Quasinormal modes and greybody factors of charged symmergent black hole

Abstract In this paper, we investigate quasinormal modes (QNMs) and greybody factors within the framework of Symmergent gravity, an emergent gravity model with an $$R + R^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mo>+</mml:mo> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> curvature sector. Building on our previous work on static spherically-symmetric solutions [Puliçe et al. in Class Quantum Gravity 40(19):195003, 2023], we explore the effects of the key parameters, including the quadratic curvature coupling parameter $$c_\textrm{O}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>c</mml:mi> <mml:mtext>O</mml:mtext> </mml:msub> </mml:math> and the vacuum energy parameter $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> . For all the three perturbations considered here viz., scalar, electromagnetic and gravitational perturbations, an increase in $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> leads to a nearly linear rise in both oscillation frequencies and damping rates. The other parameter $$c_\textrm{O}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>c</mml:mi> <mml:mtext>O</mml:mtext> </mml:msub> </mml:math> affects the QNMs spectrum nonlinearly. Additionally, the charge Q of the black hole introduces nonlinear behavior, where higher charges amplify the black hole’s electromagnetic field, resulting in increased oscillation frequencies and faster stabilization. These findings enhance our understanding of charged black hole stability and gravitational wave astrophysics. Further, the analysis of greybody factors reveals that increasing $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> , $$c_\textrm{O}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>c</mml:mi> <mml:mtext>O</mml:mtext> </mml:msub> </mml:math> , and Q reduces the absorption of radiation, with gravitational perturbations reaching maximum absorption at slightly lower frequencies compared to electromagnetic and scalar perturbations.