On some classical and quantum effects due to gravitational fields

Abstract

We consider the gravitational fields generated by a cosmic string, a global monopole and a tubular matter with interior magnetic field (Safko-Witten space-time), and examine some classical and quantum effects due to these fields. We investigate the Aharonov-Bohm effect in the space-time of a cosmic string, using the loop variables. In the space-time of a global monopole, we calculate the total energy radiated by a uniformly moving charged scalar particle, for small solid angle deficit. We show that the radiated energy is proportional to the cube of the velocity of the particle and to the cube of the Lorenz factor, in the non-relativistic and ultra-relativistic cases, respectively. In the Safko-Witten space-time, we investigate the existence of an electrostatic self-force on a charged particle. We also consider a hydrogen atom in the background space-time generated by a cosmic string and we find the solutions of the corresponding Dirac equation and we determine the energy levels of the atom. We investigate how the topological features of this space-time lead to shifts in the energy levels as compared with the flat Minkowski space-time. We study the behavior of non-relativistic quantum particles interacting with a Kratzer potential in the space-time generated by a global monopole and we find the energy spectrum in the presence of this topological defect. In the Safko-Witten space-time, an investigation is also made concerning the interaction of an harmonic oscillator with this background gravitational field.

On the spin- 1/2 Aharonov–Bohm problem in conical space: Bound states, scattering and helicity nonconservation

“…The idealized situation of a relativistic quantum particle in the presence of a cosmic string is an example of gravitational effect of topological origin, where a particle is transported along a closed curve around the cosmic string [8]. This situation corresponds to the gravitational analogue of the electromagnetic AB effect with the cosmic string replacing the flux tube [9][10][11][12][13].…”

“…The effect reveals that the electromagnetic potentials, rather than the electric and magnetic fields, are the fundamental quantities in quantum mechanics. The interest in this issue appears in the different contexts, such as solid-state physics [3], cosmic strings [4][5][6][7][8][9][10][11][12][13][14] κ-Poincaré-Hopf algebra [15,16], δ-like singularities [17][18][19], supersymmetry [20,21], condensed matter [22,23], Lorentz symmetry violation [24], quantum chromodynamics [25], general relativity [26], nanophysics [27], quantum ring [28][29][30], black hole [31,32] and noncommutative theories [33,34].…”

“…The effect reveals that the electromagnetic potentials, rather than the electric and magnetic fields, are the fundamental quantities in quantum mechanics. The interest in this issue appears in the different contexts, such as solid-state physics [3], cosmic strings [4][5][6][7][8][9][10][11][12][13][14] κ-Poincaré-Hopf algebra [15, 16], δ-like singularities [17-19], supersymmetry [20, 21], condensed matter [22, 23], Lorentz symmetry violation [24], quantum chromodynamics [25], general relativity [26], nanophysics [27], quantum ring [28-30], black hole [31, 32] and noncommutative theories [33, 34].In the AB effect of spin-1/2 particles [7], besides the interaction with the magnetic potential, an additional two dimensional δ-function appears as the mathematical description of the Zeeman interaction between the spin and the magnetic flux tube [18,19]. This interaction is the basis of the spin-orbit coupling, which causes a splitting on the energy spectrum of atoms depending on the spin state.…”

Perspectives on Gravity-Induced Radiative Processes in Astrophysics

“…Though the gravitational field selected above is stationary, energy conservation must be introduced, because the energy contribution of the field is contained in the generalized momentum of P . We further approximate the Bessel function K 0 (bq z ) π/2bq z e −bqz [1 − 1/8bq z + ...], itself a distribution, by K 0 (bq z )/π 2πδ(bq z ) and eliminate δ 4 (q) from Equations (10) and (11). Conservation of energy-momentum will reappear as a factor (2π) 4 δ 4 (q) in the expression for the radiated power W defined below.…”

“…[3,4] in the propagation of particles, be these treated classically or according to quantum mechanics. In the latter case, scattering by a Newtonian potential has been the subject of several investigations, [5][6][7], but bremsstrahlung [8][9][10][11], the emission of Cêrenkov radiation [12] and other processes [13] have also been studied in connection with various gravitational sources. As stated above, external gravitational fields do alter the dispersion relations of a particle propagating in a gravitational background at least to the extent that the particle is no longer on shell.…”