Boundary Obstructions and Lapse Freedom in Static Spherical Hollow Cores

[2608.15000] Boundary Obstructions and Lapse Freedom in Static Spherical Hollow Cores Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search General Relativity and Quantum Cosmology arXiv:2608.15000 (gr-qc) [Submitted on 15 Aug 2026] Title: Boundary Obstructions and Lapse Freedom in Static Spherical Hollow Cores Authors: Nelson Bolívar , Gabriel Abellán , Ivaylo Vasilev View a PDF of the paper titled Boundary Obstructions and Lapse Freedom in Static Spherical Hollow Cores, by Nelson Bol\'ivar and Gabriel Abell\'an and Ivaylo Vasilev View PDF HTML (experimental) Abstract: We analyze a sharply delimited comparison problem for a static spherical hollow core: an empty, flat cavity surrounded by a positive matter wall. In the unit-lapse, flat-slice radial Painleve--Gullstrand (PG) class the Type-I source obeys $p_r=-\rho$ and $p_\perp=-\rho-r\rho'/2$. A regular nonnegative density that rises out of the cavity must therefore violate the transverse null and weak energy conditions. We quantify this boundary obstruction by an exact weighted onset budget and a depth--width bound, and show that the sharp limit has the same negative tangential pressure as its symmetry-invariant regularized Israel layer. We then close the adjacent unit-lapse, curved-slice route under a monotone areal-radius hypothesis. Finally, when only the lapse is released, an incomplete-beta family gives regular hollow shells with flat cavities, Schwarzschild exteriors, no thin shells, and NEC/WEC/SEC/DEC on an explicit compactness interval. The family is conditionally characterized in the minimum-degree and $p_r=0$ sectors and admits a fixed-ADM-mass cavity redshift benchmark. The result is a static boundary theorem and construction, not a general hollow-shell existence theorem, a transport result, or an experimental feasibility claim. Comments: 11 pages, 1 figure Subjects: General Relativity and Quantum Cosmology (gr-qc) Cite as: arXiv:2608.15000 [gr-qc] (or arXiv:2608.15000v1 [gr-qc] for this version) https://doi.org/10.48550/arXiv.2608.15000 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Nelson Bolivar [ view email ] [v1] Sat, 15 Aug 2026 03:17:18 UTC (163 KB) Full-text links: Access Paper: View a PDF of the paper titled Boundary Obstructions and Lapse Freedom in Static Spherical Hollow Cores, by Nelson Bol\'ivar and Gabriel Abell\'an and Ivaylo Vasilev View PDF HTML (experimental) TeX Source view license Current browse context: gr-qc < prev | next > new | recent | 2026-08 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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