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In this paper we have implemented quantum corrections for the Schwarzschild black hole metric using the generalized uncertainty principle (GUP) in order to investigate the scattering process. We mainly compute, at the low energy limit, the differential scattering and absorption cross section by using the partial wave method. We determine the phase shift analytically and verify that these quantities are modified by the GUP. We found that due to the quantum corrections from the GUP the absorption is not zero as the mass parameter goes to zero. A numerical analysis has also been performed for arbitrary frequencies.
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We consider quantum corrections for the Schwarzschild black hole metric by using the generalized uncertainty principle (GUP) to investigate quasinormal modes, shadow and their relationship in the eikonal limit. We calculate the quasinormal frequencies of the quantum-corrected Schwarzschild black hole by using the sixth-order Wentzel-Kramers-Brillouin (WKB) approximation, and also perform a numerical analysis that confirms the results obtained from this approach. We also find that the shadow radius is nonzero even at very small mass limit for finite GUP parameter.
We present the detailed analyses of a model of loop quantum Schwarzschild interior coupled to a massless scalar field and extend the results in our previous rapid communication arXiv:2006.08313 to more general schemes. It is shown that the spectrum of the black hole mass is discrete and does not contain zero. This indicates the existence of a black hole remnant after Hawking evaporation due to loop quantum gravity effects. Besides to show the existence of a stable black hole remnant in the vacuum case, the quantum dynamics for the non-vacuum case is also solved and compared with the effective one.
The classical Raychaudhuri equation predicts the formation of conjugate points for a congruence of geodesics, in a finite proper time. This in conjunction with the Hawking-Penrose singularity theorems predicts the incompleteness of geodesics and thereby the singular nature of practically all spacetimes. We compute the generic corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole, arising from modifications to the algebra inspired by the generalized uncertainty principle (GUP) theories. Then we study four specific models of GUP, compute their effective dynamics as well as their expansion and its rate of change using the Raychaudhuri equation. We show that the modification from GUP in two of these models, where such modifications are dependent of the configuration variables, lead to finite Kretchmann scalar, expansion and its rate, hence implying the resolution of the singularity. However, the other two models for which the modifications depend on the momenta still retain their singularities even in the effective regime.
We calculate the probability amplitude for tree-level elastic electron-muon scattering in Minkowski spacetime with carefully prepared initial and final wave packets. The obtained nonzero amplitude implies a nonvanishing probability for detecting a recoil electron outside the light-cone of the initial muon. Transposing this Minkowski-spacetime scattering result to a near-horizon spacetime region of a massive Schwarzschild black hole and referring to a previously proposed Gedankenexperiment, we conclude that, in principle, it is possible to have information transfer from inside the black-hole horizon to outside.
The analysis of gravitino fields in curved spacetimes is usually carried out using the Newman-Penrose formalism. In this paper we consider a more direct approach with eigenspinor-vectors on spheres, to separate out the angular parts of the fields in a Schwarzschild background. The radial equations of the corresponding gauge invariant variable obtained are shown to be the same as in the Newman-Penrose formalism. These equations are then applied to the evaluation of the quasinormal mode frequencies, as well as the absorption probabilities of the gravitino field scattering in this background.
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