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Correspondence of Many-flavor Limit and Kaluza-Klein Degrees of Freedom in the Description of Compact Stars

We present the correspondence between non-interacting multi-hadron fermion star equation of state in the many-flavor limit and the degrees of freedom of a Kaluza\,--\,Klein compact star. Many flavors can be interpreted in this framework as one extra compacti\-fied spatial dimension with various, more-and-more massive hadron state excitations. The effect of increasing the degrees of freedom was investigated on the equation of state and in connection with the mass-radius relation, $M(R)$. The maximum mass of the star, $M_{\mathrm{max}}$ were also calculated as a function of the maximum number of excited states, $n$ and the size of the compactified extra dimension, $R_{\mathrm{c}}$.