Tidal forces in Reissner–Nordström spacetimes

Luís C B Crispino,Ednilton S De Oliveira,Leandro A Oliveira,Atsushi Higuchi

doi:10.1140/epjc/s10052-016-3972-5

Luís C B Crispino, Ednilton S De Oliveira + Show 2 more

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https://doi.org/10.1140/epjc/s10052-016-3972-5

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Abstract

We analyze the tidal forces produced in the spacetime of Reissner–Nordstrom 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 toward 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.

Highlights

In this paper we focus on Reissner–Nordström black holes, which are spherically symmetric, and which have a nonzero electric charge but no angular momentum
It is well known that a body falling toward the event horizon of a static uncharged black hole experiences stretching in the radial direction and compression in the angular directions [10,11,12,13,14]
In this paper we investigated tidal forces in Reissner– Nordström spacetimes, which depend on the charge-to-mass ratio of the black hole

Summary

Introduction

In this paper we focus on Reissner–Nordström black holes, which are spherically symmetric, and which have a nonzero electric charge but no angular momentum. They are exact solutions of the Einstein–Maxwell equations [9], and in the case of vanishing electric charge, they reduce to the Schwarzschild black holes. Whether a body may experience stretching or compression in either direction (radial or angular) in Reissner–Nordström spacetime depends on the charge-to-mass ratio of the black hole and where the body is located We solve the geodesic deviation equations to analyze the changes in size of a test body consisting of neutral dust particles in-falling radially toward the Reissner–Nordström black hole. 3 and study tidal forces for charged static black holes in Sect. We use the metric signature (+, −, −, −) and set the speed of light c and Newtonian gravitational constant G to 1 throughout this paper

Reissner–Nordström black holes

Radial geodesics in Reissner–Nordström spacetimes

Radial tidal force

Angular tidal forces

Conclusion