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 Λ6. 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 ω1 in the internal space. For example, ω1 = 1 and ω1 = 2 correspond to the monopole two-forms and the Casimir effect, respectively. In the particular case Λ6 = 0, the parameter ω1 is also absent: ω1 = 0. In the weak-field approximation, we perturb the background ansatz by a point-like mass. We demonstrate that in the case ω1 > 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/ √ ω1 6 × 10 −3 cm. Therefore, in the Solar system the parameterized post-Newtonian parameter γ 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 ω1 > 0. However, if ω1 = 0, then the parameterized post-Newtonian parameter γ = 1/3, which strongly contradicts the observations.

Exact and asymptotic black branes with spherical compactification

“…These relations exactly coincide with the relations in [1]. From these relations we can conclude thatε > 0 ⇒ ω 1 > −1 and sign Λ 6 = sign ω 1 .…”

“…As we pointed out in [1], in the case of uniformly smeared (over the internal space) perturbation, the perturbed metrics preserves its diagonal form and in isotropic coordinates reads…”

“…Choosing different values of ω 1 (with the vacuumlike equation of state in the external space), we can simulate different forms of matter. For example, ω 1 = 1 and ω 1 = 2 correspond to the monopole formfields (the Freund-Rubin scheme of compactification) and the Casimir effect, respectively [1,[13][14][15]. It is worth noting that in the case of the zero cosmological constant Λ 6 = 0, the parameter ω 1 should also be equal to zero:…”

“…It is natural to generalize such approach to our multidimensional model assuming the dustlike equations of state in all spatial dimensions and to perturb the background R 4 × S 2 by such massive source. This problem was considered in papers [1,2]. It was shown that the Einstein equations are compatible only if the background matter also undergoes perturbations, i.e.…”

“…However, the physical meaning of tension for ordinary astrophysical objects (such as our Sun) is still not clear. Black strings/branes have a topology (four-dimensional Schwarzschild spacetime)×(flat inter- * Electronic address: alexey.chopovsky@gmail.com † Electronic address: maxim.eingorn@gmail.com ‡ Electronic address: ai˙zhuk2@rambler.ru 1 In the most cases, when we use the word "pointlike", we usually mean a gravitating mass which has a delta-shaped form in the external space and is uniformly smeared over the internal space. In this case, the nonrelativistic gravitational potential exactly coincides with the Newtonian one [6].…”