We formulate axisymmetric general relativity in terms of real Ashtekar-Barbero variables. We study the constraints and equations of motion and show how the Kerr, Schwarzschild and Minkowski solutions arise. We also discuss boundary conditions. This opens the possibility of a midisuperspace quantization using loop quantum gravity techniques for spacetimes with axial symmetry and time dependence.
Publication Source (Journal or Book title)
Classical and Quantum Gravity
Gambini, R., Mato, E., Olmedo, J., & Pullin, J. (2019). Classical axisymmetric gravity in real Ashtekar variables. Classical and Quantum Gravity, 36 (12) https://doi.org/10.1088/1361-6382/ab1d82