Weak-field limit of Kaluza-Klein models with spherical compactification: experimental constraints

Abstract

We investigate the classical gravitational tests for the six-dimensional Kaluza-Klein model with spherical (of a radius $a$) compactification of the internal space. The model contains also a bare multidimensional cosmological constant ${\Lambda }_6$. The matter, which corresponds to this ansatz, can be simulated by a perfect fluid with the vacuum equation of state in the external space and an arbitrary equation of state with the parameter ${\omega }_1$ in the internal space. For example, ${\omega }_1=1$ and ${\omega }_1=2$ correspond to the monopole two-forms and the Casimir effect, respectively. In the particular case ${\Lambda }_6=0$, the parameter ${\omega }_1$ is also absent: ${\omega }_1=0$. In the weak-field approximation, we perturb the background ansatz by a point-like mass. We demonstrate that in the case ${\omega }_1>0$ the perturbed metric coefficients have the Yukawa type corrections with respect to the usual Newtonian gravitational potential. The inverse square law experiments restrict the parameters of the model: $a/\sqrt{{\omega }_1}\lesssim 6\times 10^{-3}cm$. Therefore, in the Solar system the parameterized post-Newtonian parameter $\gamma$ is equal to 1 with very high accuracy. Thus, our model satisfies the gravitational experiments (the deflection of light and the time delay of radar echoes) at the same level of accuracy as General Relativity. We demonstrate also that our background matter provides the stable compactification of the internal space in the case ${\omega }_1>0$. However, if ${\omega }_1=0$, then the parameterized post-Newtonian parameter $\gamma =1/3$, which strongly contradicts the observations.

8 pages, no figures, revised version, equations and references added, accepted for publication in Phys. Rev. D. arXiv admin note: significant text overlap with arXiv:1107.3387

References in corpus (5)

• Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
• Nonlinear multidimensional cosmological models with form fields: stabilization of extra dimensions and the cosmological constant problem
• Classical tests of multidimensional gravity: negative result
• Kaluza-Klein models: can we construct a viable example?
• Weak-field limit of f(R)-gravity in three and more spatial dimensions

Cited by in corpus (11)

• Quantum field theory on toroidal topology: algebraic structure and applications
• Double Higgs Production with a Jet Substructure Analysis to Probe Extra Dimensions
• Remarks on gravitational interaction in Kaluza-Klein models
• Kaluza-Klein models with spherical compactification: observational constraints and possible examples
• Black branes and black strings in the astrophysical and cosmological context
• Significance of tension for gravitating masses in Kaluza-Klein models
• Exact and asymptotic black branes with spherical compactification
• Weak-field limit of Kaluza-Klein model with non-linear perfect fluid
• Self-Gravitating Relativistic Models of Fermions with Anisotropy and Cutoff Energy in their Distribution Function
• Effects of nonlinearity of $f(R)$ gravity and perfect fluid in Kaluza-Klein models with spherical compactification
• Is it possible to unify three kinds of Dark Matters into a Kaluza-Klein Neutrino?