UCM 48 — The Correct Gullstrand-Painlevé Form of the Kerr Metric and the Ricci Tensor for Rotating Substrate Flows
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| Format: | Recurso digital |
| Sprache: | Englisch |
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2026
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| _version_ | 1866901848432050176 |
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| author | Prebeck, Norbert |
| author_facet | Prebeck, Norbert |
| contents | <p>Paper 12 (Part K) of the UCM preprint series derived the Kerr metric from the Doran substrate flow using a Gullstrand-Painlevé line element with flat spatial slices (g_rr = 1, g_r_phi = 0). We show by explicit coordinate transformation from Boyer-Lindquist that the correct Doran metric has g_rr = Sigma / (r^2 + a^2) and a non-vanishing cross-term g_r_phi. The corrected metric satisfies R_mu_nu = 0 exactly by coordinate invariance, closing Open Problem 3 of Part K. Theorem 6.1 of Part K (consistency with the Einstein field equations) is promoted from conditional to unconditional. All other Part K results — frame-dragging, Lense-Thirring precession, Carter-Robinson uniqueness, Klainerman-Szeftel stability — remain valid.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19533927 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | UCM 48 — The Correct Gullstrand-Painlevé Form of the Kerr Metric and the Ricci Tensor for Rotating Substrate Flows Prebeck, Norbert Kerr metric Doran coordinates Gullstrand-Painleve Ricci-tensor rotating black holes U-Cell Model erratum <p>Paper 12 (Part K) of the UCM preprint series derived the Kerr metric from the Doran substrate flow using a Gullstrand-Painlevé line element with flat spatial slices (g_rr = 1, g_r_phi = 0). We show by explicit coordinate transformation from Boyer-Lindquist that the correct Doran metric has g_rr = Sigma / (r^2 + a^2) and a non-vanishing cross-term g_r_phi. The corrected metric satisfies R_mu_nu = 0 exactly by coordinate invariance, closing Open Problem 3 of Part K. Theorem 6.1 of Part K (consistency with the Einstein field equations) is promoted from conditional to unconditional. All other Part K results — frame-dragging, Lense-Thirring precession, Carter-Robinson uniqueness, Klainerman-Szeftel stability — remain valid.</p> |
| title | UCM 48 — The Correct Gullstrand-Painlevé Form of the Kerr Metric and the Ricci Tensor for Rotating Substrate Flows |
| topic | Kerr metric Doran coordinates Gullstrand-Painleve Ricci-tensor rotating black holes U-Cell Model erratum |
| url | https://doi.org/10.5281/zenodo.19533927 |