Classical axisymmetric gravity in real Ashtekar variables

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.

arXiv comment14 pages, no figures, RevTex. Published version

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Cited by in corpus (4)

• Spherically symmetric loop quantum gravity: analysis of improved dynamics
• On the value of the Immirzi parameter and the horizon entropy
• Axisymmetric gravity in real Ashtekar variables: the quantum theory
• Connection Dynamics of Reduced 5-dimensional Kaluza-Klein Theory and Its Deparametrization