A new four-parameters family of constitutive functions for spherically symmetric elastic bodies is introduced which extends the two-parameters class polytropic fluid models widely used in several applications mechanics. The four parameters model are exponent \(\gamma \), bulk modulus \(\kappa shear \(\beta \) and Poisson ratio \(\nu \in (-1,1/2]\). arises as a special case when =1/2\) =\gamma \...

The post-Newtonian approximation of the general relativistic Liouville’s equation is presented. Two integrals of motion, generalizations of the classical energy and angular momentum, are obtained. Polytropic models are constructed as an application.

We investigate spherically symmetric, static matter configurations with polytropic equation of state for a class of fðRÞmodels in Palatini formalism and show that the surface singularities recently reported in the literature are not physical in the case of Planck scale modified Lagrangians. In such cases, they are just an artifact of the idealized equation of state used. In fact, we show that f...