The road toward a general relativistic metric inside the Earth and its effect on neutrino travel from CERN to GRAN-SASSO Laboratory

TL;DR

This paper investigates how general relativity affects neutrino travel time inside the Earth, focusing on Earth's density profile and neglecting rotation and terrain, resulting in a tiny delay of about 4.2 picoseconds.

Contribution

It provides a first estimate of relativistic effects on neutrino travel within Earth based on geophysical density models, neglecting Earth's rotation and surface variations.

Findings

Relativistic delay of approximately 4.2 picoseconds for neutrinos from CERN to Gran Sasso.

Neglecting Earth's rotation and terrain simplifies the model but still yields measurable effects.

Density profile from geophysical models influences the magnitude of the relativistic delay.

Abstract

In a first attempt to describe the effect on neutrino travel inside the Earth caused by general relativity in the case of a dense Earth, we have neglected the Earth's rotation, the Earth's ellipticity and also the surface terrain variation, nevertheless we have focused our attention on the density description of the Earth interior provided by geophysic's models such as PREM. Assuming a non rotating Earth, the general relativistic effect on neutrino travelling from CERN to GRAN-SASSO happened to produce a delay of $\delta t=4.1863 \, picosecond$.