In this paper, we reviewtwo approaches that can describe, in a geometrical way, the kinematics of particles that are affected by Planck-scale departures, named Finsler and Hamilton geometries. By relying on maps that connect the spaces of velocities and momenta, we discuss the properties of configuration and phase spaces induced by these two distinct geometries. In particular, we exemplify this approach by considering the so-called q-de Sitter-inspired modified dispersion relation as a laboratory for this study. We finalize with some points that we consider as positive and negative ones of each approach for the description of quantum configuration and phases spaces.
We consider perturbations of the massless Dirac field in the background of a black hole solution found by Bodendorfer, Mele, and Münch (BMM), using a polymerization technique that furnishes contributions inspired by Loop Quantum Gravity (LQG) Theory. Using the sixth order WKB method, we analyzed its quasinormal modes for several modes, multipole numbers and the two classes of BMM black holes. We also considered the potential that governs these perturbations to analyze the bound on the Greybody Factor (GF) due the emission rates of particles. As results, we found that the Loop Quantum Gravity parameters are responsible for raising the potential and the real and imaginary parts of the quasinormal frequencies and decrease the bound on the Greybody Factor for the two classes of black holes (with more more prominent effects for the de-amplification case, which is compatible with previous analyses done for other fields).
In this paper, we obtain the metric of the space-time generated by a charged and rotating gravitational body surrounded by a loud of strings, namely, the Kerr–Newman black hole space-time with the addition of a cloud of strings. In this background, we find the radial solutions of the Dirac equation for massive particles and show that they are given in terms of the Generalized Heun functions. The dependence of these solutions on the parameter that codifies the presence of the cloud of strings is pointed out.
We consider perturbations of the massless Dirac field in the background of a black hole solution found by Bodendorfer, Mele, and Münch (BMM), using a polymerization technique that furnishes contributions inspired by Loop Quantum Gravity (LQG) Theory. Using the sixth order WKB method, we analyzed its quasinormal modes for several modes, multipole numbers and the two classes of BMM black holes. We also considered the potential that governs these perturbations to analyze the bound on the Greybody Factor (GF) due the emission rates of particles. As results, we found that the Loop Quantum Gravity parameters are responsible for raising the potential and the real and imaginary parts of the quasinormal frequencies and decrease the bound on the Greybody Factor for the two classes of black holes (with more prominent effects for the de-amplification case, which is compatible with previous analyses done for other fields).
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