Accelerating Black Holes and their Dynamics

Abstract

Many modifications and deformations have been introduced in the Kerr black hole (BH) to test the no-hair theorem in strong fields. The hypothesis of this BH can be tested in strong gravitational field by using the top-bottom approach and the bottom top approach. The first approach leads to theoretical models which do not describe the spacetime. The second approach contains some phenomenological modification of the metric. In this approach, the metric can be the solution of some BH in the context of some theory of gravitation. One such modification was introduced by Johannsen and Psaltis. We have presented the accelerating version of this BH in this thesis and studied its properties. According to the work of Stephan Hawking, BH could radiate quantum mechan ically. These objects could shrink by losing energy and eventually evaporate by the emission of Hawking radiation. But this discovery set up a long-standing puzzle that what happens to the information when the evaporation takes place? BH evapora tion opens up a new window of research to study the decay rates of different BHs. Small BHs will decay quickly into charged leptons and photons. Understanding of microscopic BHs is important from the point of view of quantum gravity and it also contributes towards reconciling general relativity and quantum theory. In this dissertation, we have investigated the evaporation process of accelerating and rotating BHs through Hawking radiation and Penrose process via tunneling ap proach. Forbidden regions are calculated to study the screening of particles because they play the role of potential barrier in radial motion of particles. Chapter 1 contains a background of general relativity and its application to the theory of BHs. The process of energy extraction, Hawking radiation and Penrose process are also addressed in this chapter. The origin of accelerating and rotating BHs and their importance is discussed. In Chapter 2, we propose a non-Kerr BH (and its charged extension) that is accelerating as well. The no-hair theorem can be tested in the strong gravity regime by using the top-bottom approach and the bottom-top v approach. The non-Kerr spacetime of the latter approach is an ideal framework to do the tests in the region very close to the BHs. These new objects are studied for their basic properties and thermodynamics. Chapter 3 deals with the tunneling probabilities and Hawking temperature of recently discovered accelerating non-Kerr spacetimes. The horizon of the metric is calculated with numerical techniques to study the tunneling phenomenon. A critical analysis of incoming and outgoing, charged and uncharged scalar and Dirac particles, has been made. The Hawking temperature of massive and massless Dirac particles has been found in the background of accelerating non-Kerr BHs. The centre-of-mass energy of colliding particles has also been worked out and presented graphically. The classical expression of action for the massive and massless fermionic particles with electric and magnetic charges, is also presented. In Chapter 4, the screening effect of Hawking radiation and shielding of particles in the Penrose process in the accelerating and rotating BHs is studied. These objects are very interesting as, in addition to the usual horizons of rotating BHs, they have acceleration horizons as well. We study these processes by analysing geodesics for the motion of massive particles in equatorial plane in the field of these BHs by employing the Hamilton-Jacobi method. Further, the effect of these decay processes on the evaporation of BHs is also studied by employing the tunnelling approach and using the tunnelling probability of particles. We establish the dependence of the energy and angular momentum of the particles on the width of classically forbidden regions. If we neglect the acceleration parameter, the corresponding results for the Kerr BH can be recovered. Chapter 5 discusses the dynamics of massive particles near the horizons of rotating and accelerating BHs, when they are charged. We have done this particular, from the aspect of studying screening of Hawking radiation and shielding effect of the Penrose process in the case of these BHs. This has been done by identifying forbidden regions, that is the regions in which particles possess negative kinetic energy. The screening vi and shielding processes are studied via quantum tunnelling of particles through these regions. The dependence of these processes on angular momentum and energy of particles, and the role of acceleration and the charge of BHs is explored in detail. We summarize our results in the last chapter and give some concluding remarks of this dissertation