
| title_sort | estimation of critical collapse solutions to black holes with nonlinear statistical models |
| topic | mathematical physics black holes statistical analysis |
| url | https://www.mdpi.com/2227-7390/10/23/4537 |
| work_keys_str_mv | AT ehsanhatefi estimationofcriticalcollapsesolutionstoblackholeswithnonlinearstatisticalmodels AT arminhatefi estimationofcriticalcollapsesolutionstoblackholeswithnonlinearstatisticalmodels |