- Conference date: 23–27 April 2012
- Location: PetrÃ³polis - RJ, Brazil
In this paper we are concerned to reveal that any spacetime structure 〈M, g, D, τ g , ↑〉, which is a model of a gravitational field in General Relativity generated by an energy-momentum tensor T - and which contains at least one nontrivial Killing vector field A - is such that the 2-form field F = dA (where A = g(A,)) satisfies a Maxwell like equation - with a well determined current that contains a term of the superconducting type- which follows directly from Einstein equation. Moreover, we show that the resulting Maxwell like equations, under an additional condition imposed to the Killing vector field, may be written as a Navier-Stokes like equation as well. As a result, we have a set consisting of Einstein, Maxwell and Navier-Stokes equations, that follows sequentially from the first one under precise mathematical conditions and once some identifications about field variables are evinced, as explained in details throughout the text. We compare and emulate our results with others on the same subject appearing in the literature. In Appendix A we fix our notation and recall some necessary material concerning the theory of differential forms, Lie derivatives and the Clifford bundle formalism used in this paper. Moreover, we comment in Appendix B on some analogies (and main differences) between our results to the ones obtained long ago by Bergmann and Kommar which are reviewed and briefly criticized.
- Maxwell equations
- Navier Stokes equations
- Einstein Maxwell equations
- Vector fields
- General relativity
Daniel Baumann, Mark G. Jackson, Peter Adshead, Alexandre Amblard, Amjad Ashoorioon, Nicola Bartolo, Rachel Bean, Maria Beltrán, Francesco de Bernardis, Simeon Bird, Xingang Chen, Daniel J. H. Chung, Loris Colombo, Asantha Cooray, Paolo Creminelli, Scott Dodelson, Joanna Dunkley, Cora Dvorkin, Richard Easther, Fabio Finelli, Raphael Flauger, Mark P. Hertzberg, Katherine Jones‐Smith, Shamit Kachru, Kenji Kadota, Justin Khoury, William H. Kinney, Eiichiro Komatsu, Lawrence M. Krauss, Julien Lesgourgues, Andrew Liddle, Michele Liguori, Eugene Lim, Andrei Linde, Sabino Matarrese, Harsh Mathur, Liam McAllister, Alessandro Melchiorri, Alberto Nicolis, Luca Pagano, Hiranya V. Peiris, Marco Peloso, Levon Pogosian, Elena Pierpaoli, Antonio Riotto, Uroš Seljak, Leonardo Senatore, Sarah Shandera, Eva Silverstein, Tristan Smith, Pascal Vaudrevange, Licia Verde, Ben Wandelt, David Wands, Scott Watson, Mark Wyman, Amit Yadav, Wessel Valkenburg and Matias Zaldarriaga
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