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Math is fine ZZ, but the mathematical model has to be judiciously applied to the situation, otherwise it leads to non-sensical results like dimensionless points of infinite density.

What's your point? The math was applied correctly and it reflects the mainstream literature I quoted.

 

So while its true no outside observer will ever know Bob's fate once he reaches the event horizon, Bob will definitely know.

I never claimed otherwise, nor is the discussion about that. It is about where the "spaghettification" occurs: outside the EH vs. inside.

Only if you are on something to support you, which is not the case when falling into a black hole.

True for freefall. Not true for the realistic case of approaching the BH in aby type of spaceship. The electromagnetic force of the ship will work against your enormous weight.

Thank you for working out the math.

Why would a large acceleration turn you into a pancake? Wouldn't it accelerate each part of you equally, preserving your shape?

Because you would collapse under your own weight. Imagine that you weighed 10 tonnes. Your skieleton would not be able to support you.

We don't know what happens inside the EH. We will NEVER know (because no information escapes from beyond the EH).

Correct. To put it in math form, let's say the spaghettification occurs for an acceleration of [math]a=k*g[/math] where [math]k[/math] is a value greater than 100 and [math]g=\frac{GM}{r^2}[/math].

On the other hand, the EH is at [math]r_s=\frac{2GM}{c^2}[/math]

 

So, spaghettification happens at a distance [math]r[/math] from the singularity:

 

[math]k*g=\frac{r_s c^2}{2r^2}[/math]

 

i.e.

 

[math]r=c \sqrt{\frac{r_s}{2k*g}}[/math]

 

It is possible to have [math]r<r_s[/math] if :

 

[math]r_s>\frac{c^2}{2k*g}[/math]

 

The above condition can be fulfilled for supermassive BHs. For BH with [math]r_s<\frac{c^2}{2k*g}[/math] the spaghettification occurs way outside the EH. The main lesson from this thread is that the language of physics is MATH. We need to learn to express ourselves in mathematical terms.

I was trying to keep things simple, since some of you argued for using the gravitational acceleration GRADIENT instead of the acceleration proper (acceleration proper makes you into a "pancake", not a "spaghetti"), here is the more complex treatment for "spaghetti":

[math]a=\frac{2GMd}{r^3}[/math]

where d is the length of the object and [math]a[/math] is the acceleration gradient over the distance d. Re-doiing the calculations:

[math]r=(\frac{r_sc^2d}{k*g})^{1/3}[/math]

The points I made stand, depending on the characteristics of the BH spaghettification can occur inside the EH or way outside it, you need to compare [math](\frac{r_sc^2d}{k*g})^{1/3}[/math] with [math]r_s[/math]

I just noticed that the interior Schwarzschild solution is for a uniform density. I guess this means it is not a realistic description of what actually happens inside a black hole.

We don't know what happens inside the EH. We will NEVER know (because no information escapes from beyond the EH).

So as is it says in problem #5, if the BH is large enough, it is possible for Bob to cross the EH without realizing it? At least for a while.

Correct. To put it in math form, let's say the spaghettification occurs for an acceleration of [math]a=k*g[/math] where [math]k[/math] is a value greater than 100 and [math]g=\frac{GM}{r^2}[/math].

On the other hand, the EH is at [math]r_s=\frac{2GM}{c^2}[/math]

So, spaghettification happens at a distance [math]r[/math] from the singularity:

[math]k*g=\frac{r_s c^2}{2r^2}[/math]

i.e.

[math]r=c \sqrt{\frac{r_s}{2k*g}}[/math]

It is possible to have [math]r<r_s[/math] if :

[math]r_s>\frac{c^2}{2k*g}[/math]

The above condition can be fulfilled for supermassive BHs. For BH with [math]r_s<\frac{c^2}{2k*g}[/math] the spaghettification occurs way outside the EH. The main lesson from this thread is that the language of physics is MATH. We need to learn to express ourselves in mathematical terms.

The answer to problem #3 is meaningless.

There are no such things as stellar sized BHs with the mass of the Sun, as they could not possibly undergo gravitational collapse.

They cannot even form neutron stars and are destined to be dwarfs in their senior years.

 

Most galactic center BHs consist of millions, if not billions, of solar masses, and you could easily pass right through the event horizon without even noticing it. The fact that an outside observer would never see this does not change your reality and future meeting with the ( possible ) singularity.

 

An excellent, non-mathematical reference is Kip Thorne's Black Holes and Time Warps.

You completely miss the point, a BH of Sun's mass will spaghettify an object at 100 km distance.

How massive would the BH have to be to make the tidal force at the EH not be noticed by Bob? Say M = 10^70. Would that make the EH radius about 10^ 47? Would the tidal force at that distance from the singularity be small enough to be unnoticed by Bob? Sorry my math is not great, but do I have the orders of magnitude right?

[math]\frac{G}{c^2}=10^{-27}[/math]

See the answer to problem 3

Wouldn't it depend on the mass of the BH? The more massive the BH is, the larger the EH Radius is. Every bit of information that falls into the BH adds another Planck area to the surface area of the EH. So if the mass of BH is sufficiently large, the EH could be far enough away from the singularity, because the tidal force falls off with square of the distance, that Bob could pass through the EH without feeling the spaghetifing tidal force.

The radius of the EH (also known as the Schwarzschild radius) is extremely small (for the Sun is 3km, as an example (the Earth is 9mm). The reason is the [math]c^2[/math] in the [math]r_s=\frac{2GM}{c^2}[/math]

The "G" is not helping either.

You might want to see this lecture by Leonard Susskind. Apparently Bob would not even know he crossed the event horizon until the tidal forces spaghetatized him, but Alice would see Bob slow down and never cross.

 

Actually, if you listened to him to the end , you would have found out that we can never find out what happened to Bob near or at the EH. Though ANY experiment. Which is exactly what I said earlier. What we DO know is that the tidal forces WAY OUT of a BH (far from the EH) spaghettify Bob. Tidal forces are REAL, they are not a coordinate "artifact".

 

 

And theory says ... ?

 

I am assuming there is only one theoretical answer. (Based on the fact that, as far as I now, we only have one theory describing black holes: GR.) Maybe that is not the case.

 

Also, does the type of black hole matter? Is a Schwarzschild black hole different from a Kerr black hole in this respect?

The theory gives us the "internal solution" for the EFEs in the form of metric that is quite different from the :external solution". The metric IS the "theory", it predicts how test probes would move inside the EH. We can only say that the predictions are quite different from the ones made by the "external" solution. We will never know because we will never be able to test it.

To your second question, I only know of the internal Schwarzschild solution, I do not know about the internal solutions for Kerr, Riessner, etc.

 

This is the part that's hanging you up. There's no canceling effect if the pull from every direction is towards a single direction, and if it is a singularity at the center, it's dimensionless.

 

Can someone clear up this conflict?

This question is unanswerable since no information can escape from beyond the EH. We cannot know what happens, we can only theorize.

The point of the thread is the question of whether or not the force of the Singularity will cancel itself out once past the event horizon.

There is no such thing as "the force of the Singularity", so your questions are ill-posed.

Because if every direction leads to Singularity, then Singularity will pull you from every direction.

Did you get the part where the "spaghettification" due to tidal forces happens OUTSIDE the event horizon?

 

Maybe tidal forces are only present outside the event horizon. I don't know.

yes

Irrelevant link.

 

[math]a^a=b \Rightarrow a=\log_a b =(^a\sqrt{b})[/math].

The link is fully relevant, he's trying to find "a" as a function of "b". You can't do that.

Of course this generalizes - [math]x^y=z \Rightarrow y=log_xz\,\,\ne \,\,(^y\sqrt{z})[/math]

This is a DIFFERENT problem. Do you see the difference?

Yes, there is no path to escape, because all path leads to the singularity. Thus, every direction leads towards singularity. So, you are getting pulled towards singularity in every direction.

 

But, if you get pulled towards the singularity in every direction, they should cancel out.

The "ripping apart" happens BEFORE the object crosses the event horizon. A picture will help.

take the inverse of 16

add 7

take the inverse of that

add 3

 

or consider using only inverse (dividing 1 by the number) multiplication, addition and the numbers 2 and 3.

 

Simple as 1 2 3

 

take the inverse of 2 times 2 times 2 times 2

add 2 times 2 plus 3

take the inverse of that

add 3

 

3.1415929203539823008849557522124 is close enough to 3.141592653589973238462643383279 for a lot of purposes. So if you forget 355/113 and want that exact approximation, to 6 digits, just take 16 inverse it, add 7, and inverse that, and add 3.

This is because:

[latex]\frac{355}{113}=3+\frac{16}{113}=3+\frac{1}{7+\frac{1}{16}}[/latex]

So, you replaced one division with two inversions (which are divisions themselves). The net effect is more error and more calculations.

Hmmmm.... I see . Moreover the sound of 13 MHz can't be detected by our ears. Our ears can detect only 20Hz to 20kHz.

You do not understand the notion of "noise". Try studying it.

Suppose you are given the relation that [math] a^a= b [/math] . Then how you do you proceed to find a in terms of b ? Or, the solution doesn't exist.

Transcendental equations

Hi,

 

I got this question in my head....... Of course it seems quite true that there is no sound in space. But there might be exceptions. So is our universe completely silent??

It isn't "silent", there is noise in the 13 Mhz range. See here

Sorry, I really can't understand your solution. What are [latex]A[R],B[R][/latex]? What is R? Where is x, with a single body replacing the two?

 

For the last time: if you think you can calculate the distance in question, please do. I can't and I give up.

You need to read the paper I linked, all the notions are explained on pages 3 and 4.

Now, I have another question.

Suppose there are two bodies of mass [math]m_1[/math] and [math]m_2[/math] respectively, separated by a finite distance of [math]S[/math]. They will attract each other according to Newton's law of universal gravitation as -

[math]F=G\frac{m_1m_2}{S^2}[/math]

Since their distance will change at every moment, each of them will experience a variable acceleration. Considering the case of [math]m_1[/math],

[math]a(t)=G\frac{ m_2}{S(t)^2}[/math]

And [math]j=\frac{da(t)}{dt}[/math] , where [math]j[/math] is jerk.

 

Am I on the right track???

yes

Hmmm. that link someone posted above says this:

 

In 1887, mathematicians Heinrich Bruns^[4] and Henri Poincaré showed that there is no general analytical solution for the three-body problem given by algebraic expressions and integrals.

 

That's what I meant by "no closed form solution." Seems that a number of specific solutions, for specific cases have been found.

You should kept on reading.

Yes, if all the masses are free to move. The three body problem I'm most familiar with is a satellite moving in the Earth / Moon system, where you can neglect the mass of the satellite. I don't think the fully general three-body problem has a closed form solution, does it?

Yes, it has a closed solution.

The big question that someone asked above and I didn't notice an answer for is whether or not M1 and M2 are fixed. If you have to consider their motion as well this gets a lot more complicated. If they're fixed then 1) if M1=M2, your test body should stay on the centerline at all times - it will accelerate until it gets to the vertical centerline through M1 and M2 and then decelerate. If it's velocity is high enough it will go on off to infinity, slowing down the whole time. If it's not high enough, it will oscillate back and forth along the horizontal centerline.

 

For non-equal M1 and M2, the test object path will curve toward the heavier one. If it's velocity is high enough it will follow a curved path to infinity. The really interesting case is for unequal M1 and M2 without escape velocity - your test object will enter some kind of orbit, and I suppose it's possible that orbit might hit M1 or M2 (more likely the lower mass one). But you'd have to calculate that.

It is more complicated than that. The problem has a rigorous mathematical formalism, it is known as the three-body problem

Thanks - this line from there:

 

While Maxwell's equations are invariant under Lorentz transformations, the GEM equations were not. The fact that ρ_g and j_g do not form a four-vector (instead they are merely a part of the stress–energy tensor) is the basis of this problem.

 

was particularly helpful.

you are welcome