Tidal Forces in Reissner-Nordstr\"om Spacetimes

TL;DR

This paper investigates the unique tidal force behaviors in Reissner-Nordström black holes, revealing how charge influences the sign changes of tidal components and the geodesic deviation of falling bodies.

Contribution

It provides a detailed analysis of tidal forces in charged black hole spacetimes, highlighting differences from uncharged Schwarzschild black holes, including sign changes and geodesic deviation behavior.

Findings

Radial tidal force component changes sign outside the horizon near charge-to-mass ratio of 1.

Angular tidal force component changes sign between the outer and inner horizons.

Radial geodesic deviation vector decreases inside the event horizon, unlike in Schwarzschild spacetime.

Abstract

We analyze the tidal forces produced in the spacetime of Reissner-Nordstr\"om black holes. We point out that the radial component of the tidal force changes sign just outside the event horizon if the charge-to-mass ratio is close to $1$ unlike in Schwarzschild spacetime of uncharged black holes, and that the angular component changes sign between the outer and inner horizons. We solve the geodesic deviation equations for radially falling bodies towards the charged black hole. We find, for example, that the radial component of the geodesic deviation vector starts decreasing inside the event horizon unlike in the Schwarzschild case.