Models of a point particle in a three-dimensional AdS universe
In 2+1-dimensional gravity, a conical deficit is commonly interpreted as a point-like particle. A distributional description of such a source is problematic since the Einstein equations are non- linear. Moreover, the total mass of the spacetime with nontrivial asymptotics is obfuscated by the infinite amount of background energy in the distant regions. In this work, we support the standard claim that the mass of a point particle is given by the angular deficit of the asymptotic geometry. We approximate the singular matter source by a sufficiently regular energy distribution, and we study the limit of negligible size for such a distribution while keeping the asymptotic geometry intact. Comparing spacetimes with equal asymptotics ensures that we correctly identify and remove the cosmological matter. We find that the angular deficit of the resulting conical spacetime is given by a limit of the local mass of the object, where the local mass is a natural concept of additive mass in 2+1 gravity. Surprisingly, the limiting mass is different from the BTZ mass parameter, although both masses are closely related.