Nonlinear electrodynamics effects on the black hole shadow, deflection angle, quasinormal modes and greybody factors

In this paper, we discuss the effects of nonlinear electrodynamics (NED) on non-rotating black holes, parametrized by the field coupling parameter β and magnetic charge parameter P in detail. Particularly, we survey a large range of observables and physical properties of the magnetically charged black hole, including the thermodynamic properties, observational appearance, quasinormal modes and absorption cross sections. Initially, we show that the NED black hole is always surrounded by an event horizon and any magnetic charge is permissible. We then show that the black hole gets colder with increasing charge. Investigating the heat capacity, we see that the black hole is thermally stable between points of phase transition. Introducing a generalized uncertainty principle (GUP) with a quantum gravity parameter λ extends the range of the stable region, but the effect on temperature is negligible. Then we compute the deflection angle at the weak field limit, by the Gauss-Bonnet theorem and the geodesic equation, and find that even at the first order, the magnetic charge has a contribution due to the "field mass"term. Small changes of the charge contributes greatly to the paths of null geodesics due to the P2 dependence of the horizon radius. Using a ray-tracing code, we simulate the observational appearance of a NED black hole under different emission profiles, thin disk and spherical accretion. We find that the parameter P has a very strong effect on the observed shadow radius, in agreement with the deflection angle calculations. We finally consider quasinormal modes under massless scalar perturbations of the black hole and the greybody factor. We find that the charge introduces a slight difference in the fundamental frequency of the emitted waveform. We find that the greybody factor of the NED black hole is strongly steepened by the introduction of increasing charge. To present observational constrains, we show that the magnetic charge of the M87∗ black hole is between 0 ≤ P ≤ 0.024 in units of M, in agreement with the idea that real astrophysical black holes are mostly neutral. We also find that LIGO/VIRGO and LISA could detect NED black hole perturbations from BHs with masses between 5 M and 8.0 • 108 M. We finally show that for black holes with masses detected with LIGO so far, charged NED black holes would deviate from Schwarzschild by 5∼10 Hz in their fundamental frequencies.