Can gravitation accelerate neutrinos?

The Lagrangian equations of motion for massive spinning test particles (tops) moving on a gravitational background using General Relativity are presented. The paths followed by tops are nongeodesic. An exact solution for the motion of tops on a Schwarzschild background which allows for superluminal propagation of tops is studied. It is shown that the solution becomes relevant for particles with small masses, such as neutrinos. This general result is used to calculate the necessary condition to produce superluminal motion in part of the trajectory of a small mass particle in a weak gravitational field. The condition for superluminal motion establishes a relation between the mass, energy and total angular momentum of the particle.Comment: 7 pages, accepted in Class. Quantum Gra

Birefringent light propagation on anisotropic cosmological backgrounds

Exact electromagnetic wave solutions to Maxwell equations on anisotropic Bianchi I cosmological spacetime backgrounds are studied. The waves evolving on Bianchi I spacetimes exhibit birefringence (associated to linear polarization) and dispersion. The particular case of a vacuum--dominated anisotropic Universe, which reproduces a Friedmann-Robertson-Walker Universe (for late times) while for earlier times it matches a Kasner Universe, is studied. The electromagnetic waves do not, in general, follow null geodesics. This produces a modification of the cosmological redshift, which is now dependent on light polarization and dispersion and its non-null geodesic behavior. New results presented here may help to tackle some issues related to the "horizon" problem.Comment: Accepted in Physical Review

New non-linear modified massless Klein--Gordon equation

The massless Klein--Gordon equation on arbitrary curved backgrounds allows for solutions which develop "tails" inside the light cone and, therefore, do not strictly follow null geodesics as discovered by DeWitt and Brehme almost sixty years ago. A modification of the massless Klein--Gordon equation is presented which always exhibits null geodesic propagation of waves on arbitrary curved spacetimes. This new equation is derived from a Lagrangian which exhibits current--current interaction. Its non--linearity is due to a self--coupling term which is related to the quantum mechanical Bohm potential

Phenomenological dynamics of COVID-19 pandemic: meta-analysis for adjustment parameters

We present a phenomenological procedure of dealing with the COVID--19 data provided by government health agencies of eleven different countries. Instead of using the (exact or approximate) solutions to the SIR (or other) model(s) to fit the data by adjusting the time--independent parameters included in those models, we introduce dynamical parameters whose time--dependence may be phenomenologically obtained by adequately extrapolating a chosen subset of the daily provided data. This phenomenological approach works extremely well to properly adjust the number of infected (and removed) individuals in time, for the countries we consider. Besides, it can handle the sub--epidemic events that some countries may experience. In this way, we obtain the evolution of the pandemic without using any a priori model based on differential equations