A nuclear many-body theory with Tsallis statistics

Within the generalized statistics developed by Tsallis, we study nuclear matter at high densities in the framework of an effective many-body field theory at finite temperature. Thermodynamics properties of nuclear matter are studied considering the Sommerfeld approximation. We perform the calculations by using the nonlinear Boguta and Bodmer model, extended by the inclusion of the fundamental baryon octet and leptonic degrees of freedom. Through the integration of the Tolman-Oppenheimer-Volkoff equations we obtain, beyond the standard relations for the masses of protoneutron stars as functions of the central density, new results for these quantities as a function of temperature. The above formalism, which so far was not yet discussed in the study of many-body dense nuclear systems, predicts substantial differences from calculations based on standard statistics.