# Classical axisymmetric gravity in real Ashtekar variables

## TL;DR

This paper reformulates axisymmetric general relativity using real Ashtekar variables, deriving key solutions and discussing boundary conditions, paving the way for loop quantum gravity quantization of axially symmetric spacetimes.

## Contribution

It introduces a real Ashtekar variable formulation for axisymmetric gravity, enabling potential loop quantum gravity applications for such spacetimes.

## Key findings

- Derivation of Kerr, Schwarzschild, and Minkowski solutions
- Analysis of constraints and equations of motion
- Discussion of boundary conditions

## Abstract

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.