Echoes of charged black-bounce spacetimes

Abstract

In present work, the evolution of scalar field and electromagnetic field under the background of the charged black-bounce spacetimes are investigated, and we obtain an obvious echoes signal which appropriately reports the properties of the charged black-bounce spacetimes and disclose the physical reasons behind such phenomena. Furthermore, by studying the quasinormal ringdown, we analyze the three states of the charged black-bounce spacetimes in detail, our results show that the echoes signal only appears when $$(|{Q}|\le m)$$ ( | Q | ≤ m ) and $$(|{l}|> m+ \sqrt{m ^{2}-Q^{2} })$$ ( | l | > m + m 2 - Q 2 ) in this spacetime, while when the parameters demand $$(|{Q}|>m)$$ ( | Q | > m ) , the echoes signal will be transformed into a quasinormal ringdown of the two-way traversable wormhole, and the charged black-bounce is a regular black hole with normal horizons by requiring $$(|{Q}|\le m)$$ ( | Q | ≤ m ) and $$(|{l}|< m-\sqrt{m ^{2}-Q^{2} })$$ ( | l | < m - m 2 - Q 2 ) .

Probing the Bardeen–Kiselev black hole with the cosmological constant caused by Einstein equations coupled with nonlinear electrodynamics using quasinormal modes and greybody bounds

“…Finally, with regard to the QNM's oscillation shape, we use the finite difference method to study the dynamical evolution of the nonlinear electrodynamics field perturbations and gravitational perturbations in the time domain [60,61] and examine the stability of the Bardeen-Kiselev BH with the cosmological constant. Figure 5 shows the evolution of perturbation in log scale.…”