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arXiv · 2511.20852

Generalizing Shell Theorem to Constant Curvature Spaces in All Dimensions and Topologies

Ava K. Tse·Olivia M. Markowich·Trung V. Phan
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Abstract

A gravitational potential has the spherical property when the field outside any uniform spherical shell is indistinguishable from that of a point mass at the center. We present the general potentials that possess this property on constant curvature spaces, using the Euler-Poisson-Darboux identity for spherical means. Our results are consistent with known findings in flat three-dimensional space and reduce to Gurzadyan's cosmological theorem when the rescaling factor is exactly $1$. Our approach naturally extends to nontrivial spatial topologies.

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Ava K. Tse, Olivia M. Markowich, Trung V. Phan. 2025-11-25. Generalizing Shell Theorem to Constant Curvature Spaces in All Dimensions and Topologies. https://doi.org/10.1134/s0202289326700180

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