Quasinormal modes of a d-dimensional regular black hole featuring an integrable singularity

Abstract In this paper, we exhaustively investigate the quasinormal modes (QNMs) of a probe scalar field over a d -dimensional regular black hole (BH) characterized by the parameter A . The quasinormal frequencies (QNFs) exhibit different behaviors with respect to the parameter A for $$d=4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> and $$d&gt;4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> . Firstly, the trends of QNFs with respect to A exhibit completely opposite patterns for the case of $$d=4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> and $$d&gt;4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> . Secondly, in the four-dimensional regular BH, a non-monotonic behavior with respect to A is observed in the imaginary part of the fundamental modes with vanishing angular quantum number. In contrast, for nonzero angular quantum number or $$d&gt;4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> , non-monotonic behavior is observed only in the overtones. Thirdly, an overtone outburst accompanied by an oscillatory patter is observed only in the case of $$d&gt;4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> , but not in $$d=4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> .