The 2+1 Kepler Problem and Its Quantization

TL;DR

This paper investigates a two-particle system coupled to 3D Einstein gravity, revealing quantum gravity effects like minimal distances, spacetime foaminess, and quantized geometry, impacting the universe's possible asymptotic states.

Contribution

It introduces a quantization of the 2+1 Kepler problem, highlighting novel quantum gravity phenomena and geometric restrictions in a simplified gravitational model.

Findings

Discovery of minimal distances due to quantum effects

Identification of spacetime foaminess at Planck scale

Quantization of possible asymptotic geometries

Abstract

We study a system of two pointlike particles coupled to three dimensional Einstein gravity. The reduced phase space can be considered as a deformed version of the phase space of two special-relativistic point particles in the centre of mass frame. When the system is quantized, we find some possibly general effects of quantum gravity, such as a minimal distances and a foaminess of the spacetime at the order of the Planck length. We also obtain a quantization of geometry, which restricts the possible asymptotic geometries of the universe.