{"work":{"id":"22fcc5d0-5415-4a5a-ad4e-adc5a4805dab","openalex_id":null,"doi":null,"arxiv_id":"gr-qc/0703035","raw_key":null,"title":"3+1 Formalism and Bases of Numerical Relativity","authors":null,"authors_text":"Gourgoulhon, E","year":2007,"venue":"gr-qc","abstract":"These lecture notes provide some introduction to the 3+1 formalism of general relativity, which is the foundation of most modern numerical relativity. The text is rather self-contained, with detailed calculations and numerous examples. Contents: 1. Introduction, 2. Geometry of hypersurfaces, 3. Geometry of foliations, 4. 3+1 decomposition of Einstein equation, 5. 3+1 equations for matter and electromagnetic field, 6. Conformal decomposition, 7. Asymptotic flatness and global quantities, 8. The initial data problem, 9. Choice of foliation and spatial coordinates, 10. Evolution schemes.","external_url":"https://arxiv.org/abs/gr-qc/0703035","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-07-10T22:37:36.492994+00:00","pith_arxiv_id":"gr-qc/0703035","created_at":"2026-05-10T10:14:09.404916+00:00","updated_at":"2026-07-10T22:37:36.492994+00:00","title_quality_ok":true,"display_title":"3+1 Formalism and Bases of Numerical Relativity","render_title":"3+1 Formalism and Bases of Numerical Relativity"},"hub":{"state":{"work_id":"22fcc5d0-5415-4a5a-ad4e-adc5a4805dab","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":15,"external_cited_by_count":null,"distinct_field_count":4,"first_pith_cited_at":"2012-02-27T00:47:39+00:00","last_pith_cited_at":"2026-07-07T18:48:48+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-08-20T12:20:08.520318+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":3},{"context_role":"method","n":1}],"polarity_counts":[{"context_polarity":"background","n":3},{"context_polarity":"use_method","n":1}],"runs":{},"summary":{},"graph":{},"authors":[]}}