Non-Uniformity of the Positive Mass Theorem in a Gaussian Model Delta Net for the Geon
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2026
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| _version_ | 1866901465722781696 |
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| author | Cramer, Claes |
| author_facet | Cramer, Claes |
| contents | <p>Given the distribution geometry arising from a sequence of homotopic and globally hyperbolic spacetimes converging, in the sense of distributions within a renormalised Gaussian distribution algebra, to a distribution with singular support on the null characteristic, we prove that although the distributional strong and weak energy conditions hold at the singular support, there exist neighbourhoods of the singular support and spacetime elements in the sequence such that, within these neighbourhoods, there are points at which neither the strong nor the weak energy condition holds. Consequently, the positive mass theorem cannot be applied uniformly across geometric scales in this distribution-geometric framework, since the dominant energy condition fails on suitable open sets at finite scale.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18226400 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Non-Uniformity of the Positive Mass Theorem in a Gaussian Model Delta Net for the Geon Cramer, Claes <p>Given the distribution geometry arising from a sequence of homotopic and globally hyperbolic spacetimes converging, in the sense of distributions within a renormalised Gaussian distribution algebra, to a distribution with singular support on the null characteristic, we prove that although the distributional strong and weak energy conditions hold at the singular support, there exist neighbourhoods of the singular support and spacetime elements in the sequence such that, within these neighbourhoods, there are points at which neither the strong nor the weak energy condition holds. Consequently, the positive mass theorem cannot be applied uniformly across geometric scales in this distribution-geometric framework, since the dominant energy condition fails on suitable open sets at finite scale.</p> |
| title | Non-Uniformity of the Positive Mass Theorem in a Gaussian Model Delta Net for the Geon |
| url | https://doi.org/10.5281/zenodo.18226400 |