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arXiv · 2602.23308

Spherically Symmetric Gravity on a Graph I: Theoretical Foundations

Klaus Liegener·Saeed Rastgoo·Jorden Roberts
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Abstract

This manuscript is the first in a series of instalments that investigate spherically symmetric solutions within the effective dynamics program of Loop Quantum Gravity. The choice of lattice is adapted such that it remains invariant under a set of symmetry transformations maximally mapping spherical symmetry to the discrete setting. The conditions for symmetry restriction of the dynamics are investigated and a subspace is identified to make computations feasible. Afterwards symplectic structure and scalar constraint are explicitly computed on this subspace. This lays the groundwork to target several particular solutions, such $k=1$ cosmology and black holes, which will serve as the subjects of forthcoming follow-up papers.

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Klaus Liegener, Saeed Rastgoo, Jorden Roberts. 2026-02-26. Spherically Symmetric Gravity on a Graph I: Theoretical Foundations. https://arxiv.org/abs/2602.23308

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