Dynamics of charged particles around a magnetically deformed Schwarzschild black hole

Abstract

The motion of a charged particle around a deformed Schwarzschild black hole in an external magnetic field is studied. If a magnetic parameter is small, the sign and magnitude of deformation parameter affect the shape of effective potential. The radius of an innermost stable circular orbit on the equatorial plane increases as the magnitude of negative deformation parameter increases, but decreases as a positive deformation parameter increases. When the energy and angular momentum are given appropriately, the magnetic parameter has two critical values, small and large values. For the magnetic parameter smaller than the small value or larger than the large value, the deformation parameter does not have an explicit effect on the dynamics of particles on the non-equatorial plane. The former dynamics is ordered, whereas the latter dynamics is strongly chaotic. If the magnetic parameter runs from the small value to the large one, the negative deformation parameter is helpful to strengthen the extent of chaos with its magnitude increasing. However, chaos is weakened with an increase of the positive deformation parameter.