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We study the static stellar equilibrium configurations ofuncharged andcharged spheres composed by a relativistic polytropic fluid, and compare withthose of spheres composed by a non-relativistic polytropic fluid, the latercase already being studied in a previous work [J. D. Arba\~nil, P. S. Lemos, V.T. Zanchin, Phys. Rev. D \textbf{88}, 084023 (2013)]. In the relativistic fluidcase, a relativistic polytropic equation of state, $p=\omega\delta^{\gamma}$,is assumedd. Here, $\delta=\rho-p/(\gamma-1)$, with $\delta$ and $\rho$ beingthe rest mass density and the energy density, respectively, and $\omega$ and$\gamma$ are respectively the polytropic constant and the polytropic exponent.We assume that the charge density $\rho_e$ is proportional to the energydensity $\rho$, $\rho_e = \alpha\, \rho$, with $\alpha$ being a constant suchthat $0\leq |\alpha|\leq 1$. Some properties of the charged spheres such asmass, total electric charge, radius, redshift, and the speed of sound areanalyzed. The dependence of such properties with the polytropic exponent isalso investigated. In addition, some limits that arise in general relativity,such as the Chandrasekhar limit, the Oppenheimer-Volkoff limit, the Buchdahlbound and the Buchdahl-Andr\'easson bound, i.e., the Buchdahl bound for theelectric case, are studied. As in a charged non-relativistic polytropic sphere,the charged relativistic polytropic sphere with $\gamma\to\infty$ and $\alpha\to 1$ saturates the Buchdahl-Andr\'easson bound, thus indicating that itreaches the quasiblack hole configuration. We show by means of numericalanalysis that, as expected, the major differences between the two cases appearin the high energy density region.

Relativistic polytropic spheres with electric charge: Compact stars, compactness and mass bounds, and quasiblack hole configurations