as a consequence of a non-trivial isotropy subgroup. The Hamiltonian constraint can again be computed explicitly .
Spherically-symmetric models are usually used for applications to non-rotating black holes, but they can also be useful for cosmological purposes. They are particularly interesting as models for the evolution of inhomogeneities as perturbations, which can be applied to gravitational collapse but also to cosmology. In such a context, one often reduces the spherically-symmetric configuration even further by requiring a spatial metric
where is related to by . One example for such a metric is the spatial part of a flat Friedmann–Robertson–Walker spacetime, where . This allows one to study perturbations around a homogeneous spacetime, which can also be done at the quantum level.
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