Abstract
In this note we wish to complement some recent work in the cosmological literature concerning the Weyl conformal curvature tensor and its parts. In particular, we shall give a clear-cut definition of the Newtonian limits of electric and magnetic parts of the Weyl tensor. We also discuss that only a subset of the relativistic equations is needed to obtain a closed system of equations in the Newtonian limit.
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References
Barnes A., Rowlingson R.R.: Class. Quantum Gravit. 6, 949 (1989)
Bertschinger E., Hamilton A.J.S.: Astrophys. J. 435, 1 (1994)
Bertschinger E., Jain B.: Astrophys. J. 431, 486 (1994)
Brauer U.: J. Math. Phys. 33, 1224 (1992)
Brauer U., Rendall A., Reula O.: Class. Quantum Gravit. 11, 2283 (1994)
Bruni M., Matarrese S., Pantano O.: Astrophys. J. 445, 958 (1995)
Buchert T., Götz G.: J. Math. Phys. 28, 2714 (1987)
Buchert T.: Astron. Astrophys. 223, 9 (1989)
Buchert, T.: In: Bonometto, S., Primack, J., Provenzale, A. (eds.) Proc. IOP ‘Enrico Fermi’, Course CXXXII (Dark Matter in the Universe), Varenna 1995, pp. 543–564. IOS Press, Amsterdam (1996)
Buchert T.: Gen. Relativ. Gravit. 40, 467 (2008)
Croudace K., Parry J., Salopek D., Stewart J.: Astrophys. J. 423, 22 (1994)
Ehlers, J.: Akad. Wiss. Lit. Mainz, Abh. Math.-Nat. Klasse 11, p. 793 (in German) (1961); translated: Gen. Relativ. Gravit. 25, 1225 (1993)
Ehlers, J.: In: Nitsch, J., et al. (eds.) Grundlagenprobleme der Modernen Physik. Bibliograph. Inst. Mannheim, pp. 65–84 (in German) (1981)
Ehlers, J.: In: Fenarese, G. (ed.) Classical Mechanics and Relativity: Relationship and Consistency, pp. 95–106. Bibliopolis, Naples (1991)
Ehlers J.: Class. Quantum Gravit. 14, A119 (1997)
Ehlers J., Buchert T.: Gen. Relativ. Gravit. 29, 733 (1997)
Ellis, G.F.R.: In: Sachs, R. (ed.) General Relativity and Cosmology. Academic Press, New York (1971)
Ellis G.F.R., Dunsby P.K.S.: Astrophys. J. 479, 97 (1997)
Kofman L., Pogosyan D.: Astrophys. J. 442, 30 (1995)
Komar A.: Phys. Rev. 104, 544 (1956)
Künzle H.P.: Gen. Relativ. Gravit. 7, 445 (1976)
Künzle H.P., Nester J.M.: J. Math. Phys. 25, 1009 (1984)
Lesame W.M., Ellis G.F.R., Dunsby P.K.S.: Phys. Rev. D 53, 738 (1996)
Matarrese S., Pantano O., Saez D.: Mon. Not. R. Astron. Soc. 271, 513 (1994)
Matarrese, S.: In: Bonometto, S., Primack, J., Provenzale, A. (eds.) Proc. IOP ‘Enrico Fermi’, Course CXXXII (Dark Matter in the Universe), Varenna 1995, p. 601. IOS Press, Amsterdam (1996)
Matarrese S., Terranova D.: Mon. Not. R. Astron. Soc. 283, 400 (1996)
Sachs R.K.: Zeitschrift für Physik 157, 462 (1960) (in German)
Szekeres P., Rankin J.R.: J. Austral. Math. Soc. 20, 114 (1977)
Trümper M.: J. Math. Phys. 6, 584 (1965)
van Elst H., Uggla C., Lesame W.M., Maartens R., Maartens R., Maartens R.: Class. Quantum Gravit. 14, 1151 (1997)
van Elst H., Uggla C.: Class. Quantum Gravit. 14, 2673 (1997)
Acknowledgments
In 1996, TB was supported by the “Sonderforschungsbereich 375-95 für Astro-Teilchenphysik der Deutschen Forschungsgemeinschaft”. He would like to thank the Albert-Einstein-Institut in Potsdam for generous hospitality during a working visit in 1996, where this work has been written. TB would also like to thank Henk van Elst for digging out the preprint, as well as for help and comments during the preparation of this manuscript.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Ehlers, J., Buchert, T. On the Newtonian limit of the Weyl tensor. Gen Relativ Gravit 41, 2153–2158 (2009). https://doi.org/10.1007/s10714-009-0855-1
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DOI: https://doi.org/10.1007/s10714-009-0855-1