Pardon my ignorance, but wouldn't it just be that the measurement of the distance traveled in a particular coordinate is different for a local observer vs. an observer in a different inertial frame? So if only a single coordinate is curved then only the distance measured for that coordinate would be different? sigh I wish I understood the math...

@JohnRennie I've rolled back my edits and asked the revised version as a new question, in case anybody wants to take a crack at it. physics.stackexchange.com/questions/122392/…

@DavidZ Understood

@JohnRennie (2 above), I had thought about doing that, but apparently I'm on notice for low quality posts (because my only 2 questions are on-hold/closed), and want to try getting them re-opened so I don't have to worry about getting banned from asking questions

Check the revision history, the original version of my question was... muddled by an attempt to deconstruct the question into a series of thought experiments that ultimately invalidated the feature I was trying to get an answer to. I'm hoping my last revision will fix this.

@JohnRennie: I realize you must be correct, my ignorance on the subject is astounding. But if something can curve space and not time, then the only thing you would need to introduce a curvature in time w/o space would be to negatively curve the space in an area. Or is that the part that isn't possible?

@JohnRennie: Wait, how can it curve space but not time? Wouldn't that change the local speed of light? I thought the whole reason that both time and space needed to curve were to preserve the constancy of the speed of light.

Space-time isn't a medium, like glass or air. It's not something that can be picked up, stored, or moved elsewhere. What you and I call 1 meter, 1 second, or a straight line (our concept of space and time) aren't absolute but can be different depending on where you are and what you are doing. Things with mass "bend" both time and space towards themselves, which adds a very small amount of acceleration towards other masses. This acceleration is gravity. The black hole isn't pulling on the light so much as it's twisting up the road. That's why so many call it "the fabric" of space-time.