Hyperons and $\Delta$'s in Rotating Protoneutron Stars I: global properties

Rotation plays an important role in the evolution of most types of stars, in particular, it can have a strong influence on the evolution of a newly born proto-neutron star. In this study, we investigate the effects of rotation on four snapshots of the evolution of proto-neutron stars with hyperons and $\Delta$-resonances in their cores, from birth as neutrino-rich objects to maturity as cold, catalyzed neutron stars. We focus on the effects of uniform rotation on the macroscopic structure of the star at three rotational frequencies -- 346.53 Hz, 716 Hz, and the Kepler frequency. Our investigation indicates that the impact of rotation at frequencies of $346.53$~Hz and $716$~Hz causes minor changes in the maximum gravitational mass but leads to significant changes in the stellar radius, particularly for stars with masses smaller than $2$~\msun. However, we observe drastic changes in the star's mass and radius when considering the Kepler frequency. In addition, we investigate other relevant characteristics of the rotating proto-neutron stars as they evolve such as the moment of inertia, compactness, central temperature, and Kerr parameter. Our results suggest that the inclusion of new degrees of freedom in the stellar core lead the star to be more sensitive to rotational dynamics, owing to an increase in compactness, a decrease in the central temperature, and a decrease in the moment of inertia.