Echoes of charged black-bounce spacetimes
Sai Wu, B. Q. Wang, Dong Liu, Zheng‐Wen Long
Abstract
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 $$(|{Q}|\le m)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>|</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>|</mml:mo> <mml:mo>≤</mml:mo> <mml:mi>m</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and $$(|{l}|> m+ \sqrt{m ^{2}-Q^{2} })$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>|</mml:mo> <mml:mi>l</mml:mi> <mml:mo>|</mml:mo> <mml:mo>></mml:mo> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:msqrt> <mml:mrow> <mml:msup> <mml:mi>m</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>-</mml:mo> <mml:msup> <mml:mi>Q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:msqrt> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> in this spacetime, while when the parameters demand $$(|{Q}|>m)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>|</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>|</mml:mo> <mml:mo>></mml:mo> <mml:mi>m</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , 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 $$(|{Q}|\le m)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>|</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>|</mml:mo> <mml:mo>≤</mml:mo> <mml:mi>m</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and $$(|{l}|< m-\sqrt{m ^{2}-Q^{2} })$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>|</mml:mo> <mml:mi>l</mml:mi> <mml:mo>|</mml:mo> <mml:mo><</mml:mo> <mml:mi>m</mml:mi> <mml:mo>-</mml:mo> <mml:msqrt> <mml:mrow> <mml:msup> <mml:mi>m</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>-</mml:mo> <mml:msup> <mml:mi>Q</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:msqrt> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> .