Skip to main content
SpringerLink
Log in
Book cover

Relativity and Gravitation pp 287–290Cite as

Electric and Magnetic Weyl Tensors in Higher Dimensions

  • Conference paper
  • First Online:

  • 1728 Accesses

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

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.

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

Learn about 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

  1. Faculty of Science and Technology, University of Stavanger, 4036, Stavanger, Norway

    S. Hervik

  2. Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Prague 1, Czech Republic

    M. Ortaggio

  3. Faculty of Applied Sciences TW16, Ghent University, Galglaan 2, 9000, Ghent, Belgium

    L. Wylleman

Authors
  1. S. Hervik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Ortaggio
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. Wylleman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Ortaggio .

Editor information

Editors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic

    Jiří Bičák

  2. Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic

    Tomáš Ledvinka

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

Search

Navigation