Relativistic corrections to the Di{\'o}si-Penrose model
Abstract
The Di{\'o}si-Penrose model is explored in a relativistic context. Relativistic effects were considered within a recently proposed Grave de Peralta approach [L. Grave de Peralta, {\em Results Phys.} {\bf 18} (2020) 103318], which parametrize the Schr{\"o}dinger-like hamiltonian so as to impose that the average kinetic energy of the system coincide with its relativistic kinetic energy. As a case of study, the method is applied to a particle in a box with good results. In the Di{\'o}si-Penrose model we observed that the width of a quantum matter field confined by its own gravitational field [L. Di{\'o}si, {\em Phys. Lett}. {\bf 105A} (1984) 199], sharply drop to zero for a mass of the order of the Planck mass, indicating a breakdown of the model at the Planck scale.
Keywords
Cite
@article{arxiv.2103.00994,
title = {Relativistic corrections to the Di{\'o}si-Penrose model},
author = {Luis A. Poveda and Luis Grave de Peralta and Arquimedes Ruiz-Columbié},
journal= {arXiv preprint arXiv:2103.00994},
year = {2021}
}