Point particles on the string in a three-dimensional AdS universe

BTZ spacetime is a long-known locally AdS solution to the Einstein equations in 1 timelike and 2 spacelike dimensions. Its static variant is interpreted as a black hole whose mass is related to the period of the angular coordinate. This solution can be parametrically continued into one without horizons but with a conical deficit in the center. Such a solution is interpreted as a spacetime with a massive particle. It has been shown that this particle can be in static equilibrium with a cosmic string passing through the spacetime to infinity. In this work, we explore the interaction of point particles with strings, such as a bound system of two particles connected by a string of finite length. We identify additive local mass in the static spacetimes and apply it to the case of particles and strings. Finally, using the cut and glue method, we construct the system of two particles oscillating on the string, which goes out of the scope of static systems.