Gravitational dressing: from the crossed product to more general algebraic and mathematical structure
Abstract
The crossed product, and consequent transition from von Neumann algebras of type III to II, is recovered from a truncation of more general gravitational dressing constructions, about certain spacetimes. This is done by extending "standard dressing" constructions previously used to give a perturbative definition of "gravitational splittings," defining approximate localization of information. This result appears to illustrate that this algebraic transition is a small piece of a more general algebraic, or other mathematical, structure associated with quantum gravity. The leading-order structure involves noncommutativity from separated regions, and at the nonperturbative level connects with a possible explanation of holographic behavior for gravity.
Cite
@article{arxiv.2510.24833,
title = {Gravitational dressing: from the crossed product to more general algebraic and mathematical structure},
author = {Steven B. Giddings},
journal= {arXiv preprint arXiv:2510.24833},
year = {2026}
}
Comments
10 pages + refs; 3 figures. v2 additional construction noted. v3 reference and other minor update