I've been revisiting classical physics (in the sense of Newtonian mechanics and Galilean relativity) and I was thinking why can't we have an event horizon in classical physics? Is it because the structure of space is absolute, the Euclidean geometry, or because time is absolute, so simultaneity is absolute? Or both?
Not the technical answer you're looking for, but perhaps a helpful thought that occurred to me when first read your question.
It's a well-known feature of (special) relativity that you can recover Galilean relativity (and thereby Newtonian mechanics) by taking the limit as c goes to infinity of any result in SR (for example, look at the velocity addition formula).
Combining this fact with the intuitive idea that the event horizon occurs at the distance where the strength of gravity creates an escape velocity equal to the speed of light, we see that event horizons don't make much classical sense since the speed of light is infinity. Sure, you could just use the experimental value for the speed of light instead, but then you shouldn't be using Galilean relativity, since you can do a simple experiment with a light clock that proves...etc.