Ok, so they go through the black hole and come out to a planet similar to Earth or maybe Earth. Maximilian goes through and ends up in some sort of hell dimension where he is like the devil or something? He sort of looked like he was in charge.
There is no official explanation, but I like to think that the ending is what Kate wanted or imagined during the high pressure trip through the vortex. The camera zeroes in on her before showing us visions of heaven and hell. Earlier in the film, Durant called the black hole something straight out of Dante's Inferno, with Pizer adding that one would expect to see someone with a pitchfork and a tail. Later, after Kate learns the truth about the crew of the Cygnus, she tells Reinhardt that if there is any justice at all, the black hole will be his grave. All of this plays into the idea of the black hole representing the afterlife.
I think these are merely visions that Kate has as they spiral through the vortex. Why else would the camera zoom in on her mind's eye exclusively? She sees what she wanted to see, Reinhardt getting what was coming to him, etc. His being trapped inside the shell of Maximillian would be justice served to a man who lobotomized his crew and made them his slave robots. Kate may be religious for all we know, as it is never addressed in the film, but if so, it could account for why she sees an angel leading them through a heavenly hallway as they exit the black hole.
As for the planet at the end, I do not think it is Earth. I think they survived the trip through the vortex and they emerged somewhere else in the galaxy. The ending of the movie is basically them confronting the unknown as they head towards the obscured mystery planet. It may or may not be a happy ending, depending on whether or not the planet can sustain life. The probe ship won't be good for anything else. For it to be Earth, one would have to take the heaven/hell sequences literally, with a real angel leading them home.
- - - - - - - I am not a fan. I just happen to enjoy movies. Fans are embarrassing.
There was an angelic type figure leading them through arched frames, then the interior had bright light coming through. Since Durant ended up in a hell type rock burning environment, the survivors found their way to Heaven.
I would think that Reinhardt has melted with Maximilian and both have gone to hell. And the crew most likely also died (thats the female angel (most likely her, cause she is the only female in this movie) flying through the heaven gates and then they cut directly to probe ship) and gone to heaven.
I always contended that the director/writers intended it to be vague because even today most scientists are still debating what is at the core of the Black Hole at the enter of our Galaxy