Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0905.1501

Spin foam models for quantum gravity from lattice path integrals

Valentin Bonzom
View original source ↗Read source document ↗Export metadata ↓

Abstract

Spin foam models for quantum gravity are derived from lattice path integrals. The setting involves variables from both lattice BF theory and Regge calculus. The action consists in a Regge action, which depends on areas, dihedral angles and includes the Immirzi parameter. In addition, a measure is inserted to ensure a consistent gluing of simplices, so that the amplitude is dominated by configurations which satisfy the parallel transport relations. We explicitly compute the path integral as a sum over spin foams for a generic measure. The Freidel-Krasnov and Engle-Pereira-Rovelli models correspond to a special choice of gluing. In this case, the equations of motion describe genuine geometries, where the constraints of area-angle Regge calculus are satisfied. Furthermore, the Immirzi parameter drops out of the on-shell action, and stationarity with respect to area variations requires spacetime geometry to be flat.

Explore related subjects

gr-qc

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Valentin Bonzom. 2009-09-23. Spin foam models for quantum gravity from lattice path integrals. https://doi.org/10.1103/physrevd.80.064028

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

An upper bound on the minimum orbital period of black holes

Previous research has focused on establishing lower bounds on the minimum orbital period of black holes. In this work, we explore the complementary question of whether an upper bound exists for the minimum orbital period of black holes. We investigate the minimum orbital periods of three types of black holes: Schwarzschild, Reissner-Nordström and Kerr-Newman black holes. We find that the minimum orbital period of these black holes is bounded by an upper limit $T_{min} \leqslant 6\sqrt{3}πM$, where $M$ is the black hole mass. Our results suggest that this upper bound on the minimum orbital period may be a general property in black hole spacetimes.

gr-qc↗
arXiv2026

Bounds on the minimum orbital period in the background of 5-dimensional charged black holes

In this paper, we study the upper and lower bounds on the minimum orbital period of 5-dimensional charged black holes. Our results indicate that the upper bound of the minimum orbital period corresponds to non-charged black holes, while the lower bound is achieved in the case of maximally charged black holes. We further establish precise analytical expressions for the upper and lower bounds of the minimum orbital period. Our findings provide valuable insights into 5-dimensional charged black holes and help constrain theoretical gravity models.

gr-qc↗
arXiv2026

Analysis of minimum orbital periods around d-dimensional charged black holes

This paper investigates the bounds on the minimum orbital period for test objects around d-dimensional charged black holes in asymptotically flat spacetimes. We derive the exact critical radius and the minimum orbital period. We then prove analytically that the minimum orbital period decreases strictly as the charge of the black hole increases. Thus, the upper limit is reached for an uncharged black hole, while the lower limit is attained for a maximally charged one, and the two bounds take the closed form $\frac{2π(d-2)}{d-3}[(d-2)M]^{\frac{1}{d-3}}\leqslant T_{min} \leqslant 2π\sqrt{\frac{d-1}{d-3}}\,[(d-1)M]^{\frac{1}{d-3}}$. Since the minimum period equals $2π$ times the shadow radius, the upper bound is equivalently a universal upper bound on the shadow radius. These results improve our understanding of dynamics around d-dimensional black holes and impose constraints on candidate gravity theories.

gr-qc↗