Abstract Can models that are degenerate in electromagnetic observations (i. e. , having identical shadows) be distinguished by their dynamical behaviors and quantum radiation properties? To address this question, this paper considers a unique charged black hole with logarithmic term corrections in NED (Mazharimousavi in Phys Lett B 841: 137948, 2023, https: //doi. org/10. 1016/j. physletb. 2023. 137948, arXiv: 2305. 01048 gr-qc). It is found that for models degenerate with the shadow of a Schwarzschild black hole, although the oscillation frequencies (real parts) of their quasinormal modes (QNMs) are almost indistinguishable, their decay rates (imaginary parts) exhibit significant sensitivity. This provides the primary criterion for breaking the observational degeneracy. Furthermore, to investigate the effect of parameters, it is observed that when the parameter ζ is fixed, the deviation behavior of QNM frequencies from those of the Schwarzschild black hole follows a more distinct pattern: the oscillation frequency decreases almost linearly with the increase in charge q, while the decay rate shows a stronger nonlinear dependence. In addition, the analysis of greybody factors (GFs) offers a second approach for distinction. It reveals a more complex non-monotonic behavior: in the low-frequency region, the transmittance of the Schwarzschild black hole is higher; however, above a cross frequency, the transmittance of the NED model rapidly surpasses that of the former. These results indicate that the damping time of QNMs and the precise shape of the Hawking radiation spectrum, rather than the shadow size, are more sensitive physical observables for detecting such logarithmic corrections. This study provides specific and distinguishable theoretical criteria for testing and constraining such NED models using gravitational wave astronomy and high-precision radiation observations in the future.
Liang et al. (Mon,) studied this question.