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Constraints on Kaluza–Klein gravity from Gravity Probe B

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Abstract

Using measurements of geodetic precession from Gravity Probe B, we constrain possible departures from Einstein’s General Relativity for a spinning test body in Kaluza–Klein gravity with one additional space dimension. We consider the two known static and spherically symmetric solutions of the 5D field equations (the soliton and canonical metrics) and obtain new limits on the free parameters associated with each. The theory is consistent with observation but must be “close to 4D” in both cases.

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Notes

  1. The properties of the induced matter are obtained by decomposing the 5D field equations \(R_{AB}=0\) into \(\alpha \beta \)-, \(\alpha \ell \)- and \(\ell \ell \)-components. Requiring that the 4D field equations take their usual form, \(G_{\alpha \beta }=(8\pi G/c^4)T_{\alpha \beta }\), one obtains an expression for the energy-momentum tensor \(T_{\alpha \beta }\) of an induced 4D matter fluid that is a manifestation of pure geometry in 5D.

  2. For simplicity we have set to zero a constant of the motion (\(k\) in [15]) associated with momentum along the extra dimension. This has the effect of “switching off” the \(S^{\ell }\)-component for the soliton metric and might be worth revisiting in future work.

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Acknowledgments

J. M. O. thanks C. W. F. Everitt, R. J. Adler, A. Silbergleit and the other members of the Gravity Probe B theory group for discussions. R. D. E. acknowledges the Fisher College of Science and Mathematics at Towson University for travel support to present these results.

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Authors and Affiliations

  1. Department of Physics, Astronomy and Geosciences, Towson University, Towson, MD, 21252, USA

    J. M. Overduin & R. D. Everett

  2. Department of Physics and Astronomy, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    P. S. Wesson

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  1. J. M. Overduin
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Correspondence to J. M. Overduin.

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Overduin, J.M., Everett, R.D. & Wesson, P.S. Constraints on Kaluza–Klein gravity from Gravity Probe B. Gen Relativ Gravit 45, 1723–1731 (2013). https://doi.org/10.1007/s10714-013-1551-8

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