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

Abstract

In Kaluza-Klein models, we investigate soliton solutions of Einstein equation. We obtain the formulas for perihelion shift, deflection of light, time delay of radar echoes and PPN parameters. We find that the solitonic parameter k should be very big: |k|\geq 2.3\times10^4. We define a soliton solution which corresponds to a point-like mass source. In this case the soliton parameter k=2, which is clearly contrary to this restriction. Similar problem with the observations takes place for static spherically symmetric perfect fluid with the dust-like equation of state in all dimensions. The common for both of these models is the same equations of state in our three dimensions and in the extra dimensions. All dimensions are treated at equal footing. To be in agreement with observations, it is necessary to break the symmetry between the external/our and internal spaces. It takes place for black strings which are particular examples of solitons with k\to \infty. 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 dust-like equation of state p_0=0 in the external/our space and very specific equation of state p_1=-(1/2)εin 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.

11 pages, Revtex4, no figures, appendix and references added

References in corpus (8)

• Nonlinear multidimensional cosmological models with form fields: stabilization of extra dimensions and the cosmological constant problem
• Solar System motions and the cosmological constant: a new approach
• Multidimensional cosmological models: cosmological and astrophysical implications and constraints
• Stresses and Strains in the First Law for Kaluza-Klein Black Holes
• Classical tests of multidimensional gravity: negative result
• Conventional cosmology from multidimensional models
• Spherically-symmetric solutions with a chain of n internal Ricci-flat spaces
• Schwarzschild-like exteriors for stars in Kaluza-Klein gravity

Cited by in corpus (2)

• Weak-field limit of f(R)-gravity in three and more spatial dimensions
• Stars in five dimensional Kaluza Klein gravity