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Lemaître model and cosmic mass

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Abstract

The mass of a sphere of simmetry in the Lemaître universe is discussed using the Hawking–Hayward quasi-local energy and clarifying existing ambiguities. A covariantly conserved current introduced by Cahill and McVittie is shown to be a multiple of the Kodama energy current.

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Notes

  1. By “sphere of symmetry” we mean a 2-dimensional surface which is an orbit of the isometry of the spacetime manifold describing spherical symmetry (of course, such orbits exist through any point of a spherically symmetric spacetime).

  2. In retrospect, this is a good argument because there is little arguing on the physical mass of the Schwarzschild spacetime, and the choice proved to give the correct answer (see below).

References

  1. Lemaître, G.: Ann. Soc. Sci. Bruxelles A 53, 51 (1933) [reprinted in Gen. Relativ. Gravit. 29, 641 (1997)]

  2. Tolman, R.C.: Proc. Natl. Acad. Sci. USA 20, 169 (1934)

    Article  ADS  Google Scholar 

  3. Bondi, H.: Mon. Not. R. Astron. Soc. 107, 410 (1947)

    Article  MathSciNet  ADS  Google Scholar 

  4. Krasiński, A.: Inhomogeneous Cosmological Models. Cambridge University Press, Cambridge (1997)

    Book  Google Scholar 

  5. Bolejko, K., Celerier, M.-N., Krasiński, A.: Class. Quantum Grav. 28, 164002 (2011)

    Article  ADS  Google Scholar 

  6. Alfedeel, A.A.H., Hellaby, C.: Gen. Relativ. Gravit. 42, 1935 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  7. Pavlidou, V., Tetradis, N., Tomaras, T.N.: JCAP 1405, 017 (2014)

    Article  ADS  Google Scholar 

  8. Bolejko, K., Hellaby, C., Alfedeel, A.H.A.: JCAP 1109, 011 (2011)

    Article  ADS  Google Scholar 

  9. Nogueira, F.A.M.G.: arXiv:1312.5005

  10. Iribarrem, A. et al.: arXiv:1308.2199

  11. Marra, V., Paakkonen, M.: JCAP 1201, 025 (2012)

    Article  ADS  Google Scholar 

  12. Clarkson, C., Regis, M.: JCAP 1102, 013 (2011)

    Article  ADS  Google Scholar 

  13. Clarkson, C., Maartens, R.: Class. Quantum Grav. 27, 124008 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  14. Moradi, R., Firouzjaee, J.T., Mansouri, R.: arXiv:1301.1480

  15. Leithes, A., Malik, K.A.: arXiv:1403.7661

  16. Durrer, R.: The Cosmic Microwave Background. Cambridge University Press, Cambridge (2008)

    Book  Google Scholar 

  17. Hawking, S.W.: J. Math. Phys. 9, 598 (1968)

    Article  ADS  Google Scholar 

  18. Hayward, S.A.: Phys. Rev. D 49, 831 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  19. Kodama, H.: Prog. Theor. Phys. 63, 1217 (1980)

    Article  ADS  Google Scholar 

  20. Misner, C.W., Sharp, D.H.: Phys. Rev. 136, B571 (1964)

    Article  MathSciNet  ADS  Google Scholar 

  21. Hernandez, W.C., Misner, C.W.: Astrophys. J. 143, 452 (1966)

    Article  ADS  Google Scholar 

  22. Cahill, M.E., McVittie, G.C.: J. Math. Phys. 11, 1382 (1970)

    Article  MathSciNet  ADS  Google Scholar 

  23. Wald, R.M.: General Relativity. University of Chicago Press, Chicago (1984)

    Book  Google Scholar 

  24. Szabados, L.: Living Rev. Relat. 7, 4 (2004)

    ADS  Google Scholar 

  25. Hayward, S.A.: Phys. Rev. D 53, 1938 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  26. Faraoni, V.: Phys. Rev. D 84, 024003 (2011)

    Article  ADS  Google Scholar 

  27. Carrera, M., Giulini, D.: Rev. Mod. Phys. 82, 169 (2010)

    Article  ADS  Google Scholar 

  28. McVittie, G.C.: Mon. Not. R. Astron. Soc. 93, 325 (1933)

    Article  ADS  Google Scholar 

  29. Nielsen, A.B., Visser, M.: Class. Quantum Grav. 23, 4637 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  30. Abreu, G., Visser, M.: Phys. Rev. D 82, 044027 (2010)

    Article  ADS  Google Scholar 

  31. Booth, I., Brits, L., Gonzalez, J.A., van den Broeck, V.: Class. Quantum Grav. 23, 413 (2006)

    Article  ADS  Google Scholar 

  32. Gao, C., Chen, X., Shen, Y.-G., Faraoni, V.: Phys. Rev. D 84, 104047 (2011)

    Article  ADS  Google Scholar 

  33. Di Criscienzo, R., Hayward, S.A., Nadalini, M., Vanzo, L., Zerbini, S.: Class. Quantum Grav. 27, 015006 (2010)

    Article  ADS  Google Scholar 

  34. Faraoni, V.: Galaxies 1, 114 (2013). [arXiv:1309.4915]

    Article  ADS  Google Scholar 

  35. Faraoni, V.: Lectures on Cosmological and Black Hole Apparent Horizons. Springer, New York (2015)

    Book  Google Scholar 

Download references

Acknowledgments

This work is supported by Bishop’s University and by the Natural Sciences and Engineering Research Council of Canada (NSERC).

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Authors and Affiliations

  1. Physics Department and STAR Research Cluster, Bishop’s University, 2600 College Street, Sherbrooke, QC, J1M 1Z7, Canada

    Valerio Faraoni

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  1. Valerio Faraoni
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Correspondence to Valerio Faraoni.

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Faraoni, V. Lemaître model and cosmic mass. Gen Relativ Gravit 47, 84 (2015). https://doi.org/10.1007/s10714-015-1926-0

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