# Time-energy uncertainty relation for neutrino oscillations in curved spacetime

## TL;DR

This paper extends the time-energy uncertainty relation to neutrino oscillations in curved spacetime, analyzing how gravity influences neutrino energy uncertainty and oscillation length in various gravitational geometries.

## Contribution

It derives a covariant uncertainty relation for neutrinos in curved spacetime and evaluates gravity effects on neutrino energy uncertainty in different geometries.

## Key findings

- Gravity modifies neutrino energy uncertainty compared to flat spacetime.
- Explicit deviations are calculated for Schwarzschild, Lense-Thirring, and Rindler geometries.
- Spacetime curvature impacts the neutrino oscillation length.

## Abstract

We derive the Mandelstam-Tamm time-energy uncertainty relation for neutrino oscillations in a generic stationary curved spacetime. In particular, by resorting to Stodolsky covariant formula of the quantum mechanical phase, we estimate gravity effects on the neutrino energy uncertainty. Deviations from the standard Minkowski result are explicitly evaluated in Schwarzschild, Lense-Thirring and Rindler (uniformly accelerated) geometries. Finally, we discuss how spacetime could affect the characteristic neutrino oscillation length in connection with the recent view of flavor neutrinos as unstable particles.