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Intrinsic time in Geometrodynamics: introduction and application to Friedmann cosmology
General Relativity and Quantum Cosmology · Submitted 30 Jun 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The physical interpretation of the modern data from concept of conformal magnitudes is simpler, so is preferable.
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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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The abstract, sentence by sentence
An intrinsic local time in Geometrodynamics is obtained with using a scaled Dirac's mapping. By addition of a background metric, one can construct a scalar field. It is suitable to play a role of intrinsic time. Cauchy problem was successfully solved in conformal variables because they are physical ones. First, the intrinsic time as a logarithm of determinant of spatial metric, was applied to a cosmological problem by Misner. A global time is exist under condition of constant mean curvature slicing of spacetime. A volume of hypersurface and the so-called mean York's time are canonical conjugated pair. So, the volume is the intrinsic global time by its sense. The experimentally observed redshift in cosmology is the evidence of its existence. An intrinsic time of homogeneous models is global. The Friedmann equation by its sense ties time intervals. Exact solutions of the Friedmann equation in Standard cosmology with standard and conformal units are presented. Theoretical curves interpolated the Hubble diagram on latest supernovae are expressed in analytical form. The class of functions in which the concordance model is described is Weierstrass meromorphic functions. The Standard cosmological model is used for fitting the modern Hubble diagram. The physical interpretation of the modern data from concept of conformal magnitudes is simpler, so is preferable.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | An intrinsic local time in Geometrodynamics is obtained with using a scaled Dirac's mapping. | contribution 0.73 | 0.80 | 0.26 | asserted 1.00 |
| s1 | By addition of a background metric, one can construct a scalar field. | method 0.82 | 0.51 | 0.05 | asserted 0.68 |
| s2 | It is suitable to play a role of intrinsic time. | interpretation 0.72 | 0.35 | 0.11 | asserted 0.62 |
| s3 | Cauchy problem was successfully solved in conformal variables because they are physical ones. | result 0.53 | 0.48 | 0.10 | asserted 1.00 |
| s4 | First, the intrinsic time as a logarithm of determinant of spatial metric, was applied to a cosmological problem by Misner. | background 1.00 | 0.04 | 0.05 | asserted 1.00 |
| s5 | A global time is exist under condition of constant mean curvature slicing of spacetime. | background 0.86 | 0.19 | 0.09 | asserted 0.99 |
| s6 | A volume of hypersurface and the so-called mean York's time are canonical conjugated pair. | background 0.81 | 0.19 | 0.08 | asserted 1.00 |
| s7 | So, the volume is the intrinsic global time by its sense. | interpretation 0.93 | 0.26 | 0.16 | asserted 0.99 |
| s8 | The experimentally observed redshift in cosmology is the evidence of its existence. | interpretation 0.71 | 0.11 | 0.10 | asserted 1.00 |
| s9 | An intrinsic time of homogeneous models is global. | result 0.41 | 0.28 | 0.13 | asserted 1.00 |
| s10 | The Friedmann equation by its sense ties time intervals. | interpretation 0.60 | 0.20 | 0.08 | asserted 0.99 |
| s11 | Exact solutions of the Friedmann equation in Standard cosmology with standard and conformal units are presented. | contribution 0.74 | 0.83 | 0.13 | asserted 1.00 |
| s12 | Theoretical curves interpolated the Hubble diagram on latest supernovae are expressed in analytical form. | result 0.72 | 0.80 | 0.13 | asserted 1.00 |
| s13 | The class of functions in which the concordance model is described is Weierstrass meromorphic functions. | result 0.88 | 0.69 | 0.12 | asserted 1.00 |
| s14 | The Standard cosmological model is used for fitting the modern Hubble diagram. | method 0.82 | 0.37 | 0.09 | asserted 1.00 |
| s15 | The physical interpretation of the modern data from concept of conformal magnitudes is simpler, so is preferable. | interpretation 0.98 | 0.42 | 0.28 | asserted 0.99 |
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The paper
Original abstract
An intrinsic local time in Geometrodynamics is obtained with using a scaled Dirac's mapping. By addition of a background metric, one can construct a scalar field. It is suitable to play a role of intrinsic time. Cauchy problem was successfully solved in conformal variables because they are physical ones. First, the intrinsic time as a logarithm of determinant of spatial metric, was applied to a cosmological problem by Misner. A global time is exist under condition of constant mean curvature slicing of spacetime. A volume of hypersurface and the so-called mean York's time are canonical conjugated pair. So, the volume is the intrinsic global time by its sense. The experimentally observed redshift in cosmology is the evidence of its existence. An intrinsic time of homogeneous models is global. The Friedmann equation by its sense ties time intervals. Exact solutions of the Friedmann equation in Standard cosmology with standard and conformal units are presented. Theoretical curves interpolated the Hubble diagram on latest supernovae are expressed in analytical form. The class of functions in which the concordance model is described is Weierstrass meromorphic functions. The Standard cosmological model is used for fitting the modern Hubble diagram. The physical interpretation of the modern data from concept of conformal magnitudes is simpler, so is preferable.
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How the literature uses it
1 arXiv paper cite this in 1 sentence
Papers citing it
Uses its data or values 1 paper
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* arXiv: To incorporate contemporary topics, we scrape problems and solutions from approximately $100$ theoretical physics arXiv manuscripts [ref] , from which we collect $397$ seeds for evaluation[We consider the following arXiv categories: hep-th, hep-ph, hep-lat, cond-mat, nucl-th, gr-qc, quant-ph, astro-ph, nlin, physics, and math-ph.
Fine-Tuning Small Reasoning Models for Quantum Field Theory · Problem Seeds · 0.83
What it cites · 12 sentences without a confident label
Uses the method or tool of 1 paper
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For getting a global time in general case, let us set the CMC gauge [ref] (consideration especially for closed manifolds see [ref] ) on every slice, which labeled by the coordinate time $t$, K≡-3κ=K(t), where [equation] is a mean curvature of the hypersurface $Σ_t$ – arithmetic mean of the principal curvatures $κ_1, κ_2, κ_3$.
Initial Value Problem in General Relativity · Global time · 0.86
Cites as background 2 papers
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The some authors (see, for example, [ref] ) prefer utilizing the York time as a real time and a volume of the Universe as an operator of evolution.
Frequently asked questions about Shape Dynamics · Conclusions · 0.83
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The some authors (see, for example, [ref] ) prefer utilizing the York time as a real time and a volume of the Universe as an operator of evolution.
Classical and quantum cosmology with York time · Conclusions · 0.83
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