{"work":{"id":"44291068-e4b0-439e-902e-a2b21dd3ce73","openalex_id":null,"doi":null,"arxiv_id":"gr-qc/9302012","raw_key":null,"title":"Geometry of the 2+1 Black Hole","authors":null,"authors_text":"M","year":1993,"venue":"gr-qc","abstract":"The geometry of the spinning black holes of standard Einstein theory in 2+1 dimensions, with a negative cosmological constant and without couplings to matter, is analyzed in detail. It is shown that the black hole arises from identifications of points of anti-de Sitter space by a discrete subgroup of $SO(2,2)$. The generic black hole is a smooth manifold in the metric sense. The surface $r=0$ is not a curvature singularity but, rather, a singularity in the causal structure. Continuing past it would introduce closed timelike lines. However, simple examples show the regularity of the metric at $r=0$ to be unstable: couplings to matter bring in a curvature singularity there. Kruskal coordinates and Penrose diagrams are exhibited. Special attention is given to the limiting cases of (i) the spinless hole of zero mass, which differs from anti-de Sitter space and plays the role of the vacuum, and (ii) the spinning hole of maximal angular momentum . A thorough classification of the elements of the Lie algebra of $SO(2,2)$ is given in an Appendix.","external_url":"https://arxiv.org/abs/gr-qc/9302012","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-05-25T07:25:28.907898+00:00","pith_arxiv_id":"gr-qc/9302012","created_at":"2026-05-09T06:10:43.336191+00:00","updated_at":"2026-05-25T07:25:28.907898+00:00","title_quality_ok":false,"display_title":"Geometry of the (2+1) black hole","render_title":"Geometry of the (2+1) black hole"},"hub":{"state":{"work_id":"44291068-e4b0-439e-902e-a2b21dd3ce73","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":15,"external_cited_by_count":null,"distinct_field_count":2,"first_pith_cited_at":"2025-04-15T05:00:20+00:00","last_pith_cited_at":"2026-05-18T16:33:31+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":"2026-05-27T01:37:15.781871+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":7}],"polarity_counts":[{"context_polarity":"background","n":7}],"runs":{},"summary":{},"graph":{},"authors":[]}}