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

TL;DR

This paper analyzes a many-body gravitational system in Kaluza-Klein models with toroidal extra dimensions, revealing that internal pressure or tension causes mass smearing and absence of KK modes, challenging quantum physics consistency.

Contribution

It constructs the Lagrange function for a many-body system in Kaluza-Klein models with arbitrary equations of state in extra dimensions and examines implications for gravitational tests and quantum physics.

Findings

Gravitational tests require the sum of equations of state parameters to be near the latent soliton value.

Internal pressure or tension leads to mass smearing over extra dimensions.

Mass smearing results in the absence of KK modes, conflicting with quantum physics expectations.

Abstract

In this paper, 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 energy density much greater than 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,\ldots,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 and periastron advances) 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 view of quantum physics.