Axisymmetric gravity in real Ashtekar variables: the quantum theory

Abstract

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. We discuss its action including the matrix elements and its solutions. 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.