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arXiv · 2610.03479

Unimodular boundary time for Regge calculus

Steffen Gielen·Sofie Ried
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Abstract

Henneaux-Teitelboim gravity is a diffeomorphism-invariant formulation of unimodular gravity that is locally equivalent to general relativity but includes an extra boundary variable, unimodular time, whose difference between hypersurfaces measures the enclosed 4-volume. In general, unimodular versions of quantum gravity can be expected to deviate from theories based on general relativity, but a discrete path-integral formulation for Henneaux-Teitelboim gravity has not yet been established. In this paper, we discretise Henneaux-Teitelboim gravity using the methods of Euclidean Regge calculus. Testing this framework in a symmetry-reduced model of Regge cosmology, we reproduce results in previous literature and demonstrate that the continuum limit can be naturally defined using unimodular time rather than proper time. Because unimodular time appears as boundary data as opposed to being a degree of freedom in the bulk, this approach allows for the comparison of general simplicial triangulations, beyond highly symmetric discretisations, to the continuum. Our work provides a first step towards a discrete path-integral formulation of Henneaux-Teitelboim gravity and adds a new perspective on time as a boundary variable in quantum gravity.

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Steffen Gielen, Sofie Ried. 2026-10-02. Unimodular boundary time for Regge calculus. https://arxiv.org/abs/2610.03479

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