Pith. Sign in

RECORD

A Conformal Hyperbolic Formulation of the Einstein Equations

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
Miguel Alcubierre, Bernd Brugmann, Mark Miller, Wai-Mo Suen

General Relativity and Quantum Cosmology · Submitted 8 Mar 1999

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

The authors' main claim We propose a re-formulation of the Einstein evolution equations that cleanly separates the conformal degrees of freedom and the non-conformal degrees of freedom with the latter satisfying a first order strongly hyperbolic system.

how it is stated · asserted 0.98 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDgr-qc/9903030 (version 1)
Pith IDTXEBLVSA, Pith's permanent record of this paper and its review
CitationBernd Brugmann, Mark Miller, Miguel Alcubierre, Wai-Mo Suen. "A Conformal Hyperbolic Formulation of the Einstein Equations." arXiv:gr-qc/9903030 (1999). https://pith.science/paper/TXEBLVSA
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, 4,447 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.27 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.55 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We propose a re-formulation of the Einstein evolution equations that cleanly separates the conformal degrees of freedom and the non-conformal degrees of freedom with the latter satisfying a first order strongly hyperbolic system. The conformal degrees of freedom are taken to be determined by the choice of slicing and the initial data, and are regarded as given functions (along with the lapse and the shift) in the hyperbolic part of the evolution. We find that there is a two parameter family of hyperbolic systems for the non-conformal degrees of freedom for a given set of trace free variables. The two parameters are uniquely fixed if we require the system to be ``consistently trace-free'', i.e., the time derivatives of the trace free variables remains trace-free to the principal part, even in the presence of constraint violations due to numerical truncation error. We show that by forming linear combinations of the trace free variables a conformal hyperbolic system with only physical characteristic speeds can also be constructed.

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 We propose a re-formulation of the Einstein evolution equations that cleanly separates the conformal degrees of freedom and the non-conformal degrees of freedom with the latter satisfying a first order strongly hyperbolic system. contribution 1.00 0.94 0.59 asserted 0.98
s1 The conformal degrees of freedom are taken to be determined by the choice of slicing and the initial data, and are regarded as given functions (along with the lapse and the shift) in the hyperbolic part of the evolution. method 0.91 0.58 0.10 asserted 0.99
s2 We find that there is a two parameter family of hyperbolic systems for the non-conformal degrees of freedom for a given set of trace free variables. result 0.97 0.95 0.16 asserted 1.00
s3 The two parameters are uniquely fixed if we require the system to be ``consistently trace-free'', i.e., the time derivatives of the trace free variables remains trace-free to the principal part, even in the presence of constraint violations due to numerical truncation error. result 0.58 0.88 0.18 asserted 1.00
s4 We show that by forming linear combinations of the trace free variables a conformal hyperbolic system with only physical characteristic speeds can also be constructed. result 0.77 0.94 0.26 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.55 · 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

We propose a re-formulation of the Einstein evolution equations that cleanly separates the conformal degrees of freedom and the non-conformal degrees of freedom with the latter satisfying a first order strongly hyperbolic system. The conformal degrees of freedom are taken to be determined by the choice of slicing and the initial data, and are regarded as given functions (along with the lapse and the shift) in the hyperbolic part of the evolution. We find that there is a two parameter family of hyperbolic systems for the non-conformal degrees of freedom for a given set of trace free variables. The two parameters are uniquely fixed if we require the system to be ``consistently trace-free'', i.e., the time derivatives of the trace free variables remains trace-free to the principal part, even in the presence of constraint violations due to numerical truncation error. We show that by forming linear combinations of the trace free variables a conformal hyperbolic system with only physical characteristic speeds can also be constructed.

Human review

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

How the literature uses it

2 arXiv papers cite this in 2 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 · 1 sentence without a confident label

Cites it as background 1 paper

Discussion

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