Properties of Particle Trajectory Around a Weakly Magnetized Black Hole**Project grant of Goverment of West Bengal, Department of Higher Education, Science and Technology and Biotechnology, File no:- ST/P/S&T/16G-19/2017, AH wishes to thank the Department of Mathematics, the University of Burdwan for the research facilities provided during the work. RB thanks IUCAA, Pune, India for providing Visiting Associateship

Abstract

In this paper, we consider charged accelerating AdS black holes with nonlinear electromagnetic source. The metric chosen by us is of a regular black hole, which shows regular nature at poles and a conical effect, which corresponds to a cosmic string. In such a space time construction of the Lagrangian for a charged particle is done. Cyclic coordinates as well as the corresponding symmetry generators, i.e., the Killing vectors are found. Conservation laws corresponding to the symmetries are counted. Euler-Lagrange equations are found. The orbit is mainly taken to be a circular one and effective potential is found. The minimum velocity obtained by a particle to escape from innermost stable circular orbit is found. The value of this escape velocity is plotted with respect to the radius of the event horizon of the central black hole for different parametric values. The nature of the escape velocity is studied when the central object is working with gravitational force and charge simultaneously. Effective potential and effective force are also plotted. The range of radius of event horizon for which the effective force turns to be positive is found out. A pathway of future studies of accretion disc around such black holes is made.