Shortly after its birth in a gravitational collapse, a protoneutron star enters in a phase of quasistationary evolution characterized by large gradients of the thermodynamical variables and intense neutrino emission. In a few tens of seconds, the gradients smooth out while the star contracts and cools down, until it becomes a neutron star. In this paper we study this phase of the protoneutron star life including rotation, and employing finite-temperature equations of state. We model the evolution of the rotation rate, and determine the relevant quantities characterizing the star. Our results show that an isolated neutron star cannot reach, at the end of the evolution, the maximum values of mass and rotation rate allowed by the zero-temperature equation of state. Moreover, a mature neutron star evolved in isolation cannot rotate too rapidly, even if it is born from a protoneutron star rotating at the mass-shedding limit. We also show that the I-Love-Q relations are violated in the first second of life, but they are satisfied as soon as the entropy gradients smooth out.

Abstract. We report on numerical constructions of fully non-linear geons in asymptotically anti-de Sitter (AdS) spacetimes in four dimensions. Our approach is based on 3+1 formalism and spectral methods in a gauge combining maximal slicing and spatial harmonic coordinates. We are able to construct several families of geons seeded by different families of spherical harmonics. We can reach unprecedentedly high amplitudes, with mass of order ∼ 1/2 of the AdS length, and with deviations of the order of 50% compared to third order perturbative approaches. The consistency of our results with numerical resolution is carefully checked and we give extensive precision monitoring techniques. All global quantities like mass and angular momentum are computed using two independent frameworks that agree each other at the 0.1% level. We also provide strong evidence for the existence of excited (i.e. with one radial node) geon solutions of Einstein equations in asymptotically AdS spacetimes by constructing them numerically.