Skip to main content
SpringerLink
Log in

Massive Field Equations of Arbitrary Spin in Schwarzschild Geometry: Separation Induced by Spin-\({{3\over2}}\) Case

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

The separation of variables of the spin-\({3\over 2}\) field equation is performed in detail in the Schwarzschild geometry by means of the Newman Penrose formalism. The separated angular equations coincide with those relative to the Robertson-Walker space-time. The separated radial equations, that are much more entangled, can be reduced to four ordinary differential equations, each in one only radial function. As a consequence of the particular nature of the spin coefficients it is shown, by induction, that the massive field equations can be separated for arbitrary spin. baselineskip=12 pt

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Boulware, D. G. (1975). Quantum field theory in Schwarzschild and Rindler spaces. Physical Review D 11, 1404.

    Article  MathSciNet  ADS  Google Scholar 

  • Boulware, D. G. (1975a). Spin-1/2 quantum field theory in Schwarzschild space. Physical Review D 12, 350.

    Article  ADS  Google Scholar 

  • Chandrasekhar, S. (1976). The solution of Dirac's equation in Kerr geometry. Proceedings of the Royal Society (London), A349, 571.

    Article  MathSciNet  ADS  Google Scholar 

  • Chandrasekhar, S. (1983). The Mathematical Theory of Black Holes, Oxford University Press, New York.

  • Gal'tsov, G. V., Pomerantseva, G. A., and Chizhov, G. A. (1984). Behaviour of massive vector particles in a Schwarzschild field. Soviet Physics Jept 27, 697.

    Article  ADS  Google Scholar 

  • Illge, R. (1993). Massive fields of arbitrary spin in curved space-times. Communications in Mathematical Physics 158, 433.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Illge, R. and Schimming, R. (1999). Consistent field equations for higher spin on curved spacetime. Annals of Physics 8, 319.

    Article  MATH  MathSciNet  Google Scholar 

  • Konoplya, R. A. (2006). Massive vector field perturbations in the Schwarzschild background: Stability and quasinormal spectrum. Physical Review D73, 024009.

    ADS  MathSciNet  Google Scholar 

  • Mukhopadhyay, B. and Chakrabarti, S. K. (1999). Semi-analytical solution of Dirac equation in Schwarzschild geometry. Classical and Quantum Gravity 16, 3165.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Newman, E. T. and Penrose, R. (1962). An Approach to Gravitational Radiation by a Method of Spin Coefficients. Journal of Mathematical Physics 3, 566.

    Article  MathSciNet  ADS  Google Scholar 

  • Penrose, R. and Rindler, W. (1984). Spinors and Space-Time, Cambridge University Press. Cambridge.

  • Zecca, A. (2000). Scalar field equation in Schwarzschild space-time. Il Nuovo Cimento B 115, 625.

    MathSciNet  ADS  Google Scholar 

  • Zecca, A. (1996). The Dirac equation in the Robertson Walker space-time. Journal of Mathematical Physics 37, 874.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Zecca, A. (1996b). Separation of the massless field equations for arbitrary spin in the Robertson-Walker space-time. Journal of Mathematical Physics 37, 3539.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Zecca, A. (1998). Dirac equation in Schwarzschild geometry. Il Nuovo Cimento B 113, 1309.

    MathSciNet  ADS  Google Scholar 

  • Zecca, A. (2005). Solution of the massive spin-1 equation in expanding universe. Il Nuovo Cimento B 120, 513.

    MathSciNet  ADS  Google Scholar 

  • Zecca, A. (2006). Separation of massive field equations of arbitrary spin in Robertson-Walker space-time. Submitted.

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica dell' Universita', Via Celoria 16, I-20133, Milano, Italy

    Antonio Zecca

Authors
  1. Antonio Zecca
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antonio Zecca.

Additional information

PACS 04.20.Cv- Fundamental problems and general formalism.

PACS 03.65.Pm- Relativistic wave equations.

PACS 02.30.Jr- Partial differential equations.

PACS 04.20.Jb- Exact solutions.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zecca, A. Massive Field Equations of Arbitrary Spin in Schwarzschild Geometry: Separation Induced by Spin-\({{3\over2}}\) Case. Int J Theor Phys 45, 2208–2214 (2006). https://doi.org/10.1007/s10773-006-9185-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-006-9185-1

Keywords

Search

Navigation