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Quasilocal Energy and Conserved Charges Derived from the Gravitational Action

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J. David Brown, James W. York

General Relativity and Quantum Cosmology · Submitted 29 Sep 1992

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

how it is stated · asserted 1.00 read the record →

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arXiv IDgr-qc/9209012 (version 1)
Pith ID2HA3PZX5, Pith's permanent record of this paper and its review
CitationJames W. York, J. David Brown. "Quasilocal Energy and Conserved Charges Derived from the Gravitational Action." arXiv:gr-qc/9209012 (1992). https://pith.science/paper/2HA3PZX5
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,142 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.96 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 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. contribution 0.55 0.87 0.24 asserted 1.00
s1 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. method 0.89 0.85 0.06 asserted 1.00
s2 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 ${}^3B$. method 0.96 0.80 0.04 asserted 1.00
s3 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 $B$. method 0.49 0.85 0.18 asserted 1.00
s4 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 $\Sigma$. result 1.00 0.89 0.25 asserted 1.00
s5 The quasilocal energy is also the value of the Hamiltonian that generates unit magnitude proper time translations on ${}^3B$ in the direction orthogonal to $B$. interpretation 0.58 0.84 0.15 asserted 1.00
s6 Conserved charges such as angular momentum are defined using the surface stress tensor and Killing vector fields on ${}^3B$. contribution 0.56 0.84 0.07 asserted 1.00
s7 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. result 0.97 0.75 0.19 asserted 1.00
s8 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. result 0.98 0.91 0.13 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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.

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References
How later papers used it

376 later papers cite it

Evidence: substantial. 376 of the citing papers share no author with it, and 157 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 634 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its method or tool 17 of 133 papers with this label
How the literature uses it

317 arXiv papers cite this in 531 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 314 sentences without a confident label

Contests it 2 papers
  • However, the central charge of right mover cannot be calculated by the covariant phase space method given by [ref] , and hence we used the quasi-local charge [ref] .

    New Near Horizon Limit in Kerr/CFT · New near horizon limit of 5D Myers-Perry black hole · contest 0.72

  • To indicate the severity of the problem, let us point out that the most well-known notion of quasi-local energy by Brown and York [ref] does not in general vanish in the Minkowski spacetime.

    Quasi-local conserved charges in General Relativity · Introduction and summary of results · contest 0.81

Builds on it 6 papers
  • The quasilocal energy inside an $r=$ constant surface placed outside the event horizon is given by [equation] Assuming the existence of a BEC with $φ≠0$ and that inside the horizon the $r$ coordinate becomes timelike with $ϵ=-1$ [equation] These expressions were derived in [ref] in the case $φ=0$.

    Analysis of some classical and quantum aspects of black holes · Quasilocal energy for a graviton condensate black hole · 0.94

  • We generalize the machinery developed in [ref] to Euclidean signature to study the boundary value problem.

    Hartle-Hawking state and its factorization in 3d gravity · Boundary value problem for the wavefunctions · 0.86

  • When $∂Σ_t$ is an inner-boundary in the bulk of the spacetime, and $ξ$ is a unit time translation, [ref] is a generalisation of the Brown-York quasi-local energy [ref] .

    Quasi-local conserved charges in General Relativity · Quasi-local charges on a boundary · 0.92

Uses its method or tool 112 papers
  • We are interested in the first magnitude (further details can be found in [ref] ); integrating the energy density along $B$ leads us directly to the definition of the quasilocal energy given in [ref] [equation] The energy result in the subtraction of the total mean curvature of $B$ as embedded in $Σ$ with the total mean curvature of $B$ as embedded in a Minkowskian reference frame, times the inverse of the Einstein's gravitational constant.

    Condensates beyond the horizons · . Quasilocal energy · 0.84

  • By using the Brown-York prescription [ref] of quasilocal energy for computing $E_grav$, we had long back [ref] defined BH horizon by equipartition of total energy into gravitational and non-gravitational energy.

    On the equilibrium of the Buchdahl star · Introduction · 0.89

  • Hence, we use the “quasi-local charge” defined by using the surface energy momentum tensor [ref] , and obtain anomalous transformations with a plausible cut-off.

    Another Realization of Kerr/CFT Correspondence · Energy-momentum tensor in CFT · 1.00

Compares with it 15 papers
Cites it as support 2 papers
  • These fall-off conditions can be motivated by demanding that the charges associated to the Brown–York stress tensor [ref] be finite and non-zero [ref] .

    Inflation in Flatland · Asymptotic symmetries of dS$_3$ · 0.98

  • This particular map from $λ$ to $E$ has been chosen such that the continuum part of the spectrum describing a (gravitationally) bound state has $E=0$ as its upper bound, and the total binding energy is[In black hole physics, the fact that the binding energy is minus the total mass $M$ is supported by the Brown-York quasi-local energy [ref] , or by the teleparallel approach to gravity [ref] .

    Black Holes and Marchenko-Pastur Distribution · MP distribution and black hole spectrum · 0.97

Cites it as background 46 papers

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