Generalizing Shell Theorem to Constant Curvature Spaces in All Dimensions and Topologies
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917224526118912 |
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| author | Tse, Ava K. Markowich, Olivia M. Phan, Trung V. |
| author_facet | Tse, Ava K. Markowich, Olivia M. Phan, Trung V. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20852 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalizing Shell Theorem to Constant Curvature Spaces in All Dimensions and Topologies Tse, Ava K. Markowich, Olivia M. Phan, Trung V. Classical Physics 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. |
| title | Generalizing Shell Theorem to Constant Curvature Spaces in All Dimensions and Topologies |
| topic | Classical Physics |
| url | https://arxiv.org/abs/2511.20852 |