Abstract
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.
Highlights
Beato, Garcia and Bronnikov successively found some static, spherically symmetric non-singular solutions [5,6,7,8]
The regular black hole (BH) discussed by us is one solution of nonlinear electrodynamics coupling with Einstein theory
All of them return to a Schwarzschild black hole when q = 0
Summary
Garcia and Bronnikov successively found some static, spherically symmetric non-singular solutions [5,6,7,8]. C (2015) 75:131 magnetic field are unrelated They found that the gravitational redshift is related to the mass–radius ratio of the object, so that this NLED effect would have impact on the metric of the black hole [11,12]. The singularity of a regular black hole may vanish under the condition that gravitation be coupled to a suitable nonlinear electrodynamics (NLED) field; we consider the QNMs of EM perturbations in specific regular spacetimes to be more meaningful. 4, we investigate the strong charged cases for the spherically symmetric regular black hole and evaluate the QNMs through a third-order WKB method, since the sixth-order WKB method may break down if the potential is complicated [22,23].
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