Tidal effects in Schwarzschild black hole in holographic massive gravity

TL;DR

This paper studies how massive gravitons influence tidal forces near a Schwarzschild black hole in holographic massive gravity, revealing unique effects on geodesic deviation and deformation patterns.

Contribution

It provides the first analysis of tidal effects in Schwarzschild black holes within holographic massive gravity, highlighting the impact of graviton mass on geodesic behavior.

Findings

Massive gravitons modify angular tidal forces.

Radial geodesic separation increases and becomes infinite after horizon crossing.

Angular deformation depends on black hole mass and graviton mass.

Abstract

We investigate tidal effects produced in the spacetime of Schwarzschild black hole in holographic massive gravity, which has two additional mass parameters due to massive gravitons. As a result, we have obtained that massive gravitons affect the angular component of the tidal force, while the radial component has the same form with the one in massless gravity. On the other hand, by solving the geodesic deviation equations, we have found that radial components of two nearby geodesics keep tightening while falling into the black hole and after passing the event horizons get abruptly infinitely stretched due to massive gravitons. However, angular components of two nearby geodesics get stretched firstly, reach a peak and then get compressed while falling into the black hole. Moreover, we have also shown that the angular components are more easily deformed near the departure position as the mass of a black hole is smaller for a fixed graviton mass.