Neutrino oscillation in the $q$-metric

TL;DR

This paper explores how the quadrupole deformation of axially symmetric space-times affects neutrino oscillations, with potential implications for astrophysical observations and future space experiments.

Contribution

It introduces the $q$-metric to analyze neutrino phase shifts in axially symmetric gravitational fields, extending beyond spherical models.

Findings

Quadrupole parameter modifies neutrino phase shifts compared to Schwarzschild case.

Detection of deviations is more probable in neutron stars and white dwarfs than in the Solar System.

Implications for constraining gravitational parameters via astrophysical neutrino observations.

Abstract

We investigate neutrino oscillation in the field of an axially symmetric space-time, employing the so-called $q$-metric, in the context of general relativity. Following the standard approach, we compute the phase shift invoking the weak and strong field limits and small deformation. To do so, we consider neutron stars, white dwarfs and supernovae as strong gravitational regimes whereas the Solar System as weak field regime. We argue that the inclusion of the quadrupole parameter leads to the modification of the well-known results coming from the spherical solution due to the Schwarschild space-time. Hence, we show that in the Solar System regime, considering the Earth and Sun, there is a weak probability to detect deviations from the flat case, differently from the case of neutron stars and white dwarfs in which this probability is larger. Thus, we heuristically discuss some implications on constraining the free parameters of the phase shift by means of astrophysical neutrinos. A few consequences in cosmology and possible applications for future space experiments are also discussed throughout the text.