Periodic orbits and their gravitational wave radiations in a polymer black hole in loop quantum gravity

This article provides a detailed investigation into the motion of surrounding particles around polymer black hole in loop quantum gravity (LQG). Using effective potential, critical bound orbits and innermost stable circular (ISCO) are analyzed. The study finds that radii angular momentum decrease with an increase parameter $A_\lambda$ which labels LQG effects, while energy ISCO also decreases $A_\lambda$. Based on these findings, we then explore periodic using rational numbers composed three integers. Our results show based classification scheme. Moreover, compared to Schwarzschild hole, consistently have lower energy, providing potential method for distinguishing from hole. Finally, examine gravitational wave radiations test object supermassive LQG, generates intricate GW waveforms can aid exhibiting structure system.