The main purpose of our paper is to construct a viable Kaluza-Klein model satisfying the observational constraints. To this end, we investigate a six-dimensional model with spherical compactification of the internal space. Background matter is considered in the form of a perfect fluid with nonlinear equations of state both in the external/our and internal spaces, and the model is set to include an additional bare cosmological constant Λ₆. In the weak-field approximation, the background is perturbed by a pressureless gravitating mass that is a static pointlike particle. The nonlinearity of the equations of state of the perfect fluid makes it possible to solve simultaneously a number of problems. The requirement that the post-Newtonian parameter γ be equal to 1 in this configuration, first, ensures compatibility with the gravitational tests in the Solar system (deflection of light and time delay of radar echoes) at the same level of accuracy as General Relativity. Second, it translates into the absence of internal space variations, so that the gravitational potential exactly coincides with the Newtonian one, securing the absence of a fifth force. Third, the gravitating mass remains pressureless in the external space, as in the standard approach to nonrelativistic astrophysical objects and, meanwhile, acquires an effective tension in the internal space.

中文翻译：

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非线性理想流体的Kaluza-Klein模型的弱场极限

本文的主要目的是构建一个满足观测约束的可行的Kaluza-Klein模型。为此，我们研究了内部空间球形压缩的六维模型。背景物质与两个外部/我们的和内部空间的状态的非线性方程理想流体的形式考虑，并且该模型被设置成包括额外的裸宇宙常数Λ ₆。在弱场近似中，背景受到无压引力质量的干扰，该质量是静态的点状粒子。理想流体状态方程的非线性使得可以同时解决许多问题。在此配置中，牛顿后参数γ等于1的要求首先确保了与太阳系中的引力测试（光的偏转和雷达回波的时延）兼容，且精度与广义相对论相同。其次，它转化为没有内部空间变化，因此重力势与牛顿势恰好重合，从而确保了没有第五力。第三，引力在外部空间保持无压，