Spacelike trajectories in BTZ spacetime and comparison with timelike and lightlike trajectories

Spacelike trajectories or the motions of tachyons in (2 + 1) dimensional BTZ spacetime are discussed. A study of the effective potential in this case has also been done and it is shown that unlike that for tardyons or photons it does not have any local or global extremum. It rather possesses an inflection point that depends, along with the blackhole parameters, on the integrals of motion. Tachyons are, however, found to be sensitive, like photons and tardyons, to the usual frame dragging effect due to the rotational feature of the BTZ spacetime and thus pure radial motion cannot persist. It is further found that circular orbits exist nowhere except at the horizon. That the timelike object shows the same behaviour in this case is a remarkable feature of (2 + 1) dimensional gravity. Moreover, the trapping of tachyons at the horizon is also indicated. Comparison of the spacelike trajectories with the timelike and the lightlike trajectories and the corresponding effective potentials have been done analytically and graphically.

Automated summary

This study investigates the spacelike trajectories or the motions of tachyons in (2 + 1) dimensional BTZ spacetime. It is found that the effective potential does not have any local or global extremum, but possesses an inflection point that depends on the integrals of motion. Tachyons are sensitive to the frame dragging effect of the BTZ spacetime, similar to photons and tardyons. Circular orbits exist only at the horizon. Additionally, the timelike object shows similar behavior in this case, and the trapping of tachyons at the horizon is indicated.