Hawking radiation screening and shielding in Kerr-Newman and charged accelerating black holes
Section snippets
Motivation
Quantum tunnelling of particles from black holes has been a subject of extreme interest lately. The emission of particles which is the result of quantum effects is taken in the background of black holes as classical objects. The idea to view this phenomenon, known as the Hawking radiation [1], [2], as a tunnelling process was expounded by Parikh and Wilczek [3]. In this process pairs of particles are created inside the event horizon of a black hole. The negative energy particle goes towards the
Geodesic trajectories in charged accelerating and rotating black holes
A large family of spacetimes is covered by the Plebański-Demiański metric [18] as it yields the well known solutions of Schwarzschild, Reissner-Nordström, Kerr, Kerr-NUT, Kerr-Newman, and various other black holes as its reductions. It also includes a very interesting case of accelerating black holes, with and without electric charge, and with vanishing cosmological constant, Λ. Its metric [15] in spherical polar coordinates (t, r, θ, ϕ) is
Role of angular momentum and energy of particles in determining the forbidden regions
Here we identify forbidden regions and establish their dependence on angular momentum and energy of particles. We note that outside any r can lie in a forbidden region. To determine the regions of negative kinetic energy of the particles for varying r, we will find the corresponding ranges of angular momentum j and energy. We will consider the kinetic energy Eq. (2.38) in terms of j and ϵ separately, both below and above (r > rs), the static limit to find the ranges of
Hawking radiation and screening reduction
The Hawking radiation is the process in which the mass of the black hole is reduced and the black hole evaporates [1], [2]. To see the impact of Hawking radiation, the tunnelling approach is very useful. In this process a pair of particles is created near the event horizon, where one with negative energy goes inside the horizon and moves towards the centre of the hole while the one with positive energy proceeds outside the event horizon [9], [11] and ultimately tunnels across the potential
Shielding of the Penrose process
The Penrose mechanism, put forward by Roger Penrose [14], states that energy extraction is possible from a rotating black hole. Penrose mechanism takes place when a particle from infinity falls in the ergosphere of a rotating black hole. This particle splits into two pieces P1 and P2 with energies E1 and E2 respectively. The particle P1 with negative energy is absorbed by the black hole which results in shrinking of mass of rotating black hole as well as decrease in its angular momentum. If
Results for the Kerr-Newman black hole
In this section we present numerical results for the of Kerr-Newman black hole. We examine how the energy and angular momentum of particles effect the formation of regions of negative kinetic energy, and the processes of screening and shielding.
Behaviour of kinetic energy for Kerr-Newman black hole
The results regarding the dependence of kinetic energy of particles on their energy and angular momentum are presented here. The negative energy regions are represented graphically for varying values
Gamow factor for accelerating and rotating black holes
We will find the relation between the width of the potential barrier, angular momentum and energy, by working out the Gamow factor. For this purpose the Schrödinger equation of one dimension, for a particle having energy E and moving with potential U(r) is consideredwhere the square of the classical momentum p(r) of the particle is . Quantum tunnelling, for the particles with E < U(r) can occur across classically forbidden region which is bounded by the turning
Conclusion
We have studied the motion of particles in the field of charged accelerating and rotating black holes and the Kerr-Newman black holes. We have done this in order to analyse the processes of Hawking radiation screening and shielding of energy extraction from these objects. The spacetime of charged accelerating and rotating black hole contains four parameters M, a, α and Q representing mass, rotation, acceleration and charge parameter, respectively. We can obtain the corresponding results for the
Declaration of Competing Interest
None.
Acknowledgement
A research grant from the Higher Education Commission of Pakistan under its Project No. 6151 is gratefully acknowledged.
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