The Event Horizon
If you calculate the size of an object whose escape velocity is the speed of light, you get the “Schwarzschild radius”, which defines the “event horizon”. This is the formal size of a black hole (even though there is nothing at that location). It is given by Rs=3km(M*/Msun). It is the horizon over which you can see no more events. Outside that at 1.5 Rs photons would orbit the hole (the photon sphere).
Far from the hole, the gravity is the same as it would be if the star were still there (so no “vacuum cleaner” effect). If the Sun collapsed to a BH, the Earth’s orbit would be unaffected. The trick is that you can approach VERY close to the full mass since the object got so dense.