Testing a possible way of geometrization of the strong interaction by a Kaluza–Klein star

Geometrization of the fundamental interactions has been extensively studied during the century. The idea of introducing compactified spatial dimensions originated by Kaluza and Klein. Following their approach, several model were built representing quantum numbers (e.g. charges) as compactified space-time dimensions. Such geometrized theoretical descriptions of the fundamental interactions might lead us to get closer to the unification of the principle theories. Here, we apply a $3+1_C+1$ dimensional theory, which contains one extra compactified spatial dimension $1_C$ in connection with the flavor quantum number in Quantum Chromodynamics. Within our model the size of the $1_C$ dimension is proportional to the inverse mass-difference of the first low-mass baryon states. We used this phenomena to apply in a compact star model — a natural laboratory for testing the theory of strong interaction and the gravitational theory in parallel. Our aim is to test the modification of the measurable macroscopical parameters of a compact Kaluza–Klein star by varying the size of the compactified extra dimension. Since larger the $R_C$ the smaller the mass difference between the first spokes of the Kaluza–Klein ladder resulting smaller-mass stars. Using the Tolman–Oppenheimer–Volkov equation, we investigate the $M$-$R$ diagram and the dependence of the maximum mass of compact stars. Besides testing the validity of our model we compare our results to the existing observational data of pulsar properties for constraints.