Pith. Sign in

RECORD

General Laws of Black-Hole Dynamics

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Sean A. Hayward

General Relativity and Quantum Cosmology · Submitted 2 Mar 1993

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

The authors' main claim A general definition of a black hole is given, and general `laws of black-hole dynamics' derived.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDgr-qc/9303006 (version 3)
Pith IDRAUD5PEA, Pith's permanent record of this paper and its review
CitationSean A. Hayward. "General Laws of Black-Hole Dynamics." arXiv:gr-qc/9303006 (1993). https://pith.science/paper/RAUD5PEA
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, 7,456 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.32 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.45 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

A general definition of a black hole is given, and general `laws of black-hole dynamics' derived. The definition involves something similar to an apparent horizon, a trapping horizon, defined as a hypersurface foliated by marginal surfaces of one of four non-degenerate types, described as future or past, and outer or inner. If the boundary of an inextendible trapped region is suitably regular, then it is a (possibly degenerate) trapping horizon. The future outer trapping horizon provides the definition of a black hole. Outer marginal surfaces have spherical or planar topology. Trapping horizons are null only in the instantaneously stationary case, and otherwise outer trapping horizons are spatial and inner trapping horizons are Lorentzian. Future outer trapping horizons have non-decreasing area form, constant only in the null case---the `second law'. A definition of the trapping gravity of an outer trapping horizon is given, generalizing surface gravity. The total trapping gravity of a compact outer marginal surface has an upper bound, attained if and only if the trapping gravity is constant---the `zeroth law'. The variation of the area form along an outer trapping horizon is determined by the trapping gravity and an energy flux---the `first law'.

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 A general definition of a black hole is given, and general `laws of black-hole dynamics' derived. contribution 1.00 0.94 0.37 asserted 1.00
s1 The definition involves something similar to an apparent horizon, a trapping horizon, defined as a hypersurface foliated by marginal surfaces of one of four non-degenerate types, described as future or past, and outer or inner. contribution 0.86 0.77 0.09 asserted 1.00
s2 If the boundary of an inextendible trapped region is suitably regular, then it is a (possibly degenerate) trapping horizon. result 0.97 0.76 0.09 asserted 0.97
s3 The future outer trapping horizon provides the definition of a black hole. contribution 0.71 0.81 0.52 asserted 1.00
s4 Outer marginal surfaces have spherical or planar topology. result 0.98 0.77 0.05 asserted 1.00
s5 Trapping horizons are null only in the instantaneously stationary case, and otherwise outer trapping horizons are spatial and inner trapping horizons are Lorentzian. result 0.97 0.82 0.07 asserted 1.00
s6 Future outer trapping horizons have non-decreasing area form, constant only in the null case---the `second law'. result 0.98 0.87 0.18 asserted 1.00
s7 A definition of the trapping gravity of an outer trapping horizon is given, generalizing surface gravity. contribution 0.95 0.88 0.06 asserted 1.00
s8 The total trapping gravity of a compact outer marginal surface has an upper bound, attained if and only if the trapping gravity is constant---the `zeroth law'. result 0.98 0.87 0.08 asserted 1.00
s9 The variation of the area form along an outer trapping horizon is determined by the trapping gravity and an energy flux---the `first law'. result 0.93 0.88 0.12 asserted 1.00

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

What was examined, and what was not

sources read
  • arXiv listing abstract v3
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

A general definition of a black hole is given, and general `laws of black-hole dynamics' derived. The definition involves something similar to an apparent horizon, a trapping horizon, defined as a hypersurface foliated by marginal surfaces of one of four non-degenerate types, described as future or past, and outer or inner. If the boundary of an inextendible trapped region is suitably regular, then it is a (possibly degenerate) trapping horizon. The future outer trapping horizon provides the definition of a black hole. Outer marginal surfaces have spherical or planar topology. Trapping horizons are null only in the instantaneously stationary case, and otherwise outer trapping horizons are spatial and inner trapping horizons are Lorentzian. Future outer trapping horizons have non-decreasing area form, constant only in the null case---the `second law'. A definition of the trapping gravity of an outer trapping horizon is given, generalizing surface gravity. The total trapping gravity of a compact outer marginal surface has an upper bound, attained if and only if the trapping gravity is constant---the `zeroth law'. The variation of the area form along an outer trapping horizon is determined by the trapping gravity and an energy flux---the `first law'.

Human review

How Pith checks papers → · Full audit of this paper →

References
How later papers used it

132 later papers cite it

Evidence: substantial. 132 of the citing papers share no author with it, and 20 of those carry a confident label from Pith's citation classifier.

Pith read 19 of the 260 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 5 of 12 papers with this label
How the literature uses it

49 arXiv papers cite this in 98 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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper
  • General laws of black-hole dynamics, some of which are analogous to the laws of thermodynamics, have recently been found for a general definition of black hole in terms of a future outer trapping horizon, a hypersurface foliated by marginal surfaces of a certain type.

    Spin-Coefficient Form of the New Laws of Black-Hole Dynamics · 0.83

Papers citing it · 64 sentences without a confident label

Builds on it 1 paper
  • Building on earlier work [ref] , an interesting area theorem in general relativity was recently proved [ref] for holographic screens, a substantive extension of apparent horizons to timelike or spacelike objects whose slices are marginally-trapped or -antitrapped surfaces [ref] .

    Area Law Unification and the Holographic Event Horizon · Introduction · 0.84

Uses its method or tool 4 papers
  • For this purpose, we follow the formalism presented by Hayward's generalized thermodynamics [ref] , in which the black-hole boundary is defined as a future outer trapping horizon, defined as the surface where the expansion of future-directed null geodesics vanishes.

    Hawking atmosphere of anti-de Sitter black holes · Dynamical Anti-de Sitter Black Holes · 0.99

  • The apparent or trapping horizons are defined here following the approach proposed by Ref. [ref] , based on a study of the optical scalars related to null congruences defined by a codimension-two foliation of the spacetime.

    Charged cosmological black holes: a thorough study of a family of solutions · Existence and number of apparent horizons · 1.00

  • Following Ref. [ref] , we classify any sphere of symmetry $S$ of the spacetime according to the expansions $Θ_±$ of the null congruences defined by outgoing and ingoing null rays, as follows, * if $Θ_+ Θ_- < 0$, we say that $S$ is regular; * if $Θ_+ Θ_- > 0$, with $Θ_± < 0$, we say that $S$ is trapped; * if $Θ_+ Θ_- > 0$, with $Θ_± > 0$, we say that $S$ is antitrapped; * if $Θ_+ Θ_- =0$, then we say that $S$ is marginal.

    Evolving black holes from conformal transformations of static solutions · Trapping horizons · 0.96

Compares with it 3 papers
  • However, this definition does not agree with that given in [ref] or [ref] and is only applicable in spherically symmetric spacetimes.

    Dynamical surface gravity · Surface gravity for marginally trapped surfaces · 0.84

  • We also remark that Eq. [ref] is similar in form to the definition of trapping horizons in standard GR [ref] .

    Quasilocal approach to general universal horizons · Dynamical cases and general definition · 0.96

  • We draw connections between the xKS form and another `(2+2)-split' ansatz, namely the double-null foliation [ref] , and show that one can identify them in special gauges.

    The extended Kerr-Schild approach to general relativity · Comparison with double-null foliation · 0.99

Cites it as background 20 papers

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.