[guest39538]

Hello, I can not access the closed thread to re-post the provided BH equations, it is showing white screen.

Could somebody please re-post them in this thread so I can discuss them and try to understand them.

[Kryptid]

Here is my post from before:

You can verify the calculation for yourself. The event horizon is simply the location where the black hole's escape velocity equals the speed of light. The equation used to calculate the escape velocity of an object is:

v_e = √((2GM)/r)

Where v_e is the escape velocity in meters per second, G is the gravitational constant (6.67 x 10^-11 m³•kg^-1•s^-2), M is the mass in kilograms and r is the radius from the center of the object in meters.

Plugging in the numbers for the Earth, we get:

v_e = √((2 x (6.67 x 10^-11 m³•kg^-1•s^-2) x (5.972 x 10²⁴ kg))/(6,371,000 meters))

v_e = 11,182 meters per second (11.182 kilometers per second)

Given how many times we've sent spacecraft into orbit, we've have plenty of occasion to thoroughly test the validity of this equation.

Now let's rearrange the equation so that what we are looking to find is not the escape velocity, but the radius at which the escape velocity takes on a particular value:

r = √((2GM)/(ve²))

Put in the relevant data for the Earth and you can verify that this rearranged equation accurately predicts the radius of the Earth based on its mass and escape velocity.

Now we can enter the speed of light as the escape velocity (299,792,458 meters per second) in order to find the distance from the center of a black hole at which the event horizon must exist for a given mass. We’ll enter the measured mass of the Cygnus X-1 black hole of 14.8 solar masses:

r = (2 x (6.67 x 10^-11 m³•kg^-1•s^-2) x (2.943 x 10³¹ kg))/(299,792,458 meters per second)²

r = 43,682 meters (43.682 kilometers)

So there you have it, a step-by-step explanation on how to calculate the radius of a black hole’s event horizon based on an experimentally-verified equation.

Calculations aside, it should be pretty obvious that the orbiting star is outside of the black hole's event horizon because we can see it.

[evan_au]

r = √((2GM)/(ve2))

I plugged this equation into a spreadsheet, and got a different answer from what you got.
It looks like the "√" is missing when you do the calculation?

[Kryptid]

I plugged this equation into a spreadsheet, and got a different answer from what you got.
It looks like the "√" is missing when you do the calculation?

Hmm, let me try to do this bit by bit and see what I get.

r = √((2GM)/(v_e²))
r = √(((2 x (6.67 x 10^-11 m³•kg^-1•s^-2) x (5.972 x 10²⁴ kg))/(11,182 meters per second)²)
r = √(((2 x (6.67 x 10^-11) x (5.972 x 10²⁴))/(125,037,124))
r = √(((1.334 x 10^-10) x (5.972 x 10²⁴)/(125,037,124))
r = √((796,024,480,000,000)/(125,037,124))
r = √(6,366,305)
r = 2,523.15 meters

It looks like you're right. For some reason, I always seem to have trouble when I rearrange equations. Does anyone recognize where I may have made my error?

EDIT: I think the error is that there should have been no square-root function in the equation to begin with. So the correct form is:

r = (2GM)/(v_e²)

[guest39538]

ve.jpg (32.62 kB . 740x464 - viewed 4159 times)

ve = > 0 mph


It is a shame the air was not denser up top, you would need less  speed to escape.  I have to say I do not think your calculation has anything to do with an event horizon, it seems to me it is the thrust needed to push against the less dense air up top.   More speed is more thrust. 

[Kryptid]

It is a shame the air was not denser up top, you would need less  speed to escape.  I have to say I do not think your calculation has anything to do with an event horizon, it seems to me it is the thrust needed to push against the less dense air up top.   More speed is more thrust. 

Yes, you could theoretically climb a sufficiently high set of stairs to leave the Earth's atmosphere without reaching escape velocity. That's what a hypothetical "space elevator" would do. However, that's not what escape velocity is about. The escape velocity is the minimum speed that an object has to travel at for its momentum alone to allow it to escape an object's gravitational field indefinitely. In other words, it's the minimum speed that you'd have to push something to so that it never comes to a stop and then falls back to the Earth.

Since this concept does apply to light (light relies only on its momentum to move, as photons are not like tiny rockets with thrusters), then light inevitably gets stuck if the escape velocity is too high. That's one reason light can't escape an event horizon. So if we can see something, then we know it isn't behind any such horizon. Hence, the fact that we can see Cygnus X-1 means that the star must be orbiting outside the event horizon of its black hole companion.

The idea of building a "staircase" to climb out of a black hole doesn't work either, but for reasons that are more difficult to understand. Apparently,space is so twisted inside of an event horizon that you are unable to travel in a direction that leads out of it. You must move inevitably towards the singularity. It's like being trapped inside of an ever-shrinking box. Perhaps someone more well-versed in that area of physics can chime in to give a better explanation.

[guest39538]

Yes, you could theoretically climb a sufficiently high set of stairs to leave the Earth's atmosphere without reaching escape velocity. That's what a hypothetical "space elevator" would do. However, that's not what escape velocity is about. The escape velocity is the minimum speed that an object has to travel at for its momentum alone to allow it to escape an object's gravitational field indefinitely. In other words, it's the minimum speed that you'd have to push something to so that it never comes to a stop and then falls back to the Earth.

I would of though it would have to be a continual force rather than a speed to escape a gravitational field.   

All BH's are finitely dense? 

There is finite mass in the observable Universe?

How can you detect a BH if they do not emit  light?   

How do you know BH's are just not a body that is black in colour?

[Kryptid]

I would of though it would have to be a continual force rather than a speed to escape a gravitational field.

Fortunately, such a thing isn't necessary (otherwise space travel would be much harder). Since gravity is a force that becomes weaker as you move further from its source, less and less energy is required to keep moving as you more further away. The total energy requirements converge on a finite value, which is equal to the maximum possible gravitational potential energy for the object that is trying to escape the gravitational field. If your total kinetic energy is equal to or above this value, then the gravitational field can slow you down over time as you move away from it, but it can never bring your speed all the way to zero.

All BH's are finitely dense?

This is an as-yet unresolved question. Relativity predicts an infinitely-dense singularity at the center of a black hole. However, most physicists seem to agree that relativity fails to make the correct prediction in such extreme environments. That's because quantum physics becomes important for predicting the behavior of very small objects and we all know about the infamous "feud" between relativity and quantum physics. My personal bet is that black holes collapse to a small, but finite, size.

There is finite mass in the observable Universe?

Yes, on the order of 10⁶⁰ kilograms if memory serves correctly.

How can you detect a BH if they do not emit  light?

 

Black holes are usually detected by their gravitational effects. If a star is seen to orbit an invisible companion, then the mass of that companion can be estimated by measuring the speed and orbital period of the star. If the observed mass is above about 3 solar masses, then we know it's too massive to be a neutron star (neutron degeneracy pressure fails at such extremes). Although there are some theoretical stars, such as electroweak stars, quark stars and preon stars that might be heavier and more compact than even neutrons stars, they will have their own upper limits before they collapse into black holes.

Another, more definitive, way to detect black holes is via gravitational waves. When two black holes merge, they emit gravitational waves in a very particular pattern. Relativity told us exactly what such a signature should look like to a detector. In 2015, the LIGO observatory detected exactly such a gravitational wave pattern. The calculated masses of the two black holes involved in the merger was about 14.2 and 7.5 solar masses: https://en.wikipedia.org/wiki/GW151226

How do you know BH's are just not a body that is black in colour?

That's because such bodies are not stable. They are too massive to support themselves against collapse. We know that the invisible companion to the star in Cygnus X-1 cannot be, say, a 14.8-solar mass ball of black carbon because carbon (or any such form of atomic matter) would not have sufficient pressure to counteract the enormous gravitational forces acting on it. White dwarfs and neutron stars are ruled out because (1) they too would collapse under such extreme masses) and (2) the Universe is not old enough for them to have cooled off sufficiently to be black.

That's not to say that the exact nature of black holes is settled. There are still alternative models to the classical relativistic black hole that are seriously considered by some physicists. Some examples of these are:

- Gravastar: https://en.wikipedia.org/wiki/Gravastar
- Dark-energy star: https://en.wikipedia.org/wiki/Dark-energy_star
- Fuzzball: https://en.wikipedia.org/wiki/Fuzzball_(string_theory)
- MECOs: https://en.wikipedia.org/wiki/Magnetospheric_eternally_collapsing_object

Another recently-predicted object that wouldn't be quite a black hole is a star supported by vacuum polarization: https://gizmodo.com/could-the-weirdness-of-quantum-physics-produce-a-new-ki-1823657773

[guest39538]

Relativity predicts an infinitely-dense singularity at the center of a black hole.

How can something be infinitely dense without being infinitely large?   

I would of thought absolute dense existed but not infinitely dense which sounds rather strange.

[guest39538]

Could a BH be transparent? 

[Kryptid]

How can something be infinitely dense without being infinitely large?

An infinitely-dense object need not take up any space in order to have a finite mass, so there's no reason to say that it must have a size at all.

I would of thought absolute dense existed but not infinitely dense which sounds rather strange.

I'm not sure what you mean when you say "absolute dense".

Could a BH be transparent?

Actually, there is a way in theoretical physics that at least some star-black hole binaries might be explained in such a way. There is a concept called "mirror matter" which behaves in a manner identically to normal matter, except its particle interactions are right-handed instead of left-handed (honestly, I'm not exactly certain what that means. The idea arose from the observation that the weak nuclear force violates parity). As a consequence of having different particle interactions than normal matter, mirror matter could only interact with normal matter through gravitation. As such, mirror matter would be invisible and intangible.

As a hypothetical black hole replacement, imagine a blue main-sequence star composed of mirror matter with 7 times the mass of the Sun and a 2.8 million kilometer radius. Around this mirror matter star orbits a regular star similar to our Sun that orbits at a distance of 5 million kilometers. Since the sun-like star orbits outside of the radius of the mirror matter star, shell theorem tells us that it should orbit it in exactly the same way that it would orbit a black hole of equal mass. With our telescopes, we could deduce that the visible star is orbiting an invisible companion that was much too heavy to be a neutron star. It would be easy to then designate the invisible star as a black hole even though it was not one.

However, there are ways to tell the difference between mirror matter stars and black holes (at least in some cases). One is by examining accretion disks. For Cygnus X-1, the accretion disk around the invisible companion is about 15,000 kilometers in radius. This would be well inside of a hypothetical mirror star of equal mass. Because of this, the accretion disk would be significantly larger and more diffuse than we would expect for a black hole of 14.8 solar masses. It's rather like how you become lighter when you go deep inside of the Earth. Gravity pulls you down less both because there is less mass below you and because there is now some mass above you. So what you would expect of a mirror matter star is that the calculated mass of the "black hole" would be less for the accretion disk than it would be for the orbiting, visible companion.

Another way to tell the difference would be through gravitational lensing. If you were fortunate enough to be in a position where the binary was passing in front of a source of light, you could see how the invisible partner bends that light (at least in theory). A black hole would bend light much more strongly than a mirror matter star of equal mass.

[guest39538]

An infinitely-dense object need not take up any space in order to have a finite mass, so there's no reason to say that it must have a size at all.

Ok, I already have an objective argument, saying something is infinitely  dense is illogical.

At some point there is a point where an objects density is at its absolute density.  There can be no such thing as an infinite density.   This is really poor use of the English language and contradicts the very meaning of infinite.

infinite
ˈɪnfɪnɪt/Submit
adjective
1.
limitless or endless in space, extent, or size; impossible to measure or calculate.

noun
1.
a space or quantity that is infinite.


There is a limit to all density, once there is no space left  between any point of the object is the D_max.  Where D is density.


A volume of space is finite  , if all points of the volume are occupied, you can't get any denser than that.

D_max =   V(k) - k where k is space and V is volume

Take note, we don't actually take away space, we occupy it with something.


Maybe in your terms


D_max =  4/3πr³ (k) -  4/3πr³ (k)

[The Spoon]

Relativity predicts an infinitely-dense singularity at the center of a black hole.

How can something be infinitely dense without being infinitely large?   

I would of thought absolute dense existed but not infinitely dense which sounds rather strange.

You dont seem to understand the difference between density and mass.

[guest39538]

Relativity predicts an infinitely-dense singularity at the center of a black hole.

How can something be infinitely dense without being infinitely large?   

I would of thought absolute dense existed but not infinitely dense which sounds rather strange.

You dont seem to understand the difference between density and mass.

Yes I do , do you?


added- That was a terrible counter argument against what I wrote

[The Spoon]

Relativity predicts an infinitely-dense singularity at the center of a black hole.

How can something be infinitely dense without being infinitely large?   

I would of thought absolute dense existed but not infinitely dense which sounds rather strange.

You dont seem to understand the difference between density and mass.

Yes I do , do you?

Yep, that is why I commented on your post.

Also, your made up equation 'Dmax =   V(k) - k where k is space and V is volume' what on earth is that supposed to mean?

[guest39538]

Relativity predicts an infinitely-dense singularity at the center of a black hole.

How can something be infinitely dense without being infinitely large?   

I would of thought absolute dense existed but not infinitely dense which sounds rather strange.

You dont seem to understand the difference between density and mass.

Yes I do , do you?

Yep, that is why I commented on your post.

Also, your made up equation 'Dmax =   V(k) - k where k is space and V is volume' what on earth is that supposed to mean?

Yes I made up , but it is not made up,

D = density

max = maximum

V = volume

k = space


It is not difficult to read or understand.


Try it this way

R³ = 1m³

R³ - R³ = 0k =  D _max

[guest39538]

In simple terms, two points adjoined to a third point make up the smallest volume, maximum density , three dimensional measure.
Quite clearly 0³ is finite and absolute.

not dependent on, conditioned by, or relative to anything else; independent: an absolute term in logic; the absolute value of a quantity in physics

The above quote is what all my work aims for.   This is why to me it is important science understands, I am trying to give absolute answers.

[The Spoon]

Relativity predicts an infinitely-dense singularity at the center of a black hole.

How can something be infinitely dense without being infinitely large?   

I would of thought absolute dense existed but not infinitely dense which sounds rather strange.

You dont seem to understand the difference between density and mass.

Yes I do , do you?

Yep, that is why I commented on your post.

Also, your made up equation 'Dmax =   V(k) - k where k is space and V is volume' what on earth is that supposed to mean?

Yes I made up , but it is not made up,

D = density

max = maximum

V = volume

k = space


It is not difficult to read or understand.


Try it this way

R³ = 1m³

R³ - R³ = 0k =  D _max

It is not that it is hard to understand. When you say k=space, what exactly do you mean by that. Also, the next equation you made up, what does R stand for, what does m stand for, how do you know that R³ - R³ = 0k (by which you mean from the previous 0 space I think. How does this actually relate to density?

[guest39538]

Relativity predicts an infinitely-dense singularity at the center of a black hole.

How can something be infinitely dense without being infinitely large?   

I would of thought absolute dense existed but not infinitely dense which sounds rather strange.

You dont seem to understand the difference between density and mass.

Yes I do , do you?

Yep, that is why I commented on your post.

Also, your made up equation 'Dmax =   V(k) - k where k is space and V is volume' what on earth is that supposed to mean?

Yes I made up , but it is not made up,

D = density

max = maximum

V = volume

k = space


It is not difficult to read or understand.


Try it this way

R³ = 1m³

R³ - R³ = 0k =  D _max

It is not that it is hard to understand. When you say k=space, what exactly do you mean by that. Also, the next equation you made up, what does R stand for, what does m stand for, how do you know that R³ - R³ = 0k (by which you mean from the previous 0 space I think. How does this actually relate to density?

By k= space I mean k equals space, k is the space, I am using k instead of the word space. 

R³ is a real coordinate space k .

How do I know R³ - R³ = 0K ?

Because I have took away the space with my equation. 

However, this particular discussion is on about density, it refers to density, what you have to consider though is the volume of a space is not actual took away, it is just occupied and took away that way.  I am filling all points in a volume so there is no free points , logically there is no free space points  inside a full volume.   You can't logically get any denser than a full space.   

[guest39538]

p.s I am using the word density correctly

density
ˈdɛnsɪti/Submit
noun
1.
the degree of compactness of a substance.


If you want to discuss density in some weird way , please define your terms of use.