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Interpreting the C-metric

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J. B. Griffiths, P. Krtous, J. Podolsky

General Relativity and Quantum Cosmology · Submitted 15 Sep 2006

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

The authors' main claim Using both the weak field limit and some invariant quantities, we give a direct physical interpretation of the parameters which appear in the new form of the metric.

how it is stated · asserted 1.00 read the record →

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arXiv IDgr-qc/0609056 (version 1)
Pith IDZEIAK23M, Pith's permanent record of this paper and its review
CitationJ. B. Griffiths, J. Podolsky, P. Krtous. "Interpreting the C-metric." arXiv:gr-qc/0609056 (2006). https://pith.science/paper/ZEIAK23M
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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.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,459 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.49 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The basic properties of the C-metric are well known. It describes a pair of causally separated black holes which accelerate in opposite directions under the action of forces represented by conical singularities. However, these properties can be demonstrated much more transparently by making use of recently developed coordinate systems for which the metric functions have a simple factor structure. These enable us to obtain explicit Kruskal-Szekeres-type extensions through the horizons and construct two-dimensional conformal Penrose diagrams. We then combine these into a three-dimensional picture which illustrates the global causal structure of the space-time outside the black hole horizons. Using both the weak field limit and some invariant quantities, we give a direct physical interpretation of the parameters which appear in the new form of the metric. For completeness, relations to other familiar coordinate systems are also discussed.

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 basic properties of the C-metric are well known. background 1.00 0.03 0.02 asserted 1.00
s1 It describes a pair of causally separated black holes which accelerate in opposite directions under the action of forces represented by conical singularities. background 1.00 0.05 0.08 asserted 1.00
s2 However, these properties can be demonstrated much more transparently by making use of recently developed coordinate systems for which the metric functions have a simple factor structure. method 0.60 0.24 0.20 asserted 0.93
s3 These enable us to obtain explicit Kruskal-Szekeres-type extensions through the horizons and construct two-dimensional conformal Penrose diagrams. method 0.51 0.85 0.11 asserted 0.99
s4 We then combine these into a three-dimensional picture which illustrates the global causal structure of the space-time outside the black hole horizons. contribution 0.63 0.92 0.14 asserted 1.00
s5 Using both the weak field limit and some invariant quantities, we give a direct physical interpretation of the parameters which appear in the new form of the metric. interpretation 0.46 0.94 0.23 asserted 1.00
s6 For completeness, relations to other familiar coordinate systems are also discussed. contribution 0.81 0.75 0.03 asserted 0.93

What kind of paper the classifier reports this is: theoretical result 0.82 · 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 basic properties of the C-metric are well known. It describes a pair of causally separated black holes which accelerate in opposite directions under the action of forces represented by conical singularities. However, these properties can be demonstrated much more transparently by making use of recently developed coordinate systems for which the metric functions have a simple factor structure. These enable us to obtain explicit Kruskal-Szekeres-type extensions through the horizons and construct two-dimensional conformal Penrose diagrams. We then combine these into a three-dimensional picture which illustrates the global causal structure of the space-time outside the black hole horizons. Using both the weak field limit and some invariant quantities, we give a direct physical interpretation of the parameters which appear in the new form of the metric. For completeness, relations to other familiar coordinate systems are also discussed.

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References
How later papers used it

59 later papers cite it

Evidence: substantial. 56 of the citing papers share no author with it, and 5 of those carry a confident label from Pith's citation classifier.

Pith read 24 of the 100 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 1 of 3 papers with this label
How the literature uses it

54 arXiv papers cite this in 94 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 · 55 sentences without a confident label

Uses its method or tool 3 papers
  • Let us write down the C-metric in spherical coordinates, following [ref] [equation] where $Q = (1 - a^2r^2)(1 - 2m/r), P = 1 + 2amcosθ$, $a$ is a positive constant and $m$ is the BH (or a point particle) mass.

    On a conformal Schwarzschild-de Sitter spacetime · Conformal Schwarzschild-de Sitter metric · 0.83

  • To begin with, we write down the C-metric in spherical coordinates, following [ref] [equation] where $Q = (1 - a^2r^2)(1 - 2m/r), P = 1 + 2amcosθ$, $a$ is a constant amd $m$ is the BH (or a point particle) mass.

    On a regular modified C-metric · Conformal Schwarzschild metric · 0.81

  • Using the restrictions in $x$ and $y$ imposed, we will use the following transformation given in [ref] , [equation] with $θ∈(0,π)$.

    Dynamical friction on black holes in scalar field environment · Accelerating BHs · 0.97

Compares with it 2 papers
  • These constants are chosen with ordering $w_1<w_2<⋯<w_2N-1<w_2N<w_A$ and with parametrisation[Parametrisation [ref] slightly differs from the standard one presented in [ref] , however it is coherent with [ref] .

    Black holes and solution generating techniques · Array of static accelerating black holes · 0.87

  • A similar bound $α≤1/(√(27) M)$ is known in the literature for a case of an uniformly accelerating black hole with magnitude of acceleration $α$ as described by the C-metric [ref] [equation] where $P=(1+2αmcosθ)$ and $Q=(1-α^2r^2)(1-2m/r)$.

    Bound on Rindler trajectories in Black Hole spacetime · Discussion · 0.94

Cites it as background 28 papers
  • Spacetime around uniformly accelerated black holes can be described by [equation] known as the C-metric [ref] , where [equation] $m$ is the mass parameter and $α$ is interpreted as the acceleration.

    Distinguishing a Slowly Accelerating Black Hole by Differential Time Delays of Images · Introduction · 0.81

  • When the nodal singularity is a deficit angle, the $$̣-like associated contribution to the energy momentum tensor is interpreted as a pulling string, while the excess angle is interpreted as a pushing strut, for a recent review about C-metrics see [ref] , [ref] .

    Thermodynamics of Regular Accelerating Black Holes · Accelerating charged black hole in an external electric field · 0.99

  • The C-metric describes an axially symmetric and stationary spacetime that contains two causally separated BHs accelerating away from each other in opposite spatial directions under the action of conical singularities along the axis [ref] .

    Quasinormal modes of accelerating spacetime · INTRODUCTION · 0.98

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