Superradiance and quasinormal modes of massive scalar fields around Kerr black holes in Einstein–Maxwell–Dilaton-axion theory with perfect fluid dark matter

Abstract We investigate the dynamics of massive scalar fields around Kerr black holes in the Einstein–Maxwell–Dilaton-Axion (EMDA) theory, incorporating the effects of perfect fluid dark matter (PFDM), characterized by the dilaton parameter $$ r_2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>r</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> and the PFDM parameter $$ \lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>λ</mml:mi> </mml:math> . These parameters modify both the ergosphere and the effective potential experienced by the scalar field. Using the asymptotic matching method, we compute superradiant amplification factors, while quasinormal mode (QNM) frequencies are obtained via the asymptotic iteration method (AIM). Our results reveal contrasting effects: increasing $$ r_2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>r</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> enhances superradiance and leads to higher QNM frequencies with greater damping, whereas increasing $$ \lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>λ</mml:mi> </mml:math> suppresses superradiance and reduces QNM frequencies with weaker damping. In combined scenarios, the influence of $$ \lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>λ</mml:mi> </mml:math> is found to be dominant. These findings extend the understanding of Kerr black holes in EMDA backgrounds and highlight the stabilizing role of PFDM in such systems.