The philosophy of time is one of the remaining bulwarks of a philosophical position called 'dualism', which holds that minds are completely separate from our bodies: if you view us as being big ropes of particle-worldlines in a 4-dimensional fixed universe, you are basically stuck with describing us as "souls" who have latched onto this rope and are traveling along it, living the experience even though the future is as set in stone as the past. It makes relativity really easy to understand, but it makes entropy comparably harder (since the premise of entropy is that our uncertainties multiply due to particle collisions until things end up in more and more uncertain states). It almost sounds like there's no free will in this perspective, but that's not quite true. Instead you get a model of free will which is a lot like you see in the movie The Matrix: "Because you didn't come here to make the choice, you've already made it. You're here to try to understand why you made it."

Relativity does not necessarily compel this. It is true, the relativistic "present" is a space between two light cones, and not just one plane. But that's not necessarily a huge obstacle: we can just pretend that there is one plane which is the "true present" and accept that the laws of physics make it impossible to know if we're truly right about which it is. As long as one of the planes is the true present you can lift up the Newtonian way of looking at time to the special-relativistic whole.

It turns out that black holes aren't really so interesting as this article claims, because there is a 'co-moving' metric which falls into the black hole's event horizon in a finite time. What happens with a black hole is, you see someone slow down more and more to a standstill as they approach the event horizon, appearing to "merge in" with that surface, redshifting into the quantum noise of the Hawking radiation there. But from their perspective, you're just seeing their "last moment in this universe"; they'll keep going on past that horizon.

But general relativity is still a problem. It describes the causal fabric of the universe as warped by the energies that inhabit each part of that fabric, and that makes it really hard to deal with time. Some of the interesting stuff here comes either from (a) alternative descriptions of relativity (like spinors/twistors, where you describe the entire world-line of a particle as a point), or (b) quantum mechanics (where you can do multiple-universe-splitting). The combination of relativity and quantum mechanics, for example, seems to give us the Wheeler-de Witt equation, which time famously "falls out" of (it plays no final role in the equation). Some physicists, notably Julian Barbour, think that this means we've got to fixate on a static universe. I'm totally undecided on this but I find it fascinating.