Nonlinear Electromagnetic Quasinormal Modes and Hawking Radiation of A Regular Black Hole with Magnetic Charge

Based on a regular exact black hole (BH) from nonlinear electrodynamics (NED) coupled to General Relativity, we investigate its stability of such BH through the Quasinormal Modes (QNMs) of electromagnetic (EM) field perturbation and its thermodynamics through Hawking radiation. In perturbation theory, we can deduce the effective potential from nonlinear EM field. The comparison of potential function between regular and RN BHs could predict their similar QNMs. The QNMs frequencies tell us the effect of magnetic charge $q$, overtone $n$, angular momentum number $l$ on the dynamic evolution of NLED EM field. Furthermore we also discuss the cases near extreme condition of such magnetically charged regular BH. The corresponding QNMs spectrum illuminates some special properties in the near-extreme cases. For the thermodynamics, we employ Hamilton-Jacobi method to calculate the near-horizon Hawking temperature of the regular BH and reveal the relationship between classical parameters of black hole and its quantum effect

Fermions Tunneling from Higher-Dimensional Reissner-Nordstr\"om Black Hole: Semiclassical and Beyond Semiclassical Approximation

Based on semiclassical tunneling method, we focus on charged fermions tunneling from higher-dimensional Reissner-Nordstr\"{o}m black hole. We first simplify the Dirac equation by semiclassical approximation, and then a semiclassical Hamilton-Jacobi equation is obtained. Using the Hamilton-Jacobi equation, we study the Hawking temperature and fermions tunneling rate at the event horizon of the higher-dimensional Reissner-Nordstr\"{o}m black hole spacetime. Finally, the correct entropy is calculation by the method beyond semiclassical approximation.Comment: 7 page

The tools related to mathematics teachers’ pedagogical reasoning: critical review

[EN] Shulman (1987) introduced pedagogical reasoning in his model of pedagogical reasoning and action, refers to the phases of activities involving comprehension, transformation, instruction, evaluation, and reflection. The present study aims at a critical review on the tools for investigating the phases of pedagogical reasoning and action for mathematics teachers. Based on a focused search in the database Scopus, 13 articles were reviewed. Findings showed three categories included mathematical tasks, teaching materials and videos. We further classified each category and connected it with Shulman’s phases of pedagogical reasoning. Mathematical tasks are classified as pure mathematical tasks and mathematical pedagogical tasks which can be connected to comprehension and transformation phases. Teaching materials are classified into three sub-categories, including materials in planning session, in implementation session, and after implementation which can be connected to comprehension and transformation, instruction, and evaluation and reflection phases, respectively. Lastly, videos are classified into three subcategories including video of self-teaching, others teaching, and movie which connected to evaluation and reflection phases. Two findings are highlighted including (1) the correspondence between the tools for pedagogical reasoning and Shulman’s phases of pedagogical reasoning and (2) the features of each sub-category of the tools related to pedagogical reasoning.This research was funded by the Ministry of Science and Technology (MOST), Taiwan, R.O.C., under the grant number MOST 107-2511-H-003 -004 -MY3.Yang, K.; Tambunan, S. (2021). The tools related to mathematics teachers’ pedagogical reasoning: critical review. En 7th International Conference on Higher Education Advances (HEAd'21). Editorial Universitat Politècnica de València. 129-136. https://doi.org/10.4995/HEAd21.2021.12698OCS12913