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Fermi coordinates in Schwarzschild spacetime: closed form expressions

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Abstract

Fermi coordinates are constructed as exact functions of the Schwarzschild coordinates around the world line of a static observer in the equatorial plane of the Schwarzschild spacetime modulo a single impact parameter determined implicitly as a function of the latter coordinates. This illustrates the difficulty of constructing explicit exact Fermi coordinates even along simple world lines in highly symmetric spacetimes.

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References

  1. Fermi E.: Nuovo Cim. 22, 176 (1921)

    Article  Google Scholar 

  2. Fermi, E.: Sopra i fenomeni che avvengono in vicinanza di una linea oraria. In: Fermi, E. (eds.) Collected Papers (Note e Memorie). Chicago University Press, Chicago (1962–1965)

  3. Bini D., Jantzen R.T.: Nuovo Cim. B 117, 983 (2002)

    ADS  Google Scholar 

  4. Manasse F.K., Misner C.W.: J. Math. Phys. 4, 735 (1963)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Synge J.L.: Relativity: The General Theory. North Holland, Amsterdam (1964)

    Google Scholar 

  6. Misner C.W., Thorne K.S., Wheeler J.A.: Gravitation. Freeman, San Francisco (1973)

    Google Scholar 

  7. Chicone C., Mashhoon B.: Phys. Rev. D 74, 064019 (2006)

    Article  ADS  Google Scholar 

  8. Klein D., Collas P.: J. Math. Phys. 51, 022501 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  9. Klein, D., Randles, E.: Fermi coordinates, simultaneity, and expanding space in Robertson-Walker cosmologies, arXiv:gr-qc/1010.0588

  10. Leaute B., Linet B.: Int. J. Theor. Phys. 22, 67 (1983)

    Article  MathSciNet  Google Scholar 

  11. Linet B.: Phys. Rev. D 70, 048101 (2004)

    Article  ADS  Google Scholar 

  12. Bini D., Geralico A., Jantzen R.T.: Class. Quantum Gravit. 22, 4729 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Hagihara Y.: Jpn. J. Astron. Geophys. 8, 67 (1931)

    MathSciNet  Google Scholar 

  14. Kraniotis G.V., Whitehouse B.S.: Class. Quantum Gravit. 20, 4817 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. Kraniotis G.V., Whitehouse B.S.: Class. Quantum Gravit. 21, 4743 (2004)

    Article  ADS  MATH  Google Scholar 

  16. Hackmann E., Lämmerzahl C.: Phys. Rev. Lett. 100, 171101 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  17. Hackmann E., Kagramanova V., Kunz J., Lämmerzahl C.: Phys. Rev. D 78, 124018 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  18. Hackmann E., Kagramanova V., Kunz J., Lämmerzahl C.: Errat. Phys. Rev. D 79, 029901 (2009)

    Article  ADS  Google Scholar 

  19. Hughes S.A.: Phys. Rev. D 61, 084004 (2000)

    Article  ADS  Google Scholar 

  20. Bird P.F., Friedman M.D.: Handbook of Elliptic Integrals for Engineers and Scientists. 2nd edn. Springer, Berlin (1971)

    Google Scholar 

  21. Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (9th printing). Chapter 18: Weierstrass Elliptic and Related Functions. Dover, New York (1972)

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Authors and Affiliations

  1. Istituto per le Applicazioni del Calcolo “M. Picone”, CNR, 00161, Rome, Italy

    Donato Bini

  2. ICRA, University of Rome “La Sapienza”, 00185, Rome, Italy

    Donato Bini & Robert T. Jantzen

  3. INFN-Sezione di Firenze, Polo Scientifico, Via Sansone 1, 50019, Sesto Fiorentino (FI), Italy

    Donato Bini

  4. Physics Department and ICRA, University of Rome “La Sapienza”, 00185, Rome, Italy

    Andrea Geralico

  5. Department of Mathematical Sciences, Villanova University, Villanova, PA, 19085, USA

    Robert T. Jantzen

Authors
  1. Donato Bini
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  2. Andrea Geralico
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  3. Robert T. Jantzen
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Correspondence to Donato Bini.

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Bini, D., Geralico, A. & Jantzen, R.T. Fermi coordinates in Schwarzschild spacetime: closed form expressions. Gen Relativ Gravit 43, 1837–1853 (2011). https://doi.org/10.1007/s10714-011-1163-0

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  • DOI: https://doi.org/10.1007/s10714-011-1163-0

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