Application of Kaluza–Klein theory in modelling compact stars: exploring extra dimensions

ABSTRACT A theoretical framework for calculating the mass–radius curve of compact stars in the Kaluza–Klein space–time is introduced, with one additional compact spatial dimension. Static, spherically symmetric solutions are considered, with the equation of state provided by a zero temperature, interacting multidimensional Fermi gas. To model the strong force between baryons, a repulsive potential is introduced, which is linear in the particle number density. The maximal mass of compact stars is calculated for different model parameters, and with a physical parameter choice, it satisfies observational data, meaning that it is possible to model simple, realistic objects within this framework. Based on this comparison, a limiting size for the observational regime of extra dimensions in compact stars is provided, with $r_\mathrm{c} \gtrsim 0.2$ fm.