Abstract
String theory [4] predicts that the universe has 10 or 26 dimensions. A salient problem is how the Einstein field equation should be written in terms of these revivified Kaluza-Klein cosmologies. The answer is by now well-known, yet nobody seems to have rewritten the seminal computation in [6] where an unnecessarily involved Euler-Lagrange variational method is employed and, curiously enough, no allusion to the Gauss-Bonnet-Chern theorem is made. We provide a more straightforward argument, which has been inspired by Hilbert's original derivation of the Einstein field equation [5].
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References
Besse, A. L. (1987).Einstein Manifolds (Springer, Berlin).
Deruelle, N., and Madore, J. (1986). In Proceedings of the 26th International Astrophysical Colloquium, Origin and Early History of the Universe (Université de Liège).
Dubois-Violette, M., and Madore, J. (1987). Comm. Math. Phys.,108, 213–223.
Green, M. B., Schwarz, J. H., and Witten, E. (1987).Superstring Theory: 1 and 2 (Cambridge University Press, Cambridge).
Hilbert, D. (1915).Nach. Ges. Wiss. Gött.,8, 395–407.
Lovelock, D. (1970).J. Math. Phys.,12, no. 3, 498–501.
Müller-Hoissen, F. (1985).Phys. Lett. B,163, 106–110.
Wheeler, J. T. (1986).Nucl. Phys. B,268, 737–746.
Zwiebach, B. (1985).Phys. Lett. B,156, 315–317.
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This research was supported by the Oskar Huttunen Foundation.
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Pekonen, O. The Einstein field equation in a multidimensional universe. Gen Relat Gravit 20, 667–670 (1988). https://doi.org/10.1007/BF00758971
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DOI: https://doi.org/10.1007/BF00758971