Accelerating into a black hole?

[spinstate]

TL;DR

If falling into a black hole would lead to you being spaghettified, and moving relativistically towards it would contract your length / etc., is there a speed at which they balance out?

I'm sure this has been asked before, but it's lost to me among all the false positives... If falling into a black hole would lead to you being spaghettified, and moving relativistically towards it would contract your length / etc., is there a speed at which they balance out? Seems calculable but there's no way I can do it, unless it's a flawed premise..?

If it is possible, what kind of acceleration would be required to maintain that as you progress? The other relativistic effects are interesting to contemplate as well.

 

[Bandersnatch]

unless it's a flawed premise..?

It is. You're not contracted in your own reference frame.

 

[jbriggs444]

You could simply free fall into a black hole with sufficient speed so that the elapsed proper time is too short for tidal stresses to result in significant spaghettification before the event horizon is passed.

Or, adopting the faller's frame, before the event horizon passes by.

 

[Ibix]

If falling into a black hole would lead to you being spaghettified, and moving relativistically towards it would contract your length / etc., is there a speed at which they balance out?

Yes and no.

Length contraction depends on your speed relative to an observer. It's not something you feel - in the frame of a particle passing the Earth at 0.99c you are severely length contracted, but it makes no difference to you. On the other hand, spaghettification is a very real stretching of you, which would be painfully detectable by you.

So you could certainly pick a velocity profile such that some chosen observers measured your length as unchanging. However it would still hurt since its only the spaghettification that's "really" happening.

Care would be needed in doing the maths since it's necessarily happening in curved spacetime and naive SR results do not apply. Also you'd need a relativistic model of the elasticity of your body to model the spaghettification. It's rather complex.

 

[spinstate]

Right, I see. Your own frame is not contracted of course. One of relativity's gotchas. >.< As with your example of a particle passing Earth at 0.99c, an observer "within" the black hole also see a contracted you coming in, but that doesn't affect what you feel. Got it.

So what about the time dilation effects? Traveling relativistically slows your clock relative to another that is not, right? So in the same scenario, what happens? From your perspective, the black hole itself is contracted. Would it be like slamming into a brick wall? But then... I've heard that certain particles from space penetrate deeper into the atmosphere before decaying than non-relativistic estimates would predict because the Earth is contracted. So from an observer's perspective, would you be get any closer before being spaghettified? Or is it incorrect to compare those two things?

 

[spinstate]

Actually, maybe I can rephrase my original question too: Would accelerating, as in a booster pushing you from behind, reduce the tidal effects?

 

[jbriggs444]

Would it be like slamming into a brick wall?

There is nothing to slam into. The event horizon is an imaginary surface. Coming up to and through it has no local effect.

Locally, the event horizon is like an imaginary surface moving at light speed toward you. You can pass through it inward toward the singularity. Once past it you cannot turn around and get back out because it is receding at light speed.

Would accelerating, as in a booster pushing you from behind, reduce the tidal effects?

Yes, but only by approximately a factor of two.

If you have a booster pushing from behind, there is compressive stress throughout your body. It is greatest at your feet where the entire weight of your body is supported by the floor. It is zero at the top of your head.

If you have tidal stresses stretching you out, there is tensile stress throughout your body. It is greatest at your midriff and zero at your head and toes.

So if you try to cancel tidal stretching with booster compression, you have the problem that the stress profiles do not match. That's what I'm hand-waving as "a factor of two".

Edit: Blood circulation is more of a problem. Standing on an accelerated floor does nothing to ensure that blood gets back from your head and toes to your heart.

 

[Ibix]

From your perspective, the black hole itself is contracted.

No - length contraction only applies in flat spacetime. There isn't an easy way to say what size and shape a black hole "actually is" from the perspective of an infalling observer. It's relatively straightforward to say how it looks to such an observer, and to write the 4d path of the light you use to see it. However, untangling which part of spacetime you regard as "space" in order to say what the black hole "actually" looks like now (removing the light speed lag) is pretty much an arbitrary process, unlike in flat spacetime where more or less any sensible approach gives you the same answer.