# Entering a black hole theoretically of course

Hey all this is my first post,

Everyone knows you can't enter a black hole because you'll be stretched/turned into noodles due to the immense change in gravity over small lengths. I was reading another thread on the physics forum and happened to come across an equation which would determine if you would get noodled. if there was a change of 10 earth g's over 2 meters you would be in trouble. Is this the main restricting factor when "entering" a black hole? If so would it be possible to find a black hole with less changes in force over a certain length. When you're being accelerated into the abyss, would it be possible to use a counter force(gravity etc) to cross the gravitational lines in a slow and controlled manner? This may be more suited for science fiction but I do have a small understanding of the universe. Any comments appreciated!
PS
(Don't flame too hard if I've violated more than one law of physics).

mfb
Mentor
Everyone knows
I hope not, because it is wrong.
It depends on the size. If the black hole is massive enough, you can cross the event horizon without getting ripped apart by tidal gravity.

Is this the main restricting factor when "entering" a black hole?
You might get issues with intense radiation from the accretion disk, high-energetic particles in general, you are still in space so you need some life support infrastructure. And there could be odd things happening at the event horizon, this is still unclear.

When you're being accelerated into the abyss, would it be possible to use a counter force(gravity etc) to cross the gravitational lines in a slow and controlled manner?
Crossing it slowly is actually more dangerous as then everything else is hitting you with high speed or energy. And it needs some science fiction magic to provide the necessary thrust for your rocket.

LightPiercing
i agree, everyone and knowing are pretty encompassing words. A better choice would be some people think.. anyways, thanks for the response. Black Holes are really weird. I recently read an article stating that singularities actually have a volume. The article stated it was smaller than any particles we encounter (protons, nuetrons, quarks, etc) but it does have a finite volume, which would clash with the theory that singularities have no volume and are infinitely dense?

do you have any thoughts on this topic?

mfb
Mentor
A singularity does not have a volume by definition. It is unclear if the center of a black hole has a singularity or maybe something else.

phinds
Gold Member
2021 Award
i agree, everyone and knowing are pretty encompassing words. A better choice would be some people think.. anyways, thanks for the response. Black Holes are really weird. I recently read an article stating that singularities actually have a volume. The article stated it was smaller than any particles we encounter (protons, nuetrons, quarks, etc) but it does have a finite volume, which would clash with the theory that singularities have no volume and are infinitely dense?

do you have any thoughts on this topic?
Changing it to "some people think" does make the statement less egregious but doesn't change the fundamental wrongness of that belief. People who think that are wrong, period, as mfb explained.

Hey all this is my first post,
Is this the main restricting factor when "entering" a black hole?

This is actually one of the most if not the most hotly debated topic in fundamental physics and quantum gravity today. Start here: http://en.wikipedia.org/wiki/Firewall_(physics)

I hope not, because it is wrong.
It depends on the size. If the black hole is massive enough, you can cross the event horizon without getting ripped apart by tidal gravity.

You might get issues with intense radiation from the accretion disk, high-energetic particles in general, you are still in space so you need some life support infrastructure. And there could be odd things happening at the event horizon, this is still unclear.

Crossing it slowly is actually more dangerous as then everything else is hitting you with high speed or energy. And it needs some science fiction magic to provide the necessary thrust for your rocket.

Maybe you can avoid the radiation by just crossing into the black hole from the direct North or South Pole, where the acretion disk isn't?

mfb
Mentor
There the full disk is visible to you, that does not make it better. And you still have starlight (or even the cosmic microwave background) that gets blueshifted to intense gamma radiation if you are slow and close enough. Just go for free fall and you avoid that issue.

If the black hole is massive enough, you can cross the event horizon without getting ripped apart by tidal gravity.

Can you estimate the minimum size of the BH to be entered alive?

And you still have starlight (or even the cosmic microwave background) that gets blueshifted to intense gamma radiation if you are slow and close enough. Just go for free fall and you avoid that issue.

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mfb
Mentor
Can you estimate the minimum size of the BH to be entered alive?
You get a reasonable estimate with Newtonian gravity:
$$\frac{da}{dr}=\frac{GM}{r^3}$$
With the Schwarzschild radius for a non-rotating black hole ##r=\frac{2MG}{c^2}## we get
$$\frac{da}{dr}=\frac{c^6}{8(MG)^2}$$ or
$$M^2=\frac{c^6}{8G^2} \frac{dr}{da}$$
With 10g over 2m, this gives about 10,000 solar masses. ~100 milliseconds might be a bit short to watch all the events, so larger black holes probably give a better view.
Why blueshifted? And see the firewall link in post 6.

You get a reasonable estimate with Newtonian gravity:
$$\frac{da}{dr}=\frac{GM}{r^3}$$

Can you show that Newtonian gravity results in a reasonable estimate at the event horizon of a black hole? That's hard to believe.

Why blueshifted?

Doppler effect and less gravitational redshift compared to a distant observer

And see the firewall link in post 6.

I'm afraid quantum field theory in curved spacetime exceeds my skills.

mfb
Mentor
Can you show that Newtonian gravity results in a reasonable estimate at the event horizon of a black hole? That's hard to believe.
Dimensional analysis. The prefactor is wrong, the order of magnitude should be right.

Doppler effect and less gravitational redshift compared to a distant observer
Ah, relative to a distant observer, okay.

I'm afraid quantum field theory in curved spacetime exceeds my skills.
Same here, that's why I just referenced that point.

Dimensional analysis.

How does this work? I would assume that the tidal acceleration need to be estimated on the basis of the relativistic trajectory of two test particles within each others rest frame. I still have doubts that this results in something similar to Newtonian tidal accelerations because the properties of the event horizon fundamentally differ from the Newtonian limit.

When you're being accelerated into the abyss, would it be possible to use a counter force(gravity etc) to cross the gravitational lines in a slow and controlled manner?
wait..wait..wait..wait.. You mean I have to exert an internal force to counter the gravitational force from a black hole's event horizon ?
Gimme a break... am not Goku.

mfb
Mentor
How does this work? I would assume that the tidal acceleration need to be estimated on the basis of the relativistic trajectory of two test particles within each others rest frame. I still have doubts that this results in something similar to Newtonian tidal accelerations because the properties of the event horizon fundamentally differ from the Newtonian limit.
There are three quantities that can influence the solution (the mass): the gravitational constant, the speed of light and the tidal gravity we want. There is a unique way to combine powers of them to get units of mass: c3 G-1 (da/dx)1/2.
While this analysis does not give the exact solution, the GR solution will have those values in those powers, multiplied by some numerical prefactor - there is no other way the formula could look like. It does not really matter whether that prefactor is .1 or 10. It is not one million.

@ImperialThinker: No, but you can use rockets. They won't help you once you cross the event horizon, but outside they can be used.

@mfb : Turning into super saiyan isn't enough ?

@mfb : Turning into super saiyan isn't enough ?

Apparently not:

It is not one million.

How did you get this result?

mfb
Mentor
Do you know any example where a dimensional analysis is off by more than a factor of 1000?
Huge numerical prefactors rarely show up in equations.

Do you have a reason to expect a large prefactor here?

Do you have a reason to expect a large prefactor here?

I have no reason not to expect it. Please provide a proper justification for your claim that the prefactor is small and don't ask me for counter-evidence.

mfb
Mentor
I have no reason not to expect it.
Then where is the point of that discussion?
Example reference. Turns out the prefactor is 8 for a non-rotating black hole.
Please provide a proper justification for your claim that the prefactor is small and don't ask me for counter-evidence.
You question a widely used method in all quantitative sciences. Why?

stevebd1
Gold Member
I did have a link to a webpage that demonstrated that the Newtonian equation for tidal forces was still relevant in GR but as is often the case it no longer exists. I can confirm that the equation is used in Wheeler and Taylor's book 'Exploring Black Holes' (though they included a factor of 2) and the same equation is used in this NASA problem sheet-

http://spacemath.gsfc.nasa.gov/blackh/4Page33.pdf

Matterwave
Gold Member
Do you know any example where a dimensional analysis is off by more than a factor of 1000?
Huge numerical prefactors rarely show up in equations.

Do you have a reason to expect a large prefactor here?

Although I tend not to agree with Dr. Stupid most of the time, this one time, I am forced to concede that he does have a point here. As an example, in special relativity, the momentum ##p=\gamma mv## as one approaches the speed of light asymptotes to infinity. There the pre-factor ##\gamma## that one misses by dimensional analysis alone actually turns out to grow arbitrarily close to infinity as the speed grows towards c. One can not a priori rule out this kind of behavior if one is simply doing dimensional analysis to try to get the answer. Of course, it might be reasonable to suspect that this behavior does not occur for the case in question, but one can't exactly totally preclude it either (without a little bit of further analysis).

mfb
Mentor
There is no possible finite value of γ that could enter, and I took the knowledge of finite tidal acceleration as granted (it is easy to check).

You question a widely used method in all quantitative sciences. Why?

Because it seemed you forgot it. With your reference above you made up for the missing justification.

mfb
Mentor
Forget what? How to do dimensional analyses?
No, I did not justify the method with the reference, that was neither possible nor necessary. I just found a numeric prefactor (took about 30 seconds, no magic involved).
Oh by the way, that is a prefactor for M^2, so the factor for M is just ~3.

Forget what?

To provide a calculation, a reference or any other kind of justification for your claim that the prefactor is small. Instead you asked me for a reason to expect a large prefactor. That's in fact the opposite of the "widely used method in all quantitative sciences". But as you fixed that in #21 we can forget it.