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
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Senovilla, J.: Super-energy tensors. Class. Quantum Grav. 17, 2799 (2000). doi:10.1088/0264-9381/17/14/313
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)
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)
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
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
Matte, A.: Sur de nouvelles solutions oscillatoires de équations de la gravitation. Can. J. Math. 5, 1 (1953)
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)
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
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
Wylleman, L.: On Weyl type II or more special spacetimes in higher dimensions (in preparation)
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
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
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
Acknowledgments
M.O. acknowledges support from research plan RVO: 67985840 and research grant no P203/10/0749.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights 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
DOI: https://doi.org/10.1007/978-3-319-06761-2_38
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06760-5
Online ISBN: 978-3-319-06761-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)