Kaluza-Klein Multidimensional Models with Ricci-Flat Internal Spaces: The Absence of the KK Particles

Abstract

In this paper we consider a multidimensional Kaluza-Klein (KK) model with a Ricci-flat internal space, e.g., a Calabi-Yau manifold. We perturb this background metrics by a system of gravitating masses, e.g., astrophysical objects such as our Sun. We suppose that these masses are pressureless in the external space but they have relativistic pressure in the internal space. We show that metric perturbations do not depend on coordinates of the internal space and gravitating masses should be uniformly smeared over the internal space. This means, first, that KK modes corresponding to the metric fluctuations are absent and, second, particles should be only in the ground quantum state with respect to the internal space. In our opinion, these results look very unnatural. According to statistical physics, any nonzero temperature should result in fluctuations, i.e. in KK modes. We also get formulae for the metric correction terms which enable to calculate the gravitational tests: the deflection of light, the time-delay of the radar echoes and the perihelion advance.

Weak-field limit of Kaluza–Klein models with spherically symmetric static scalar field: observational constraints

“…For Eq. (4.3), we can achieve this value only in the case of black string/brane Ω = −1/2 in agreement with [2,13,14]. That is, the gravitating masses should have tension in the internal space.…”

“…In Kaluza-Klein models with Ricci-flat internal space, the same value of γ as in the general relativity (i.e. γ = 1), can be achieve only for black brane value Ω = − 1/2 [1][2][3]. However, we consider this value as not very realistic since there is no any physically reasonable motivation for it up to now.…”

“…a e-mail: a.chopovsky@yandex.ru Therefore, in Refs. [1][2][3], we investigated this problem for multidimensional KK models with compact Ricci-flat (or toroidal, as a particular example) internal spaces. We considered the post-Newtonian gravitational field generated by discrete massive sources with negligible (in comparison to c) velocities.…”

Weak field limit of higher dimensional massive Brans-Dicke gravity: Observational constraints

“…Then, since EoS in the internal space is unknown, for the sake of generality, it is assumed some nonzero parameter Ω of EoS in the internal space. For this setting of the problem, it turns out that in the KK models with Ricci-flat internal spaces, in order for γ to have the value close to 1, the EoS parameter Ω must be very close to −1/2 [9,10]. To restore the value γ = 1, as in GR, it was necessary to choose Ω = −1/2, which corresponds to black strings/branes [16][17][18][19].…”

“…To answer this question, in the present paper we modify the action of the gravitational sector. We switch from the higher dimensional version of the Einstein-Hilbert action, considered in the previous works [8][9][10], to a scalartensor model, where gravity has an extra scalar degree of freedom Φ coupled to the scalar curvature R non-minimally. Such models arise naturally in the context of String Theory, and play a significant role in present-day cosmology (see [20,21] and references therein).…”