Transformation of Matter into Black Holes

[greswd]

From Wikipedia:

the average density of a supermassive black hole can be less than the density of water.

The Schwarzschild radius of a body is proportional to its mass and therefore to its volume, assuming that the body has a constant mass-density.[8] In contrast, the physical radius of the body is proportional to the cube root of its volume. Therefore, as the body accumulates matter at a given fixed density (in this example, 103 kg/m3, the density of water), its Schwarzschild radius will increase more quickly than its physical radius. When a body of this density has grown to around 136 million solar masses (1.36 × 108) M☉, its physical radius would be overtaken by its Schwarzschild radius, and thus it would form a supermassive black hole.

So, assuming we have a massive ball of water that keeps growing, but somehow manages to remain at a fixed density, the moment the Schwarzschild radius overtakes the physical radius, will the gravitational properties of the ball of water undergo a sudden, dramatic change?

 

[Arman777]

https://www.quora.com/Could-you-cre...re-and-more-mass-keeping-the-density-the-same

Here explains in a bit detail.In here It says its possible.But I don't think it would be sudden (Not sure though), cause we are adding matter in some amount so probably as we add the matter things will change in a someway, like gravity affect on the center will increase an amount so it will keep increasing with addition of matter and finally it will collapse I guess

 

[greswd]

https://www.quora.com/Could-you-cre...re-and-more-mass-keeping-the-density-the-same

Here explains in a bit detail.In here It says its possible.But I don't think it would be sudden (Not sure though), cause we are adding matter in some amount so probably as we add the matter things will change in a someway, like gravity affect on the center will increase an amount so it will keep increasing with addition of matter and finally it will collapse I guess

but what if the schwarzschild radius exceeds the physical radius while the water ball is still at a constant density?

 

[russ_watters]

So, assuming we have a massive ball of water that keeps growing, but somehow manages to remain at a fixed density, the moment the Schwarzschild radius overtakes the physical radius, will the gravitational properties of the ball of water undergo a sudden, dramatic change?

There is nothing magic about black holes; they are just massive objects. They obey the same laws of gravity other every-day objects do. So from a distance, when you add that last bit of water, nothing noticeable will change about the gravitational field.

 

[greswd]

There is nothing magic about black holes; they are just massive objects. They obey the same laws of gravity other every-day objects do. So from a distance, when you add that last bit of water, nothing noticeable will change about the gravitational field.

what if you were taking a dip in that water when the Schwarzschild radius coincided with the physical radius?

let's say you set your spaceship to hover above the water and then took a dive.

and assuming you were just fine with the massive gravitational field strength.

would you be able to climb back into your spaceship?

 

[russ_watters]

what if you were taking a dip in that water when the Schwarzschild radius coincided with the physical radius?

let's say you set your spaceship to hover above the water and then took a dive.

and assuming you were just fine with the massive gravitational field strength.

would you be able to climb back into your spaceship?

No. But bear in mind you are stretching really far into non-physical assumptions that make the scenarios less and less realistic as you go.

 

[Vanadium 50]

You have your answer. Nothing magic happens.

 

[Arman777]

There is nothing magic about black holes; they are just massive objects. They obey the same laws of gravity other every-day objects do. So from a distance, when you add that last bit of water, nothing noticeable will change about the gravitational field.

An observer who enters the region or near it will see no difference but outside observers should see a "real" black hole I think.

 

[greswd]

No. But bear in mind you are stretching really far into non-physical assumptions that make the scenarios less and less realistic as you go.

true. but its a consequence of trying to simplify it.

but that means if the Schwarzschild radius was 20 cm below the surface of the water, I would be able to climb out?

 

[russ_watters]

An observer who enters the region or near it will see no difference but outside observers should see a "real" black hole I think.

I don't know what you mean by "the region", but notice I said "nothing noticeable will change about the gravitational field". What a distant observer sees with his eyes will change.

 

[russ_watters]

true. but its a consequence of trying to simplify it.

but that means if the Schwarzschild radius was 20 cm below the surface of the water, I would be able to climb out?

Are you above or below the Schwarzschild radius? Are you a point particle or a person who is more than 20cm tall? Trying to descipher non-physical assumptions is hard...

 

[Arman777]

I don't know what you mean by "the region", but notice I said "nothing noticeable will change about the gravitational field". What a distant observer sees with his eyes will change.

The region is event-horizon/near black hole.I see your point..

 

[Vitro]

From Wikipedia:So, assuming we have a massive ball of water that keeps growing, but somehow manages to remain at a fixed density, the moment the Schwarzschild radius overtakes the physical radius, will the gravitational properties of the ball of water undergo a sudden, dramatic change?

While I don't know much about GR and black holes, I would say to an outside observer all Schwarzschild BHs of a certain size (mass) look identical no matter how they formed. In fact the mass is the only independent parameter needed to fully describe them.

As for a ball of water I don't think it can possibly maintain any finite density as the event horizon surpasses its diameter, it will have to collapse into a singularity. Nothing inside an event horizon can be static, the inside can only be a vacuum with a central singularity.

 

[greswd]

Are you above or below the Schwarzschild radius? Are you a point particle or a person who is more than 20cm tall? Trying to descipher non-physical assumptions is hard...

I'm an average height human, with my neck above the water. So the Schwarzschild level is at my stomach perhaps.

So the Schwarzschild radius hasn't coincided with the physical radius, but is 20 cm below it.

 

[greswd]

As for a ball of water I don't think it can possibly maintain any finite density as the event horizon surpasses its diameter, it will have to collapse into a singularity. Nothing inside an event horizon can be static, the inside can only be a vacuum with a central singularity.

True, bu let's say that it maintains a constant density for the sake of simplicity.

 

[Dale]

but that means if the Schwarzschild radius was 20 cm below the surface of the water, I would be able to climb out?

If you have a perfect fluid in hydrostatic equilibrium at some radius 20 cm greater than the Schwarzschild radius then there is no event horizon. You can go down to the middle and come back up again.

Note, the fluid in question cannot be water due to Buchdahl's theorem, it would have to be some unobtanium. The tidal forces would be enormous so you would have to be made of a different unobtanium.

 

[greswd]

If you have a perfect fluid in hydrostatic equilibrium at some radius 20 cm greater than the Schwarzschild radius then there is no event horizon. You can go down to the middle and come back up again.

Note, the fluid in question cannot be water, it would have to be some unobtanium.

Ok. Let's say that someone keeps pouring the unobtainium-water onto the water-ball planet, causing it to grow.

I still keep my head above the water, but the 20cm gap is shrinking.

When the gap is 1 cm, I can still climb up to my spaceship and jet off, but the moment the gap decreases to zero, there is no way I can ever leave?

 

[Dale]

As the radius becomes less than 9/8 of the Schwarzschild radius the pressure st the center becomes infinite and even your unobtanium fluid collapses. As you get near that limit the system becomes unstable and even your treading water will cause the collapse.

 

[greswd]

As the radius becomes less than 9/8 of the Schwarzschild radius the pressure st the center becomes infinite and even your unobtanium fluid collapses. As you get near that limit the system becomes unstable and even your treading water will cause the collapse.

ahh, I see. Is there a name for this 9/8 factor? I'd like to read more about it.

 

[Dale]

ahh, I see. Is there a name for this 9/8 factor? I'd like to read more about it.

Buchdahl's theorem or the Buchdahl limit

 

[russ_watters]

Ok. Let's say that someone keeps pouring the unobtainium-water onto the water-ball planet, causing it to grow.

I still keep my head above the water, but the 20cm gap is shrinking.

When the gap is 1 cm, I can still climb up to my spaceship and jet off, but the moment the gap decreases to zero, there is no way I can ever leave?

Something I think you may not have realized is if there is already a Schwarzschild radius, the object inside is already a black hole.

 

[greswd]

Something I think you may not have realized is if there is already a Schwarzschild radius, the object inside is already a black hole.

I was referring to the value of the Schwarzschild radius. for example, the Sun has one of about 3km.