Abstract: Viable corrections to the matter sector of Poisson's equation may result
in qualitatively different astrophysical phenomenology, for example, the
gravitational collapse and the properties of compact objects can change
drastically. We discuss a class of modified nonrelativistic theories and
focus on a relativistic completion, Eddington-inspired Born-Infeld
gravity. This recently proposed theory is equivalent to General
Relativity in vacuum, but its nontrivial coupling to matter prevents
singularities in early cosmology and in the nonrelativistic collapse of
noninteracting particles. We extend our previous analysis, discussing
further developments. We present a full numerical study of spherically
symmetric nonrelativistic gravitational collapse of dust. For any
positive coupling, the final state of the collapse is a regular
pressureless star rather than a singularity. We also argue that there is
no Chandrasekhar limit for the mass of a nonrelativistic white dwarf in
this theory. Finally, we extend our previous results in the fully
relativistic theory by constructing static and slowly rotating compact
stars governed by nuclear-physics inspired equations of state. In the
relativistic theory, there exists an upper bound on the mass of compact
objects, suggesting that black holes can still be formed in the
relativistic collapse.
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