Quantum corrected geodesic motion in polymer Kerr-like spacetime

Abstract Rotating black holes are prevalent in astrophysical observations, and a Kerr-like solution that incorporates quantum gravity effects is essential for constructing realistic models. In this work, we analyze the geodesic motion of massive particles in a Kerr-like polymer spacetime, incorporating quantum corrections via a parameter $$A_\lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>λ</mml:mi> </mml:msub> </mml:math> . We demonstrate that increasing $$A_\lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>λ</mml:mi> </mml:msub> </mml:math> allows for additional orbital evolution in extreme mass ratio inspiral (EMRI) systems before merging. Our results show that the radii, energy, and angular momentum of both the innermost stable circular orbit (ISCO) and marginal circular orbit (MCO) decrease as $$A_\lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>λ</mml:mi> </mml:msub> </mml:math> increases. Furthermore, when the primary object becomes a wormhole, both prograde ISCO and MCO can intersect the transition surface at the wormhole throat and vanish as $$A_\lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>λ</mml:mi> </mml:msub> </mml:math> grows. Additionally, we find that the eccentricity of periodic geodesic motion decreases monotonically with increasing $$A_\lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>λ</mml:mi> </mml:msub> </mml:math> . Finally, we explore the variation of the rational number that characterizes periodic motion and highlight the influence of the quantum parameter on different types of periodic orbits, classified by a set of integers associated with the rational number. This work contributes to the understanding of quantum gravity effects and offers potential observational signatures, particularly in the study of EMRIs.