# The Sagnac effect on a scale-dependent rotating BTZ black hole background

## TL;DR

This paper explores how the Sagnac effect manifests in a rotating BTZ black hole within scale-dependent gravity, analyzing travel time differences and phase shifts of photon beams in a 2+1 dimensional spacetime.

## Contribution

It introduces the study of the Sagnac effect in a scale-dependent rotating BTZ black hole, extending understanding of quantum effects in modified gravity backgrounds.

## Key findings

- Calculated the Sagnac time delay for photon beams in the black hole background.
- Analyzed phase shifts of counter-propagating photons in the rotating spacetime.
- Provided insights into the influence of scale-dependent gravity on interferometric effects.

## Abstract

In this paper we investigate the Sagnac effect by calculating the difference in travel time and phase shift observed for photon beams counter--propagating in a rotating interferometer on a BTZ black hole solution in the context of scale-dependent gravity, which describes the field around a massive static and rotating object in $2+1$ gravity.