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Cited by 24Cosmology and Gravitation TheoriesRelativity and Gravitational TheoryAdvanced Differential Geometry Research

Beyond the Friedmann—Lemaître—Robertson—Walker Big Bang Singularity

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Stoica, Cristi·2012·Communications in Theoretical Physics
DOI 10.1088/0253-6102/58/4/28
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Abstract

Einstein's equation, in its standard form, breaks down at the Big Bang singularity. A new version, equivalent to Einstein's whenever the latter is defined, but applicable in wider situations, is proposed. The new equation remains smooth at the Big Bang singularity of the Friedmann—Lemaître—Robertson—Walker model. It is a tensor equation defined in terms of the Ricci part of the Riemann curvature. It is obtained by taking the Kulkarni—Nomizu product between Einstein's equation and the metric tensor.

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Crossref · 10.1088/0253-6102/58/4/28

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25 of 25 references verified0 citation errors · 0 not checkable

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  • The expanded Einstein equation remains smooth at the FLRW Big-Bang singularity, isotropic singularities, 1+3 warped products with degenerate warping function, and the Schwarzschild black hole singularity.

    “In [19] we saw that our version of Einstein's equation remains smooth at the FLRW Big-Bang singularity, isotropic singularities, 1 + 3 warped products with degenerate warping function, and even at the Schwarzschild black hole singularity [17].”

    From On the Weyl curvature hypothesis (2013) · cites this paper as [19]

    Theorem 1 (Section 4; page not supplied) states that the expanded Einstein equation is smooth at the FLRW Big-Bang singularity. The paper does not establish this for isotropic singularities generally or for 1+3 warped products with a degenerate warping function. Its Conclusions mention a smooth formulation of the Schwarzschild singularity but attribute that result to Ref. [22]; the citing sentence also attaches a separate citation to Schwarzschild. (LLM, conf=0.88)

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  • Important classes of singularities are quasi-regular: the isotropic singularities, the Schwarzschild singularity, 1+3 degenerate warped products, and in particular the FLRW Big-Bang singularity.

    “As it turned out, important classes of singularities are quasi-regular: the isotropic singularities, the Schwarzschild singularity, 1 + 3 degenerate warped products, in particular the FLRW Big-Bang singularity.”

    From On the Weyl curvature hypothesis (2013) · cites this paper as [19]

    Section 3 shows that the FLRW Big-Bang singularity has smooth curvature and Ricci-decomposition tensors; the Conclusions say a coordinate change gives the Schwarzschild singularity these properties too. The copy does not call these singularities “quasi-regular” or establish the claim for isotropic singularities as a class or for 1+3 degenerate warped products (searched those terms). No page numbers were available in the indexed passages. (LLM, conf=0.86)

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  • The expanded Einstein equation is equivalent to the standard Einstein equation for non-singular metrics and remains smooth when the metric becomes degenerate.

    “The new equation is equivalent to the standard Einstein equation so long as the metric is not singular, but it can be written, and remains smooth, even in cases when the metric becomes degenerate.”

    From On the Weyl curvature hypothesis (2013) · cites this paper as [19]

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Cites

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Research works printed but not linked: 14

  1. [5]5. H.P. Robertson, The Astrophysical Journal 82 (1935) 284.
  2. [6]6. H.P. Robertson, The Astrophysical Journal 83 (1936) 187.
  3. [7]7. H.P. Robertson, The Astrophysical Journal 83 (1936) 257.
  4. [8]8. A.G. Walker, Proceedings of the London Mathematical Society 2 (1937) 90.
  5. [9]9. S. Hawking and R. Penrose, Proc. Roy. Soc. London Ser. A 314 (1970) 529.
  6. [13]13. A. Ashtekar, J. Phys. Conf. Ser. 189 (2009) 012003.
  7. [19]19. Arthur L. Besse, Einstein Manifolds, Ergebnisse der Mathematik und Ihrer Grenzgebiete (3) [Results in Math- ematics and Related Areas (3)], Vol. 10 Berlin, Springer- Verlag, New York (1987).
  8. [20]20. S. Gallot, D. Hullin, and J. Lafontaine, Riemannian Ge- ometry, 3rd ed. Berlin, Springer-Verlag, New York (2004).
  9. [21]21. C. Stoica, arXiv:gr-qc/1112.4508, December (2011).
  10. [22]22. C. Stoica, Eur. Phys. J. Plus. 127 (2012) 83, arXiv:gr- qc/1111.4837.
  11. [23]23. C. Stoica, Phys. Scr. 85 (2012) 055004, arXiv:gr- qc/1111.4332.
  12. [25]25. C. Stoica, arXiv:gr-qc/1203.3382, March (2012).
  13. [27]27. C. Stoica, arXiv:gr-qc/1205.2586, May (2012).
  14. [28]28. C. Stoica, Seminar held at JINR, Dubna, arXiv:gr- qc/1207.5303, May (2012).

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Authors
Stoica, C.
Venue
Communications in Theoretical Physics
Publisher
IOP Publishing
Published
2012-10
Volume
58
Issue
4
Pages
613-616
ISSN
0253-6102 (ISSN-L)
DOI
10.1088/0253-6102/58/4/28
OpenAlex
W2146496236
Semantic Scholar
21ddecf3571124f0a195c0a2727b6b12fbc9fd58
Cited by
24
References
25
Citations by year
2026: 1 · 2023: 1 · 2020: 1 · 2018: 1 · 2017: 1 · 2016: 5 · 2015: 4 · 2014: 5 · 2013: 4 · 2012: 1
FWCI
2.45
Type
journal article
Language
en
Open access
Locations
  • Communications in Theoretical Physics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Advanced Differential Geometry Research
Keywords
initial singularity, Friedmann-Lemaître-Robertson-Walker model, Einstein field equations, Ricci curvature, modified Einstein field equations, singularity resolution, cosmology

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