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Relativity of Observer Splitting Formalism and Some Astrophysical Applications

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Einstein Equations: Physical and Mathematical Aspects of General Relativity (DOMOSCHOOL 2018)

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Abstract

This study deals with the relativity of observer splitting formalism, powerful technique in General Relativity to meaningfully distinguish the contributions of the gravitational effects and fictitious forces on the relative motion of two non-inertial observers. In the weak field limit, this approach has a direct connection with the classical description. This technique is particularly useful to model several astrophysical situations. We show two particular applications related to radiation processes and accretion disc physics.

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Notes

  1. 1.

    Using the Lie transport the terms \(C_{\mathrm {(Lie)}}(n)^\alpha _{\beta \gamma },\ C_{\mathrm {(Lie)}}(n)^\alpha _\beta \), vanish in the Kerr metric (see [5, 6, 13], for further details).

References

  1. F. de Felice, On the gravitational field acting as an optical medium. Gen. Relativ. Gravit. 2, 347–357 (1971)

    Article  ADS  Google Scholar 

  2. M.A. Abramowicz, B. Carter, J.P. Lasota, Optical reference geometry for stationary and static dynamics. Gen. Relativ. Gravit. 20, 1173–1183 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  3. M.A. Abramowicz, G.F.R. Ellis, A. Lanza, Relativistic effects in superluminal jets and neutron star winds. Astrophys. J. 361, 470–482 (1990)

    Article  ADS  Google Scholar 

  4. M.A. Abramowicz, P. Nurowski, N. Wex, Covariant definition of inertial forces. Class. Quantum Grav. 10, L183–L186 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  5. D. Bini, P. Carini, R.T. Jantzen, The intrinsic derivative and centrifugal forces in general relativity: I. Theoretical foundations. Int. J. Mod. Phys. D 6, 1–38 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  6. F. de Felice, D. Bini, Classical Measurements in Curved Space-Times (Cambridge University Press, Cambridge, 2010)

    Book  Google Scholar 

  7. J. Frank, A. King, D.J. Raine, Accretion Power in Astrophysics. (Cambridge University Press, Cambridge, 2002)

    Google Scholar 

  8. J. H. Poynting, Radiation in the solar system: its effect on temperature and its pressure on small bodies. Mon. Not. R. Astron. Soc. 64, 1 (1903)

    Article  ADS  Google Scholar 

  9. H.P. Robertson, Dynamical effects of radiation in the solar system. Mon. Not. R. Astron. Soc. 97, 423 (1937)

    Article  ADS  Google Scholar 

  10. D. Bini, R.T. Jantzen, L. Stella, The general relativistic Poynting Robertson effect. Class. Quantum Grav. 26, 5 (2009)

    MathSciNet  MATH  Google Scholar 

  11. D. Bini, A. Geralico, R.T. Jantzen, O. Semerák, L. Stella, The general relativistic Poynting-Robertson effect: II. A photon flux with nonzero angular momentum. Class. Quantum Grav. 28, 3 (2011)

    MATH  Google Scholar 

  12. C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (W.H.Freeman and Co., San Francisco, 1973)

    Google Scholar 

  13. V. De Falco, E. Battista, M. Falanga, Lagrangian formulation of the general relativistic Poynting-Robertson effect. Phys. Rev. D 97, 8 (2019)

    MathSciNet  Google Scholar 

  14. H. Goldstein, C.P. Poole, J.L. Safko, Classical Mechanics (Addison Wesley, Boston, 2002)

    MATH  Google Scholar 

  15. K. Vogtmann, A. Weinstein, V.I. Arnol’d, Mathematical Methods of Classical Mechanics (Springer, New York, 2013)

    Google Scholar 

  16. P. Bakala, et al., The relativistic Poynting-Robertson effect: numerical models of accretion discs in the strong field regime. Astron. Astrophys. (2018, submitted)

    Google Scholar 

  17. N.I. Shakura, R.A. Sunyaev, Black holes in binary systems. Observational appearance. Astron. Astrophys. 24, 337–355 (1973)

    ADS  Google Scholar 

  18. M. Nannurelli, L. Stella, The X-ray spectrum of modified alpha-viscosity accretion disks. Astron. Astrophys. 226, 343–346 (1989)

    ADS  Google Scholar 

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Acknowledgements

I thank the International Space Science Institute (ISSI) in Bern for the support to carry out this work and the Silesian University in Opava for the partial support in participating at the Domoschool Summer School 2018. I am grateful to Pavel Bakala for the kind help in providing me the Figs. 3 and 4 in this article.

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Authors and Affiliations

  1. Research Centre for Computational Physics and Data Processing, Faculty of Philosophy & Science, Silesian University in Opava, Opava, Czech Republic

    Vittorio De Falco

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  1. Vittorio De Falco
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Correspondence to Vittorio De Falco .

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Editors and Affiliations

  1. Department of Science and High Technology, University Insubrien, Como, Italy

    Sergio Cacciatori

  2. Mathematisches Institut, Humboldt-Universität zu Berlin, Berlin, Germany

    Batu GĂĽneysu

  3. Department of Science and High Technology, University Insubrien, Como, Italy

    Stefano Pigola

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De Falco, V. (2019). Relativity of Observer Splitting Formalism and Some Astrophysical Applications. In: Cacciatori, S., Güneysu, B., Pigola, S. (eds) Einstein Equations: Physical and Mathematical Aspects of General Relativity. DOMOSCHOOL 2018. Tutorials, Schools, and Workshops in the Mathematical Sciences . Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-18061-4_7

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