{"work":{"id":"784c50da-d0c0-4d3a-894b-04a3e446a870","openalex_id":null,"doi":null,"arxiv_id":"gr-qc/9209012","raw_key":null,"title":"Quasilocal Energy and Conserved Charges Derived from the Gravitational Action","authors":null,"authors_text":"J","year":1992,"venue":"gr-qc","abstract":"The quasilocal energy of gravitational and matter fields in a spatially bounded region is obtained by employing a Hamilton-Jacobi analysis of the action functional. First, a surface stress-energy-momentum tensor is defined by the functional derivative of the action with respect to the three-metric on ${}^3B$, the history of the system's boundary. Energy density, momentum density, and spatial stress are defined by projecting the surface stress tensor normally and tangentially to a family of spacelike two-surfaces that foliate ${}^3B$. The integral of the energy density over such a two-surface $B$ is the quasilocal energy associated with a spacelike three-surface $\\Sigma$ whose intersection with ${}^3B$ is the boundary $B$. The resulting expression for quasilocal energy is given in terms of the total mean curvature of the spatial boundary $B$ as a surface embedded in $\\Sigma$. The quasilocal energy is also the value of the Hamiltonian that generates unit magnitude proper time translations on ${}^3B$ in the direction orthogonal to $B$. Conserved charges such as angular momentum are defined using the surface stress tensor and Killing vector fields on ${}^3B$. For spacetimes that are asymptotically flat in spacelike directions, the quasilocal energy and angular momentum defined here agree with the results of Arnowitt-Deser-Misner in the limit that the boundary tends to spatial infinity. For spherically symmetric spacetimes, it is shown that the quasilocal energy has the correct Newtonian limit, and includes a negative contribution due to gravitational binding.","external_url":"https://arxiv.org/abs/gr-qc/9209012","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-07-04T15:39:56.571915+00:00","pith_arxiv_id":"gr-qc/9209012","created_at":"2026-05-09T06:45:43.566540+00:00","updated_at":"2026-07-04T15:39:56.571915+00:00","title_quality_ok":true,"display_title":"Quasilocal Energy and Conserved Charges Derived from the Gravitational Action","render_title":"Quasilocal Energy and Conserved Charges Derived from the Gravitational Action"},"hub":{"state":{"work_id":"784c50da-d0c0-4d3a-894b-04a3e446a870","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":28,"external_cited_by_count":null,"distinct_field_count":3,"first_pith_cited_at":"2019-06-21T02:21:47+00:00","last_pith_cited_at":"2026-07-02T17:23:31+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":"2026-08-23T04:59:31.438132+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":11},{"context_role":"method","n":1}],"polarity_counts":[{"context_polarity":"background","n":10},{"context_polarity":"support","n":1},{"context_polarity":"use_method","n":1}],"runs":{},"summary":{},"graph":{},"authors":[]}}