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In this paper, we address the implications when a homogeneous dust model is considered for
a scenario of gravitational collapse in the context of Eddington-inspired Born-Infeld (EiBI) theory.
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In order to describe the dynamical evolution of the collapse, we present an effective equation,
which constitutes the first order corrections, in EiBI coupling parameter $\kappa$, to Einstein's field equations.
The geometry outside the collapsing object is derived by imposing the standard
Darmois-Israel junction conditions at the boundary surface of the dust.
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This induces an effective matter source in the outer region
which gives rise to a non-singular, non-Schwarzschild geometry at the final state of the collapse.
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For this exterior geometry, we find the threshold of mass for the formation of the black hole. This provides a cut-off over $\kappa$ as $|\kappa|=5.1\times10^{-97} ~kg^{-1}\cdot m^3$.
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