  Long-lived pseudo-solitonic objects, known as oscillons/oscillatons, which we
collectively call real scalar stars, are ubiquitous in early Universe cosmology
of scalar field theories. Typical examples are axions stars and moduli stars.
Using numerical simulations in full general relativity to include the effects
of gravity, we study the fate of real scalar stars and find that depending on
the scalar potential they are either meta-stable or collapse to black holes. In
particular we find that for KKLT potentials the configurations are meta-stable
despite the asymmetry of the potential, consistently with the results from
lattice simulations that do not include gravitational effects. For
$\alpha$-attractor potentials collapse to black holes is possible in a region
of the parameter space where scalar stars would instead seem to be meta-stable
or even disperse without including gravity. Each case gives rise to different
cosmological implications which may affect the stochastic spectrum of
gravitational waves.
