In a previous paper we formulated axisymmetric general relativity in terms of real Ashtekar-Barbero variables. Here we proceed to quantize the theory. We are able to implement Thiemann's version of the Hamiltonian constraint. This provides a 2 + 1 dimensional arena to test ideas for the dynamics of quantum gravity and opens the possibility of quantum studies of rotating black hole spacetimes.
Publication Source (Journal or Book title)
Classical and Quantum Gravity
Gambini, R., Mato, E., & Pullin, J. (2020). Axisymmetric gravity in real Ashtekar variables: The quantum theory. Classical and Quantum Gravity, 37 (11) https://doi.org/10.1088/1361-6382/ab7966