Kaluza-Klein models: Can we construct a viable example?

Abstract

In Kaluza-Klein models with toroidal compactification of the extra dimensions, we investigate soliton solutions of Einstein equation. The nonrelativistic gravitational potential of these solitons exactly coincides with the Newtonian one. We obtain the formulas for perihelion shift, deflection of light, time delay of radar echoes and post-Newtonian (PPN) parameters. Using the constraint on PPN parameter , we find that the solitonic parameter k should be very big: jkj ! 2:3 Â 10 4 . We define a soliton solution which corresponds to a pointlike mass source. In this case the soliton parameter k ¼ 2, which is clearly contrary to this restriction. A similar problem with the observations takes place for static spherically symmetric perfect fluid with the dustlike equation of state in all dimensions. The common for both of these models is the same (dustlike) equations of state in our three dimensions and in the extra dimensions. All dimensions are treated at equal footing. This is the crucial point. To be in agreement with observations, it is necessary to break the symmetry (in terms of equations of state) between the external/our and internal spaces. It takes place for black strings which are particular examples of solitons with k ! 1. For such k, black strings are in concordance with the observations. Moreover, we show that they are the only solitons which are at the same level of agreement with the observations as in general relativity. Black strings can be treated as perfect fluid with dustlike equation of state p 0 ¼ 0 in the external/our space and very specific equation of state p 1 ¼ Àð1=2Þ" in the internal space. The latter equation is due to negative tension in the extra dimension. We also demonstrate that dimension 3 for the external space is a special one. Only in this case we get the latter equation of state. We show that the black string equations of state satisfy the necessary condition of the internal space stabilization. Therefore, black strings are good candidates for a viable model of astrophysical objects (e.g., Sun) if we can provide a satisfactory explanation of negative tension for particles constituting these objects.

Asymptotic latent solitons, black strings, and black branes inf(R)gravity

“…We have shown in our previous paper [10] that the most natural point-like massive source with the dust-like equations of state in all dimensions contradicts the experimental data. The similar situation takes place in multidimensional linear models [11,12]. In such linear models, latent solitons, in particular, black strings and black branes, satisfy the gravitational experiments at the same level of accuracy as General Relativity.…”

“…However, we have shown that such matter source contradicts the observations in the case of extra dimensions. The similar situation takes place in multidimensional linear models [11,12], where a point-like mass with dust-like equations of state in all spatial dimensions also contradicts the experimental data. However, latent solitons, in particular, black strings and black branes, satisfy the gravitational experiments at the same level of accuracy as General Relativity.…”

“…We call these solutions asymptotic latent solitons. The asymptotic latent solitons from the first class generalize the known results [11,12] of the linear theory. The second class of asymptotic solitons exists only in multidimensional nonlinear models.…”

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

“…In our previous papers [19,25,26] devoted to KK models with toroidal compactification of the extra dimensions, we have shown that gravitating masses should have tension in the internal space to be in agreement with gravitational experiments in the Solar system. For example, black strings/branes with the parameter ω = −1/2 in the equation of state in the internal space satisfy this condition.…”

“…Therefore, such measurements can be a very good test for gravitational theories. From our previous papers [19,25,26] we know that gravitating bodies should have pressure/tension in the extra dimensions to satisfy the observable data for the deflection of light and the experimental restrictions for the PPN parameter γ . In this regard, the question arises of the possibility of building a many-body Lagrange function in the presence of pressure/tension in the extra dimensions.…”