Constraints on Kaluza–Klein gravity from Gravity Probe B

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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Fig. 1

Notes

  1. 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. 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.

References

  1. 1.

    Overduin, J.M., Wesson, P.S.: Kaluza–Klein gravity. Phys. Rep. 283, 303–378 (1997). http://arxiv.org/abs/grqc/9805018

    Google Scholar 

  2. 2.

    Wesson, P.S.: Five-Dimensional Physics. World Scientific, Singapore (2006)

    Google Scholar 

  3. 3.

    Bronnikov, K.A., Melnikov, V.N.: The Birkhoff theorem in multidimensional gravity. Gen. Relativ. Gravit. 27, 465–474 (1995)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  4. 4.

    Keresztes, Z., Gergely, L.A.: On the validity of the five-dimensional Birkhoff theorem: the tale of an exceptional case. Class. Quantum Gravit. 25, 165016 (2008)

    MathSciNet  ADS  Article  Google Scholar 

  5. 5.

    Schmidt, H.-J.: The tetralogy of Birkhoff theorems. Gen. Relativ. Gravit. (2013, in press). http://arxiv.org/abs/1208.5237

  6. 6.

    Sorkin, R.: Kaluza–Klein monopole. Phys. Rev. Lett. 51, 87–90 (1983)

    MathSciNet  ADS  Article  Google Scholar 

  7. 7.

    Gross, D.J., Perry, M.J.: Magnetic monopoles in Kaluza–Klein theories. Nucl. Phys. B 226, 29–48 (1983)

    MathSciNet  ADS  Article  Google Scholar 

  8. 8.

    Davidson, A., Owen, D.A.: Black holes as windows to extra dimensions. Phys. Lett. B 155, 247–250 (1985)

    MathSciNet  ADS  Article  Google Scholar 

  9. 9.

    Mashhoon, B., Liu, M., Wesson, P.S.: Particle masses and the cosmological constant in Kaluza–Klein theory. Phys. Lett. B 331, 305–312 (1994)

    ADS  Article  Google Scholar 

  10. 10.

    Liu, H., Wesson, P.S.: The motion of a spinning object in a higher-dimensional spacetime. Class. Quantum Gravit. 13, 2311–2318 (1996)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  11. 11.

    Mashhoon, B., Wesson, P., Liu, H.: Dynamics in Kaluza–Klein gravity and a fifth force. Gen. Relativ. Gravit. 30, 555–571 (1998)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  12. 12.

    Wesson, P.S.: The physical nature of five-dimensional solitons: a survey (2011, preprint) http://arxiv.org/abs/1104.3244

  13. 13.

    Kalligas, D., Wesson, P.S., Everitt, C.W.F.: The classical tests in Kaluza–Klein gravity. Astrophys. J. 439, 548–557 (1995)

    ADS  Article  Google Scholar 

  14. 14.

    Lim, P.H., Overduin, J.M., Wesson, P.S.: Light deflection in Kaluza–Klein gravity. J. Math. Phys. 36, 6907–6914 (1995)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  15. 15.

    Liu, H., Overduin, J.M.: Solar system tests of higher dimensional gravity. Astrophys. J. 538, 386–394 (2000). http://arxiv.org/abs/gr-qc/0003034

    Google Scholar 

  16. 16.

    Overduin, J.M.: Solar system tests of the equivalence principle and constraints on higher-dimensional gravity. Phys. Rev. D 62, 102001 (2000). http://arxiv.org/abs/gr-qc/0007047

  17. 17.

    Wesson, P.S.: A new dark matter candidate: Kaluza–Klein solitons. Astrophys. J. 420, L49–L52 (1994)

    ADS  Article  Google Scholar 

  18. 18.

    Everitt, C.W.F., et al.: Gravity Probe B: final results of a space experiment to test general relativity. Phys. Rev. Lett. 106, 221101 (2011)

    ADS  Article  Google Scholar 

  19. 19.

    Everitt, C.W.F.: The Stanford relativity gyroscope experiment (A): history and overview. In: Fairbank, J.D., Deaver, B.S., Everitt, C.W.F., Michelson, P.F. (eds.) Near Zero: New Frontiers of Physics, pp. 587–639. W.H. Freeman, New York (1988)

    Google Scholar 

  20. 20.

    Thorne, K.S.: Gravitomagnetism, jets in quasars, and the Stanford gyroscope experiment. In: Fairbank, J.D., Deaver, B.S., Everitt, C.W.F., Michelson, P.F. (eds.) Near Zero: New Frontiers of Physics, pp. 573–586. W.H. Freeman, New York (1988)

    Google Scholar 

  21. 21.

    Schiff, L.I.: Motion of a gyroscope according to Einstein’s theory of gravitation. Proc. Natl. Acad. Sci. 46, 871–882 (1960)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  22. 22.

    Adler, R.J., Silbergleit, A.S.: General treatment of orbiting gyroscope precession. Int. J. Theor. Phys. 39, 1291–1316 (2000)

    MathSciNet  MATH  Article  Google Scholar 

  23. 23.

    Will, C.M.: Covariant calculation of general relativistic effects in an orbiting gyroscope experiment. Phys. Rev. D 67, 062003 (2003)

    Google Scholar 

  24. 24.

    Li, J., et al.: On-orbit performance of Gravity Probe B drag-free translation control and orbit determination. Adv. Space Res. 40, 1–10 (2007)

    ADS  Article  Google Scholar 

  25. 25.

    Riess, A.G. et al.: A 3% solution: determination of the Hubble constant with the Hubble Space Telescope and Wide Field Camera 3. Astrophys. J. 730, 119 (2011). http://arxiv.org/abs/arXiv:1103.2976

  26. 26.

    Suzuki, N. et al.: The Hubble Space Telescope cluster supernova survey V. Astrophys. J. 746, 85 (2012). http://arxiv.org/abs/arXiv:1105.3470

    Google Scholar 

  27. 27.

    Hinshaw, G. et al.: Nine-year Wilkinson Microwave Anisotropy Probe (WMAP) observations. Astrophys. J. Suppl. (2012, in press) http://arxiv.org/abs/1212.5226

  28. 28.

    Overduin, J.M., Wesson, P.S.: Kaluza-Klein cosmology with noncompactified extra dimensions. In: Rainer, M., Schmidt, H.-J. (eds.) Current Topics in Mathematical Cosmology, pp. 293–301. World Scientific, Singapore (1998)

    Google Scholar 

  29. 29.

    Overduin, J.M., Wesson, P.S., Mashhoon, B.: Decaying dark energy in higher-dimensional gravity. Astron. Astrophys. 473, 727–731 (2007). http://arxiv.org/abs/0707.3148

    Google Scholar 

  30. 30.

    Will, C.M.: Finally, results from Gravity Probe B. Physics 4, 43 (2011). http://physics.aps.org/articles/v4/43

  31. 31.

    Overduin, J., et al.: STEP and fundamental physics. Class. Quantum Gravit. 29, 184012 (2012)

    ADS  Article  Google Scholar 

  32. 32.

    Matsuno, K., Ishihara, H.: Geodetic precession in squashed Kaluza-Klein black hole spacetimes. Phys. Rev. D 80, 104037 (2009)

    Google Scholar 

  33. 33.

    Liu, H., Wesson, P.S., de Leon, J.P.: Time-dependent Kaluza-Klein soliton solutions. J. Math. Phys. 34, 4070–4079 (1993)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  34. 34.

    Billyard, A., Wesson, P.S.: Class of exact solutions in 5D gravity and its physical implications. Phys. Rev. D 53, 731–737; erratum. Phys. Rev. D 54, 4189–4189 (1996)

    Google Scholar 

  35. 35.

    Liu, H., Wesson, P.S.: A class of Kaluza-Klein soliton solutions. Phys. Lett. B 381, 420–422 (1996)

    Google Scholar 

  36. 36.

    Liu, H., Wesson, P.S.: The physical properties of charged five-dimensional black holes. Class. Quantum Gravit. 14, 1651–1663 (1997)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  37. 37.

    Overduin, J.M.: Constraints on Lorentz violation from Gravity Probe B. In: Kostelecky, A. (ed.) CPT and Lorentz Symmetry, pp. 199–205. World Scientific, Singapore (2007)

    Google Scholar 

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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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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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Keywords

  • Higher-dimensional gravity
  • Experimental tests of gravitational theories