Many-body problem in Kaluza-Klein models: theory and observational consequences

TL;DR

This paper analyzes the gravitational behavior of many-body systems in Kaluza-Klein models with extra dimensions, revealing that internal space pressure leads to mass smearing and absence of KK modes, challenging quantum physics consistency.

Contribution

It constructs the Lagrange function for many-body systems in Kaluza-Klein models with arbitrary equations of state in extra dimensions and examines observational constraints on internal space parameters.

Findings

Gravitational tests require negligible deviation from the latent soliton value.

Pressure in internal space causes mass smearing over extra dimensions.

Presence of pressure prevents KK mode excitation, which is unnatural quantum mechanically.

Abstract

We consider a system of gravitating bodies in Kaluza-Klein models with toroidal compactification of extra dimensions. To simulate the astrophysical objects (e.g., our Sun and pulsars) with the energy density much greater than the pressure, we suppose that these bodies are pressureless in the external/our space. At the same time, they may have nonzero parameters \omega_{(\bar\alpha -3)} \, (\bar\alpha =4,...,D) of the equations of state in the extra dimensions. We construct the Lagrange function of this many-body system for any value of \Sigma =\sum_{\bar\alpha} \omega_{(\bar\alpha -3)}. Moreover, the gravitational tests (PPN parameters, perihelion/periastron advance) require negligible deviation from the latent soliton value \Sigma =-(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 the KK modes. This looks very unnatural from the point of quantum physics.