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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PAPERS| October 01 2003
Geodesics and geodesic deviation in a two-dimensional black hole
Ratna Koley, Supratik Pal, Sayan Kar; Geodesics and geodesic deviation in a two-dimensional black hole. Am. J. Phys. 1 October 2003; 71 (10): 1037–1042. https://doi.org/10.1119/1.1566426
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