Year: 2026
Type: preprint
Abstract: We identify all radial interaction potentials that generalize Newton's exterior shell theorem, for which a uniformly distributed spherical shell is indistinguishable from a point-source up to strength renormalization and radial rescaling. We call these shape-preserving shell interactions, extending Gurzadyan's cosmological theorem which considers strength renormalization alone. We further expand the theory from monopolar to multipolar sources and establish the corresponding classification in arbitrary spatial dimensions. We find potential families beyond the spherical property subclass and show that the classifications for multipolar shape-preserving interactions form a nested hierarchy, with each lower-rank class being a subset of the next higher-rank class.
Source: arXiv (Cornell University)
Institutions: Scripps College, Claremont Colleges
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221070745