Skip to main content

Electric and Magnetic Weyl Tensors in Higher Dimensions

  • Conference paper
  • First Online:
Relativity and Gravitation

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 157))

  • 1736 Accesses

Abstract

Recent results on purely electric (PE) or magnetic (PM) spacetimes in \(n\) dimensions are summarized. These include: Weyl types; diagonalizability; conditions under which direct (or warped) products are PE/PM.

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

Access this chapter

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 EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
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

Institutional subscriptions

Notes

  1. 1.

    In the sense of the Weyl operator approach of [8] (see also [9]).

References

  1. Senovilla, J.: Super-energy tensors. Class. Quantum Grav. 17, 2799 (2000). doi:10.1088/0264-9381/17/14/313

    Article  ADS  MATH  MathSciNet  Google Scholar 

  2. Senovilla, J.: General electric-magnetic decomposition of fields, positivity and Rainich-like conditions. In: Pascual-Sánchez, J., Floría, L., San Miguel, A., Vicente, F. (eds.) Reference Frames and Gravitomagnetism, pp. 145–164. World Sicentific, Singapore (2001)

    Google Scholar 

  3. Hervik, S., Ortaggio, M., Wylleman, L.: Minimal tensors and purely electric or magnetic spacetimes of arbitrary dimension, ArXiv e-prints 1203.3563 [gr-qc] (2012)

  4. Milson, R., Coley, A., Pravda, V., Pravdová, A.: Alignment and algebraically special tensors in Lorentzian geometry. Int. J. Geom. Meth. Mod. Phys. 2, 41 (2005). doi:10.1142/S0219887805000491

    Article  MATH  Google Scholar 

  5. Coley, A., Milson, R., Pravda, V., Pravdová, A.: Classification of the Weyl tensor in higher dimensions. Class. Quantum Grav. 21, L35 (2004). doi:10.1088/0264-9381/21/7/L01

    Article  ADS  MATH  Google Scholar 

  6. Matte, A.: Sur de nouvelles solutions oscillatoires de équations de la gravitation. Can. J. Math. 5, 1 (1953)

    Article  MATH  MathSciNet  Google Scholar 

  7. Stephani, H., Kramer, D., MacCallum, M., Hoenselaers, C., Herlt, E.: Exact solutions of Einstein’s field equations, 2nd edn. Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  8. Coley, A., Hervik, S.: Higher dimensional bivectors and classification of the Weyl operator. Class. Quantum Grav. 27, 015002 (2010). doi:10.1088/0264-9381/27/1/015002

    Article  ADS  MathSciNet  Google Scholar 

  9. Coley, A., Hervik, S., Ortaggio, M., Wylleman, L.: Refinements of the Weyl tensor classification in five dimensions. Class. Quantum Grav. 29, 155016 (2012). doi:10.1088/0264-9381/29/15/155016

    Article  ADS  MathSciNet  Google Scholar 

  10. Wylleman, L.: On Weyl type II or more special spacetimes in higher dimensions (in preparation)

    Google Scholar 

  11. Pravda, V., Pravdová, A., Ortaggio, M.: Type D Einstein spacetimes in higher dimensions. Class. Quantum Grav. 24, 4407 (2007). doi:10.1088/0264-9381/24/17/009

    Article  ADS  MATH  Google Scholar 

  12. Richardson, R., Slodowy, P.: Minimum Vectors for real reductive algebraic groups. J. London Math. Soc. 42, 409 (1990). doi:10.1112/jlms/s2-42.3.409

    Article  MATH  MathSciNet  Google Scholar 

  13. Hervik, S.: A spacetime not characterized by its invariants is of aligned type II, Class. Quantum Grav. 28, 215009 (2011). doi:10.1088/0264-9381/28/21/215009

Download references

Acknowledgments

M.O. acknowledges support from research plan RVO: 67985840 and research grant no P203/10/0749.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Ortaggio .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Hervik, S., Ortaggio, M., Wylleman, L. (2014). Electric and Magnetic Weyl Tensors in Higher Dimensions. In: Bičák, J., Ledvinka, T. (eds) Relativity and Gravitation. Springer Proceedings in Physics, vol 157. Springer, Cham. https://doi.org/10.1007/978-3-319-06761-2_38

Download citation

Publish with us

Policies and ethics