Skip to main content

Solution of a Class of Nonlinear Matrix Differential Equations with Application to General Relativity

  • Chapter
  • First Online:
  • 1148 Accesses

Abstract

Five-dimensional general relativity (5DGR) or Kaluza–Klein theory (KKT) [Le84] is considered as a first step towards unification of electromagnetism and gravitation. 5DGR action may be extended by appropriate quadratic terms making up the Gauss–Bonnet term (GBT) to obtain more generalized field equations including up to second–order derivatives of the metric [Lo71].

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Azreg-Aïnou, M.: Quadratic superconducting cosmic strings revisited. Europhys. Lett., 81, article 60003 (2008).

    Article  Google Scholar 

  2. Azreg-Aïnou, M., Clément, G.: Kaluza–Klein and Gauss–Bonnet cosmic strings. Class. Quantum Grav., 13, 2635–2650 (1996).

    Article  Google Scholar 

  3. Lancaster, P., Tismenetsky, M.: The Theory of Matrices with Applications, Academic Press, Orlando, FL (1985).

    MATH  Google Scholar 

  4. Lee, H.C. (ed.): An Introduction to Kaluza-Klein Theories, World Scientific, Singapore (1984).

    Google Scholar 

  5. Lovelock, D.: The Einstein tensor and its generalizations. J. Math. Phys., 12, 498–501 (1971).

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Azreg-Aïnou .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Birkhäuser Boston, a part of Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Azreg-Aïnou, M. (2010). Solution of a Class of Nonlinear Matrix Differential Equations with Application to General Relativity. In: Constanda, C., Pérez, M. (eds) Integral Methods in Science and Engineering, Volume 1. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4899-2_5

Download citation

Publish with us

Policies and ethics