Particle Dynamics and Some Thermodynamics Aspects of Black Holes

Abstract

Dynamics of particles around black holes is one of the interesting topics in general relativity. It helps us in understanding the geometrical structure of the spacetime around black holes. Geodesics of particles may display a rich structure and they can convey very reliable facts to understand the geometry of black holes. Also black holes and thermodynamics have an intimate connection and it is interesting to study thermodynamics at black hole horizons. In this thesis we have studied the e ect of a magnetic eld on 3-dimensional dynamics of charged particles in the vicinity of weakly magnetized black holes. We have considered the dynamics of test particles (both neutral and charged) moving in the vicinity of black holes, falling freely from in nity. Timelike geodesics of particles, their escaping behavior from the vicinity of black holes, e ective potentials, and center of mass energies of colliding particles are studied in detail for the following black holes: (i) The Reissner-Nordström black hole surrounded by quintessence (ii) Weakly magnetized Kiselev solution and (iii) weakly magnetised Reissner-Nordstöm black hole. E ect of the geometry of spacetimes on the motion of particles is investigated. To bring the thermodynamics of black holes into the account we have also determined products of black hole thermodynamics parameters at horizons of the Kiselev solution. In the rst chapter of the thesis basic concepts of black holes are brie y reviewed. 4 5 In the second chapter we have investigated non-singular coordinates for the Reissner-Nordström black hole surrounded by quintessence. Geodesics of particles are unde ned at horizons of a black hole. This could be avoided by removing the coordinate singularity of the spacetime. By studying the non-singular coordinate system we have obtained timelike geodesics in the new coordinate system. It is emphasized that complete geodesics of the particle can be obtained by removing the coordinate singularity. In the third and fourth chapters we have studied the dynamics of particles in the geometry of a weakly magnetized Schwarzschild black hole surrounded by quintessence and weakly magnetised Reissner-Nordström black hole respectively. Equations of motion are derived using Euler-Lagrange equations. Trajectories of escaping particles are obtained and the e ect of magnetic eld on trajectories is analysed. In the fth chapter, we have discussed some aspects of thermodynamics for the Kiselev solution. The study includes products of thermodynamics parameters at horizons of black holes.