If c were to increase in extremely bent spacetime, what would happen to a massive particle (say a neutron) traveling at near c in bent spacetime near a black hole, if it got bumped into flatter spacetime (say by a more massive particle) so that it’s exceeding the flatter-spacetime c?

The math doesn’t work out that way. There aren’t any solutions to GR equations that lead to FTL travel.

(For GR, I can only state this by an appeal to authority. For SR – Special Relativity – I can vouch for this from having personally worked the equations. SR math is pretty easy: if you can do square roots, you can do addition of velocities in SR.)

The question doesn’t make sense. What do you mean by “if c were to increase in extremely bent spacetimes”?

The math solutions to GR equations leading to FTL travel (I’m not talking about spaceships here) might work out better if c increases in extremely bent spacetime (like near the event horizon of a black hole). Letting c increase in bent spacetime wouldn’t violate causality. I can’t find anything on the web showing experimental or observational data showing this isn’t true. What do you think would happen if a massive particle were to exceed c, if only very briefly?

I suspect the Infinity Gems are involved.

You still haven’t said what you mean, here. What does it mean to say that “c increases”? I think you’ll find that any attempt you make at a definition of this will amount to just changing the definition of the meter or of the second.

My whole understanding of spacetime (what a thing to say) is that to light ain’t never bent but continues on its own merry way. And it also doesn’t pick up an acceleration boost “from” a massive black hole/Mercury/everything–that’s a problem of all those demonstrations of gravity with the rubber sheets pulled down here and there and balls funneling down them.

c is a constant with units of distance divided by time. So if you increase c, then the distance divided by time increases. I’m suggesting that c increases in extremely bend stacetime. One of the tenets of GR is that all frames of reference are equally valid, even the ones near the event horizon of a black hole. The difference between just changing the definition of distance or time is that relativistic effects would be delayed as c increases. And, a massive particle traveling at near c in extremely bent spacetime could be forced out into flatter spacetime, so that it finds itself traveling faster than c. What would happen to it, would it have infinite mass, or decay into a gravity wave, or…

No, c is a constant with units of spacetime divided by units of spacetime. It’s dimensionless, and in fact equals 1.

Pithy and memorable. /not snark