gravity - When a star becomes a black hole, does its gravitational field become stronger?

I've seen in a documentary that when a star collapses and becomes a black hole, it starts to eat the planets around.

But it has the same mass, so how does its gravitational field strength increase?

Answer

Actually, it doesn't have the same mass, it has significantly less mass than its precursor star. Something like 90% of the star is blown off in the supernova event (Type II) that causes the black holes.

The Schwarzschild radius is the radius at which, if an object's mass where compressed to a sphere of that size, the escape velocity at the surface would be the speed of light $c$; this is given by $$ r_s=\frac{2Gm}{c^2} $$ For a 3-solar mass black hole, this amounts to about 10 km. If we measure the gravitational acceleration from this point, $$ g_{BH}=\frac{Gm_{BH}}{r_s^2}\simeq10^{13}\,{\rm m/s^2} $$ and compare this to the acceleration due to the precursor 20 solar mass star with radius of $r_\star=5R_\odot\simeq7\times10^8$ m, we have $$ g_{M_\star}=\frac{Gm_\star}{r_\star^2}\simeq10^3\,{\rm m/s^2} $$ Note that this is the acceleration due to gravity at the surface of the object, and not at some distance away. If we measure the gravitational acceleration of the smaller black hole at the distance of the original star's radius, you'll find it is a lot smaller (by a factor of about 7).