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. 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.

On the Possible Spacetime Structures of Rotating Loop Quantum Black Holes

“…Moreover, within the framework of LQG and considering the semi-classical regimes, one can construct various effective (non-rotating) black hole models, with one common feature that the classical singularity is usually replaced by a transition surface that connects a black hole and a white hole regions [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] (see [16] for a recent review) a . However, a Upon using different quantization approaches, the classical singularities inside a non-rotating black hole could be altered into other interesting scenarios, such as the Nariai spacetime [17] or the technical difficulties of invoking real-valued Ashtekar-Barbero variables in axisymmetric spacetimes [21,22] largely hinder the progress of constructing effective LQG models for rotating black holes. In the literature, some attempts along this ling have been made by adopting the Newman-Janis Algorithm (NJA) [23,24,25,26].…”