| Abstract
| - The collapse of spherical neutron stars is studied in General Relativity. The initial state is a stable neutron star to which an inward radial kinetic energy has been added through some velocity profile. For two different equations of state and two different shapes of velocity profiles, it is found that neutron stars can collapse to black holes for high enough inward velocities, provided that their masses are higher than some minimal value, depending on the equation of state. For a polytropic equation of state of the form $p=K\rho^\gamma $, with $\gamma = 2$ it is found to be $1.16 \left( \frac{K}{0.1} \right)^{0.5} M_{odot}$, whereas for a more realistic one (described in Pons et al. [CITE]), it is $0.36 M_{odot} $. In some cases of collapse forming a black hole, part of the matter composing the initial neutron star can be ejected through a shock, leaving only a fraction of the initial mass to form a black hole. Therefore, black holes of very small masses can be formed and, in particular, the mass scaling relation, as a function of initial velocity, takes the form discovered by Choptuik ([CITE]) for critical collapses.
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