The Brass Tacks of Black Holes

Twin Paradox with Spacetime Curvature

None Shall Pass

Here's what the Twin Paradox looks like in the vicinity of a Schwarzschild black hole if both twins go walkabout on radial trajectories with equal and opposite velocities. Ages are quoted in terms of bystander time, not observer time (aka. coordinate time.) Note that even the light ray, which emanates from the origin, diverges off towards the end of time without ever reaching the horizon.

Escape Plan

The takeaway is, anything can escape from the grips of a black hole if you are willing to wait long enough. It's just that the longer an object spends on an inbound trajectory, the longer it takes to emerge after it turns around. However, a black hole is bad news if your personal integrity relies on travellers (or QM wave functions) reuniting at the launch pad at the same time.

Terminology

As an aside, I was once chastised by a GR expert for describing a black hole as a region in space with an unusually high concentration of mass energy. Au contraire, he said. A black hole is the causal past of a future null infinity. How's that for technobabble? He was right of course. I Googled it. In a nutshell, a black hole is the end of time for inbound trajectories, in the same sense that infinity is the end of time for outbound trajectories. It's physics talk for taking forever to get there.

Resources

Here's some good resources for further study on general relativity:

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