Effect of Magnetic Field and Tidal Force on the Motion of a Particle Orbiting a Preston-Poisson Black Hole

Abstract

Black holes are the most unusual and enthralling objects of the universe. The acute conditions found in them drives our understanding of the space and time to its very limits. These astrophysical compact objects can be used as natural testing grounds for exploring the nature of matter in very powerful gravitational elds. Thus, in the universe, a very signi cant role is played by the black holes. By investigating how a particle orbits around a black hole, one can get a lot of information about how the black hole interacts with its surroundings. The present work focuses on examining the motion of a massless and massive charged particle orbiting a Preston-Poisson black hole which is a non-rotating black hole and has an external mechanical structure (a giant solenoid) surrounding it which contributes to the uniform magnetic eld. The Preston-Poisson metric has tidal force as a parameter which characterizes the surrounding mechanical structure. This metric describes the space-time here. The presence of both the magnetic eld B and the tidal force a ects the motion of the particle. For a massless particle, one circular orbit is found to exist at B = = 0, but as soon as either the magnetic eld B or the tidal force is increased, the second orbit shows up from r 􀀀! 1 and advances towards the rst circular orbit and nally, the two orbits meld into one another, which represents the last stable orbit. On further increasing either the magnetic eld B or the tidal force to some values, no circular orbits are found. For a massive charged particle, we restricted our study to investigate how the e ective potential Ueff evolves under the in uence of the magnetic eld B and the tidal force . The thesis is divided into three chapters and chapter wise summary of each chapter is presented below : Chapter 1 This chapter is introductory in nature. In this chapter, the literature available on the subject and a summary of the present work has been presented and the basic concepts related to classical mechanics have been discussed. The derivation of the Hamilton-Jacobi equations in classical mechanics has been discussed and it is further extended to derive the Hamilton-Jacobi equations in curved space-time for both massive and massive charged particles. Chapter 2 In this chapter, a method for discussing the geodesic characteristics of a particle around a black hole has been described. Through Hamilton-Jacobi equations With the help of this method, the expressions for the e ective potential Ueff of a massive, massless and massive charged particle have been found and the conditions for stable and unstable orbits have also been presented. The expressions for the propagation and trajectory equations for massive and massless particles have nally been found. Chapter 3 In this chapter an introduction to Preston-Poisson black holes and the Preston- Poisson metric has been presented. For a massless particle orbiting around a Preston- Poisson black hole, the radii of the circular orbits and hence the number of circular orbits have been calculated. (With the help of the equation dUeff dr = 0 and putting di erent values of the magnetic eld B and the tidal force in it, di erent values of r have been obtained). A graph has then been plotted between the magnetic eld B and the tidal force showing the number of circular orbits at di erent values of B and . After that curves have also been plotted between the e ective potential Ueff and the tidal force at B = 0 (where = 0, 0.003, 0.007, 0.009, 0.012, 0.015, 0.018, 0.02 ) and curves have also been plotted between the e ective potential Ueff and the magnetic force B at = 0 (where B = 0, 0.04, 0.044, 0.088, 0.132, 0.176, 0.22, 0.264). Then for a massive charged particle orbiting around a Preston-Poisson black hole, curves have been plotted which show how the e ective potential Ueff changes with change in the values of the magnetic eld B and the tidal force for a positively charged particle.