Geodesics and geodesic deviation in a two-dimensional black hole

TL;DR

This paper presents an exactly solvable model of geodesic motion and deviation in a two-dimensional black hole spacetime, providing explicit solutions and insights into the behavior of particles and deviations in this simplified gravitational setting.

Contribution

It introduces an exactly solvable example of geodesic equations and deviation in a 2D black hole background, highlighting different potential domains and explicit solutions.

Findings

Effective potential is harmonic, inverted harmonic, or linear.

Geodesic deviation equation is exactly solvable.

Deviation vector behavior is analyzed in a specific case.

Abstract

We introduce an exactly solvable example of timelike geodesic motion and geodesic deviation in the background geometry of a well-known two-dimensional black hole spacetime. The effective potential for geodesic motion turns out to be either a harmonic oscillator or an inverted harmonic oscillator or a linear function of the spatial variable, corresponding to the three different domains of a constant of the motion. The geodesic deviation equation also is exactly solvable. The corresponding deviation vector is obtained and the nature of the deviation is briefly discussed by highlighting a specific case.