The existence of relativistic stars in f(R) gravity
  We refute recent claims in the literature that stars with relativistically
deep potentials cannot exist in $f(R)$ gravity. Numerical examples of stable
stars, including relativistic ($GM_\star/r_\star \sim 0.1$), constant density
stars, are studied. As a star is made larger, non-linear "chameleon" effects
screen much of the star's mass, stabilizing gravity at the stellar center.
Furthermore, we show that the onset of this chameleon screening is unrelated to
strong gravity. At large central pressures $P>\rho/3$, $f(R)$ gravity, like
general relativity, does have a maximum gravitational potential, but at a
slightly smaller value: $GM_\star/r_\star = 0.345 < 4/9$ for constant density
and one choice of parameters. This difference is associated with negative
central curvature $R$ under general relativity not being accessed in the $f(R)$
model, but does not apply to any known astrophysical object.
