Does spaghettification occur around a super massive black hole?

[Negeng]

I heard recently that a supermassive black hole would not tear you apart like a smaller black hole would, that you would simply “flow into it never knowing that you are doomed until it is too late”. Is this true and if so why?

 

[phinds]

I don't know whether that's true or not but it certainly could be.

spaghettification is the result in a gravity differential between your head and your feet (well, all along your body, actually). In a supermassive BH, I guess the radius could be large enough that the differential would be small enough before you hit the surface that it wouldn't and you just be smeared into it.

Once you hit the event horizon (which is not there as far as you are concerned) you are doomed no matter what size the BH is, but with smaller BHs, you get spaghettified before hitting the EH and with large ones you get it afterwards or never.

 

[Bill_K]

The tidal forces are proportional to the Riemann tensor, which is like M/r³. For constant r it gets bigger as you increase the mass, but near the horizon where r = 2M it appears to go the other way.

 

[pervect]

For small black holes you'll be torn apart earlier, before you can even cross the event horizon. For a larger hole, you'll still be torn apart after eventually, you won't avoid it, but you cross the event horizon first.

 

[Matterwave]

Although you wouldn't get spaghettified, I doubt that the experience would be "normal". All light signals that reach you inside a BH would necessarily have to come from a radius greater than the radius you are currently inhabiting. You would see everything kind of inverted at least. If you fell in feet first, beyond the EH, you would see your feet as they were at a farther out radius than your head. The nerve impulses must also be similarly screwed up, so I don't really know if you would still feel "normal"...

 

[Negeng]

So why is that you don't get spaghettified just before entering the EH of a super massive black hole?

 

[PAllen]

So why is that you don't get spaghettified just before entering the EH of a super massive black hole?

The spaghettification simply comes from there being a large curvature over, say, 6 feet, creating a large tidal tension on your body. Remember, the event horizon is not a physical singularity - it is invisible to a body passing through it (in particular, they can still see light coming in from outside). Thus, for a small black hole you would feel extreme tension before even reaching the event horizon. For bigger, it might be at the event horizon. For a billion star black hole (believed to exist in some large galaxies), it would be way inside the horizon before the curvature became extreme over 6 feet.

[edit: correction pointed out by phinds: black hole where I meant event horizon]

 

[phinds]

So why is that you don't get spaghettified just before entering the EH of a super massive black hole?

Negen, Pallen's explanation is correct and complete, but I believe that in his last sentence "For a billion star black hole (believed to exist in some large galaxies), it would be way inside the black hole before the curvature became extreme over 6 feet." He meant to say "... way inside the EVENT HORIZON ... " not " ... way inside the black hole".

It took me a while to get this also when I first started reading about it, but as he said the EH is not physical barrier of any kind. The gravity just slightly outside the EH is only slightly different than the gravity inside the EH, it's just that just outside the EH it is still theoretically possible for things to escape and inside it is not. The closer you get to the EH, the more energy it would take to escape from the BH's gravity.

To people OUTSIDE the EH, it does appear that something happens at the EH, but that is in THEIR frame of reference, not in the frame of reference of the object AT the EH.

 

[DaveC426913]

So why is that you don't get spaghettified just before entering the EH of a super massive black hole?

As PAllen points out, the spaghettification occurs because of a large difference in forces between your head and your feet. In a supermassive BH, the gradient is smaller, therefore even though the absolute value is still huge, the relative value is small.

There are analogies - such as density of an atmosphere - that might make it easier to understand.

Earth has an atmopshere that goes from 0 to 1 atmo in the space of about 100 miles.
Jupiter, while it might ultimately have a much higher pressure of hundreds or thousands of atmospheres, has a flux (change over distance) that is smaller than Earth's. It might go from 0 atmo to 1 atmo over a thousand miles (It might go from 10 atmo to 11 atmo over a thousand miles too).

So you can see that the gradient or flux or change-over-distance is much lower, even if the actual absolute values are much higher.

Back to black holes and gravity. High flux/gradient/change-over-distance is what results in spaghettification.

 

[tom.stoer]

You can callculate this rather easily for large black holes and the Newtonian limit. Using

r_s = 2GM

and

F(r) = GmM/r²

one finds

F(r_s) = m/4GM

i.e.

F(r_s) ~ 1/M

 

[stevebd1]

You can also use the following equations to see how big a black hole needs to be in order to at least reach the event horizon in one piece-

Tidal forces (change in gravity)-

$$dg=\frac{2Gm}{r^3}dr$$

and set r=r_s where r_s is the Schwarzschild radius $(r_s=2Gm/c^2)$.

If we assume that the maximum change in gravity a body can tolerate from head to toe is 1g then dg=9.81, dr=2 and you can rearrange the equation for dg relative to m. You can also consider a max of 5 or 10g (depending on how much the body can tolerate) from head to toe to see what size the (static) black hole needs to be to at least reach the EH.

You can also consider the 'ouch' radius-

$$r_{ouch}=\left(\frac{2Gm}{g_E}dr\right)^{1/3}$$

where g_E is Earth gravity and r_ouch is the radius at which you will begin to feel pain (based on the idea that pain will be felt for a dg greater than 1g from head to toe). You'll be able to see that for small black holes, this radius is some way from the EH.