Many-body problem in Kaluza–Klein models with toroidal compactification

Abstract

In this paper, we consider a system of gravitating bodies in Kaluza-Klein models with toroidal compactification of the extra dimensions. To simulate the astrophysical objects (e.g., our Sun and pulsars) with energy density much greater than the pressure, we assume that these bodies are pressureless in the external space, i.e., the space we inhabit. At the same time, they may have nonzero parameters ω (ᾱ−3) (ᾱ = 4, . . . , D) in the equations of state in the extra dimensions. We construct the Lagrange function of this many-body system for any value of = ᾱ ω (ᾱ−3) . Moreover, the gravitational tests (PPN parameters, perihelion and periastron advances) require a negligible deviation from the latent soliton value = −(D −3)/2. However, the presence of pressure/tension in the internal space results necessarily in the smearing of the gravitating masses over the internal space and in the absence of KK modes. This looks very unnatural from the point of view of quantum physics.

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

“…Both matter components result in the spacetime perturbations (2.2) where h M N can be found from the linearized 3 To provide a condition for the gravitating massive body and scalar field to stay at the same place (i.e. to be coupled), we can introduce an interacting term ∼ ρφ into action.…”

“…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

“…Based on the results of the inverse-square law experiments and, assuming that Brans-Dicke parameter ω satisfies the naturalness condition ω ∼ O(1), we obtained the lower bound on the Yukawa mass scale m 10 −11 GeV. The experimental constraints on the PPN parameter γ requires that the EoS parameter Ω must be extremely close to −1/2 similar to KK models with Ricci-flat internal spaces [9,10].…”

“…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).…”