Test Particle Motion in the Born-Infeld Black Hole

TL;DR

This paper reviews the geodesic motion of test particles in Einstein-Born-Infeld black hole spacetimes, highlighting differences from Reissner-Nordström black holes and providing explicit solutions using Weierstrass functions.

Contribution

It offers a detailed classification of geodesics in Einstein-Born-Infeld black holes and presents explicit solutions for specific cases, enhancing understanding of particle dynamics in these spacetimes.

Findings

Differences in effective potential compared to Reissner-Nordström spacetime

Explicit solutions for geodesics using Weierstrass functions

Classification of geodesic types in Einstein-Born-Infeld black holes

Abstract

In this work we review the classification of geodesics of massive test particles in the gravitational background of the black hole solutions of Einstein-Born-Infeld spacetime. Even though some features are quite similar to those of Reissner-Nordstr\"{o}m spacetime there are also important differences, particularly those related to the effective potential governing the geodesic motion. Explicit solutions involving Weierstrass functions are given for a pair of specific scenarios.