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By coordinate transformation, the form of the above equation can be given by $s_{,yy} + s_{,zz} + D(s(y,z),y,z) = 0$. Based on the form, we prove finally that the Meissner effect is not possessed by a KBH-FFM with the condition where $d\\omega/d A_{\\phi} \\leqslant 0$ and $H_{\\phi}(dH_{\\phi}/dA_{\\phi}) \\geqslant 0$,"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1603.08411","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-03-28T15:50:36Z","cross_cats_sorted":["astro-ph.HE"],"title_canon_sha256":"f4445d5170a82c51de625726d6ff8ec7d55dd4945fa14aff108c439e108d95c1","abstract_canon_sha256":"456680497075b735ff312a61b28a908acbb337cef55ff08a31e5948cd1309a82"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:06.103937Z","signature_b64":"WNnWlEfWm91xh+/FzeK9Bv8VQ1kZu6u+C7Nom79kLm/8dswfqbeo1/vb3Mtpiu1pJ68q1vPJ6aVTTkEf5JPgCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64f439aaa79fd0278387a0d24bd0e61a9fd9a2ba44124de129dfb2e6c3e9228e","last_reissued_at":"2026-05-18T01:10:06.103420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:06.103420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A mathematical form of force-free magnetosphere equation around Kerr black holes and its application to Meissner effect","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.HE"],"primary_cat":"gr-qc","authors_text":"Xiaobo Gong, Yi Liao, Zhaoyi Xu","submitted_at":"2016-03-28T15:50:36Z","abstract_excerpt":"Based on the Lagrangian of the steady axisymmetric force-free magnetosphere (FFM) equation around Kerr black holes(KBHs), we find that the FFM equation can be rewritten in a new form as $f_{,rr} / (1-\\mu^{2}) + f_{,\\mu\\mu} / \\Delta + K(f(r,\\mu),r,\\mu) = 0$, where $\\mu = -\\cos\\theta$. By coordinate transformation, the form of the above equation can be given by $s_{,yy} + s_{,zz} + D(s(y,z),y,z) = 0$. 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