Thursday, December 18, 2008

Black hole questions

Jillian's guide to black holes refers. There is the claim that hovering just above a black hole's event horizon must necessarily be painful. I believe the example used to justify this claim is specious: gravitational acceleration is stronger at a small black hole's event horizon than at a large one's. Recall that the Schwartzschild radius is directly proportional to the mass inside. If the gravitational acceleration still scales as 1/R^2, doesn't that make supermassive black holes' event horizons relatively benign?

As much as I contemplate black holes, I still don't grok this curved spacetime business. And especially not the spacetime around a rotating object - I just don't get this "frame dragging" business. Sure, I can look at the pretty spacetime diagrams and marvel at the light cones, but I'm in need of a Zen-like GR enlightenment.

So what exactly happens when you put your hand past the event horizon of a supermassive black hole (so you don't get squished in the process of hovering)? I imagine that spacetime is still flat enough that you won't feel any tidal forces, but then what happens to your hand? Does it tear off neatly as you put it in, blood spurting as you pull it out? Two conflicting "certainties" present themselves:
  • Yes, a "detachment front" passes through your hand, likely to be quite painful. Check how much of your arm is left and you know where exactly the event horizon is.
  • No, nothing happens to your hand, as far as you can tell. There's nothing special about the even horizon, they say, no signal that you've passed it.
I don't buy the rope-lowering explanation. What does it mean to "quickly" lower the rope? How many meters must we pay out? We might never see the tip pass the event horizon due to its red-shifting, but if we send Jack down the beanstalk, will he eventually reach the event horizon before climbing down an infinite length of the rope?

What happens when a system of non-black holes adopts a configuration where its whole extent fits within the Schwartzschild radius of a mass equal to the sum of the constituent masses? Imagine three borderline strangelet stars converging on a single spacetime event: Darth Vader wants them there. What happens just before they touch? We can draw a sphere around the three strangelet stars that is smaller than a Schwartzschild black hole of the same mass as the three put together. Does that mean that the 3-star system forms a black hole, even before they touch?

Update: Found a partial answer in the sci.physics FAQ.

And more puzzling still, how exactly do black holes merge? Do their event horizons bulge out toward each other or away? My reasoning for the latter is that you have two of these things fighting for the light cones between them. So how exactly do they ever manage to merge?

Oh and by the way, what is the "distance" to the center of a black hole? If I want to calculate the gravitational acceleration at a point outside its event horizon, I need to know how far I am. How do I determine that distance? A tape measure won't do, but will a triangulation give me the answer?

If anyone can explain to me what exactly a tensor is, I'd be most grateful. I once got quite far working through the problems in Schaum's Outline Series' _Tensor Analysis_, but never really "got" what those things were. To me they were just a bunch of symbols with superscripts and subscripts, which one manipulated in a particular way.

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