Geodesics and geodesic deviation in a two-dimensional black hole

Details Geodesics and geodesic deviation in a two-dimensional black hole Geodesics and geodesic deviation in a two-dimensional black hole

2003-02-17

arxiv.org/abs/gr-qc/0302065v1

Am.J.Phys. 71 (2003) 1037-1042

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, 4 figures, To be published in American Journal of Physics

Scientific paper

10.1119/1.1566426

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.

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