Dynamics of particle near time conformal slowly rotating Kerr black hole

In this work, we have developed the time conformal slowly rotating Kerr black hole using the approximate Noether symmetry approach. It is found that the slowly rotating Kerr black hole admits time conformal factor e(f(t)), where is very small perturbation and f(t) is an arbitrary function of time. We have obtained the numerical solutions of geodesics for lowly rotating Kerr black hole and time conformal slowly rotating Kerr black hole. We have discussed the neutral and charged particle dynamics moving around time conformal slowly rotating Kerr black hole in the absence/presence of magnetic field. Moreover, we have analyzed graphically the behavior of effective force, effective potential and escape velocity of particles in the absence/presence of magnetic field near the event horizon. We have examined the conditions under which particle can escape from the surrounding of black hole after colliding with another particle. We have found the unstable orbits of particles near event horizon due to the effect of magnetic field and angular momentum.