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Record W52800641

Einstein's Field Equations in Cosmology Using Harrison's Formula

2010· preprint· en· W52800641 on OpenAlex
Ioannis Haranas

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueviXra · 2010
Typepreprint
Languageen
FieldPhysics and Astronomy
TopicRelativity and Gravitational Theory
Canadian institutionsYork University
Fundersnot available
KeywordsEinsteinField equationField (mathematics)Classical field theoryMetric (unit)Mathematical physicsTheoretical physicsEinstein tensorCosmologyPhysicsEinstein field equationsGravitational fieldGravitationFreedmanEinstein equationsClassical mechanicsMathematicsGeneral relativityRiemann curvature tensorPure mathematicsGeometryQuantum mechanicsLaw
DOInot available

Abstract

fetched live from OpenAlex

The most important tool for the study of the gravitational field in Einstein’s theory of gravity is his field equations. In this short paper, we demonstrate the derivation of Einstein field equations for the Freedman cosmological model using the Robertson-Walker metric, and furthermore Harrison’s formula for the Ricci tensor. The difference is that Harrison’s formula is an actually shorter way of obtaining the field equations. The advantage is that the Cristoffel symbols do not have to be directly calculated one by one. This can actually be a very useful demonstration for somebody who would like to understand a slightly different but faster way of deriving the field equations, something that is actually rarely seen in many of undergraduate and even graduate textbooks.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.185
Threshold uncertainty score0.706

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.030
GPT teacher head0.316
Teacher spread0.285 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it