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 .
( 2000 ) ] ) , it reads 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 ( 1993 ) ] for critical collapses .