Probing regular MOG static spherically symmetric spacetime using greybody factors and quasinormal modes

Abstract We investigate the behavior of the regular modified gravity (MOG) static spherically symmetric black hole (BH) under massless scalar perturbation, gravitational perturbation, and massless Dirac perturbation. The dimensionless parameter $$\left( \alpha \right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mi>α</mml:mi> </mml:mfenced> </mml:math> distinguishes this BH from a Schwarzschild BH. We derive the effective potential equations for three perturbations in the regular MOG BH. Using the derived potentials, we calculate the bounds of greybody factors (GFs). Next, we investigate the quasinormal mode (QNM) of the MOG BH by implementing the WKB method of sixth order. By analyzing the influence of the MOG parameter $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> for the BH we study on GF and QNM, we found that as $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> increases, the GFs increase proportionally. However, both gravitational wave oscillation frequency and damping decrease as $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> increases. Moreover, we examine the behavior of QNMs by considering how their frequency changes with the shape of potentials. As a result, we found that the frequency behavior is like the quantum mechanical one. The faster the wave decays, the larger the potential.

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