From what I understand relativity predicts that outside observers would never observe external objects actually crossing into the event horizon, due to time dilation.
How does that can reconciled with the fact that the Schwarzschild radius is largely dependent on black hole mass? Then, does this imply that one can never observe an increase in the radius of the event horizon? This seems wrong to me, as there are different size black holes, and I'd like to know what I am missing.
The issue here is that you are combining ideas from two different spacetimes and arriving at a contradiction because the different spacetimes are different.
The first spacetime is the Schwarzschild spacetime. It has a few important properties:
Because it is static, it will not grow. It is eternal. And because it is vacuum there is no mass outside it to fall in.
Now, obviously this doesn’t represent the real world, but it can be a reasonable approximation in the space around a large spherical mass. But it is only this idealized case which cannot grow and where the usual coordinates produce infinite time dilation.
For a growing black hole a better example is the Oppenheimer Snyder spacetime. This spacetime is:
In this spacetime the event horizon grows as matter crosses it. The infalling matter itself alters the shape of the spacetime. As it moves the spacetime is not described by the eternal vacuum solution.
So the presence of the infalling matter means that the spacetime is not described by the static solution. Conclusions based on that spacetime need not apply to a non-static one.
Numerical solutions can be performed without spherical symmetry and with different types of matter besides pressureless dust. The general conclusion of a non-static spacetime and a growing event horizon are quite robust.
From what I understand relativity predicts that outside observers would never observe external objects actually crossing into the event horizon, due to time dilation.
External object has a field around it where gravitational potential is decreased.
Also black hole has a field around it where gravitational potential is decreased.
When gravitational potential is low enough at some place, then light can't escape that place.
So therefore, when external object gets close enough to a black hole, then light can't escape from the external object. In other words external object is behind an event horizon.
