A real scalar field coupled to a fermion via a Yukawa term can evade no-go
theorems preventing solitonic solutions. For the first time, we study this
model within General Relativity without approximations, finding static and
spherically symmetric solutions that describe fermion soliton stars. The Yukawa
coupling provides an effective mass for the fermion, which is key to the
existence of self-gravitating relativistic solutions. We systematically study
this novel family of solutions and present their mass-radius diagram and
maximum compactness, which is close to (but smaller than) that of the
corresponding Schwarzschild photon sphere. Finally, we discuss the ranges of
the parameters of the fundamental theory in which the latter might have
interesting astrophysical implications, including compact (sub)solar and
supermassive fermion soliton stars for a standard gas of degenerate neutrons
and electrons, respectively.Comment: 16 pages, 5 figure