Two questions (flat universe, black hole and the curvature of spacetime)

[ManOfSteel]

Hello,

I would like to have your explanation about these two things that I can't understand.

1. I don't understand how, according to some physicists, the Universe is considered to be flat like a sheet of paper? What exactly do they mean by that?

2. Also, what do physicists mean when they say matter is so dense in a black hole that spacetime is bent or that the curvature of spacetime becomes infinite?

Do they mean that ALL matter, when passing near the black hole, is deviated from its normal course just like light is refracted when passing through a prism?

Also how does it change the "time" part of spacetime? Does time pass slower or faster than it would if there was no black hole?

Thank you in advance.

 

PS: I'm sorry if this has already been posted, but I'm not familiar with the forum yet.

[Spyman]

1. Space is normally defined to consist of three spatial dimensions, (width, height and length), if any or all of them is bent in another dimension then space is not flat. The sheet of paper is representing two of the known spatial dimensions and the third dimension is used to show the bending in another dimension.

Link to read: http://en.wikipedia.org/wiki/Shape_of_the_Universe

 

2. According to Relativity, the force of gravity is caused by the geometry of spacetime.

Link to read: http://en.wikipedia.org/wiki/General_relativity

 

One problem is that at the Singularity, (the center of a Black Hole), the curvature becomes infinite because the density is infinite. The volume of a sphere with any mass and zero radius has infinite density and since the strength of gravity also depends on distance it's infinite too when the distance is zero.

It's thought to be unphysical and a flaw in Relativity that future revisions will sort out.

Link to read: http://en.wikipedia.org/wiki/Gravitational_singularity'>http://en.wikipedia.org/wiki/Gravitational_singularity

 

ALL matter and energy is deviated from it's course when passing by ALL matter or energy.

Take Earth, where do you think the Moon would go if Earth didn't affect it's course?

There is no difference with Black Holes, they are only more massive and dense.

Link to read: http://en.wikipedia.org/wiki/Gravitation

 

Time ticks slower on Earth than on the Moon, closer to a more massive object causes time to tick slower.

No difference with Black Holes here either.

Link to read: http://en.wikipedia.org/wiki/Time_dilation

[ManOfSteel]

Hello and thank you for your answers.

 

The volume of a sphere with any mass and zero radius has infinite density and since the strength of gravity also depends on distance it's infinite too when the distance is zero.

The distance between the singularity and what? Its own particles?

 

ALL matter and energy is deviated from it's course when passing by ALL matter or energy.

...

There is no difference with Black Holes, they are only more massive and dense.

A black hole was once a star like our sun. It has the same mass as the star had, just at a higher density. Am I right so far?

So does density have anything to do with the gravitational force or does gravitation only depend on the mass of the body? In other words, is the gravitational field (and the curvature of spacetime) around the black hole of the same intensity as the gravitational field (and the curvature of spacetime) that was once around the star?

 

Time ticks slower on Earth than on the Moon, closer to a more massive object causes time to tick slower.

And the same goes for a person on Earth and another on Pluto, right?

So a hypothetical person living near the solar surface would have his life extended by several earth years according to an observer on earth, while the other person living on Pluto or in deep space would die before his parents on earth even though both persons were in the same conditions before the experiment began.

 

I was reading the article about the "gravitational singularity" on wikipedia and there is something that is not clear:

[...] a spacetime with a singularity contains geodesics which cannot be completed in a smooth manner. The limit of such a geodesic is the singularity.

I understand the "geodesic" as a "straight line in a curved spacetime". Is that correct?

What do they mean by the "smooth manner"?

And by "limit", do they mean the straight line ends at the singularity? Why is that?

[Spyman]

The distance between the singularity and what? Its own particles?

The distance between the singularity and where you want to measure the gravity field. A Black Hole Singularity is a body with zero radius so you can measure the field from zero distance without crossing a surface of the body.

(It's a point without height, length or width)

 

A black hole was once a star like our sun. It has the same mass as the star had, just at a higher density. Am I right so far?

In nature when a star of 3 or more times mass of the Sun goes supernova and at least 1.44 times solar masses is not ejected a gravitational collapse to a Black Hole can happen. The collapse forces all the mass of the star to the singularity.

 

So does density have anything to do with the gravitational force or does gravitation only depend on the mass of the body? In other words, is the gravitational field (and the curvature of spacetime) around the black hole of the same intensity as the gravitational field (and the curvature of spacetime) that was once around the star?

Gravity depends only on the mass and the energy in the body. The curvature of spacetime is the same, but since the density is higher the body will be smaller.

 

If you where able to squeeze the Earth down to a radius of 9 millimeters it would become a Black Hole. An astronaut in the Space Station or on the Moon wouldn't notice any difference of the gravitational field around him.

(But he would have a hard time trying to spot Earth, a small black pebble.)

 

The difference is that you are able to get closer to the center of a more dence object and still be outside of the body and under the influence of it's full gravity. Earth radius is 6 378.137 km so we are that distance from the center and weights 9.81 times our mass, but if it where a Black Hole we would be 9 millimeters from the center, if standing on the Event Horizon, where we would weight around 5 000 000 000 000 000 000 times our mass.

 

And the same goes for a person on Earth and another on Pluto, right?

So a hypothetical person living near the solar surface would have his life extended by several earth years according to an observer on earth, while the other person living on Pluto or in deep space would die before his parents on earth even though both persons were in the same conditions before the experiment began.

In principle yes, but the difference wouldn't be years, it's more like below one millisecond per day for the Sun, below 100 microseconds for Earth, around a few nanosecond for the Moon/Pluto.

(All compared to a void inside the Milky Way.)

 

Note that we are still in the Suns gravitational field here on Earth or on Pluto and the Suns influence on time dilation, is bigger than Earths, even on Earth. If you where able to move outside of Milky Way to a big empty void deep in space, time would pass by around 0.5 seconds per day faster than on Earth inside.

 

I understand the "geodesic" as a "straight line in a curved spacetime". Is that correct?

What do they mean by the "smooth manner"?

And by "limit", do they mean the straight line ends at the singularity? Why is that?

The Moon are moving in a geodesic line around Earth, it is falling towards Earth in freefall but due to orbital speed always fail to hit Earth.

 

Inside the Event Horizon of a Black Hole, spacetime curvature is so high that if not moving faster than c, (lightspeed), the curvature will bring you closer to the center, since nothing can move faster than c, everything is forced to end up there. If everything ends up in the center, you get a body with zero radius and if standing on the singularity, you would weight infinite times your weight on Earth.

[Klaynos]

This isn't really my area of knowledge so forgive me for not answering more of your questions.

 

A black hole was once a star like our sun. It has the same mass as the star had, just at a higher density. Am I right so far?

So does density have anything to do with the gravitational force or does gravitation only depend on the mass of the body? In other words, is the gravitational field (and the curvature of spacetime) around the black hole of the same intensity as the gravitational field (and the curvature of spacetime) that was once around the star?

 

To work out gravity around a spherically symmetric object (star, black hole etc...), the easiest method is to form a guassian surface and use guases law.

 

http://en.wikipedia.org/wiki/Gauss's_law#Application_to_Gravity

 

So if we draw a gaussian surface around a star outside of it's radius, and then the star forms a black hole there would be no perceived effect on the gravity. So anything outside the stars radius is unaffected.

 

Within the radius of the star when it was still a star gravity decreases as you get nearer the centre, because there is now some mass above you, if you draw a Gaussian sphere the contained mass is lower. But if that star then forms a black hole you can draw Gaussian spheres infinitesimally close to the singularity and the mass contained will always be the same as the original star, so therefore the closer you get the higher the gravity and you can get infinitely close. The event horizen is the radius at which the gravity is strong enough to require a higher velocity than the speed of light.

[alan2here]

Time ticks slower on Earth than on the Moon, closer to a more massive object causes time to tick slower

 

So anyone going into a black hole then maneging to get out again would find that loads of time has passed while they where away.

 

Therefore hawking radiation leaving a black hole must be from objects that are verry old indeed?

[ManOfSteel]

Thanks for your replies.

 

Inside the Event Horizon of a Black Hole, spacetime curvature is so high that if not moving faster than c, (lightspeed), the curvature will bring you closer to the center, since nothing can move faster than c, everything is forced to end up there.

Observations show that some matter absorbed by the black hole may then be violently rejected out of it at the poles, AFAIK.

But what happens to the rest? Is it integrated to the singularity itself? In that case the singularity could keep on gaining mass, getting a theoretically infinite mass. Then, what could stop it from engulfing entire planets, stars or even galaxies with its infinitely strong gravitational field, eventually resulting in an exponentially powerful black hole (even more than supermassive black holes)?

 

I also have some additional questions:

- What are the latest discoveries about naked singularities? Are they even possible (outside a simulation)?

- Do they not have an event horizon? In that case, would it be possible to see the singularity?

[Spyman]

So anyone going into a black hole then maneging to get out again would find that loads of time has passed while they where away.

Leaving a Black Hole is thought to be impossible.

 

I think all time there is would have passed - thats infinite time or eternity.

 

Therefore hawking radiation leaving a black hole must be from objects that are verry old indeed?

Hawking radiation is newborn particles, created outside the Event Horizon.

[Spyman]

Observations show that some matter absorbed by the black hole may then be violently rejected out of it at the poles, AFAIK.

The matter is ejected from the accretion disc, not from inside the BH.

 

But what happens to the rest? Is it integrated to the singularity itself? In that case the singularity could keep on gaining mass, getting a theoretically infinite mass. Then, what could stop it from engulfing entire planets, stars or even galaxies with its infinitely strong gravitational field, eventually resulting in an exponentially powerful black hole (even more than supermassive black holes)?

All that is know is that the BH gains the mass of what it consumes.

 

Black Holes don't have any theoretical maximum size or mass that limits them.

 

When galaxies collide, the supermassive Black Holes anchoring them in the center, might merge and create a new bigger BH.

 

I also have some additional questions:

- What are the latest discoveries about naked singularities? Are they even possible (outside a simulation)?

- Do they not have an event horizon? In that case, would it be possible to see the singularity?

Black Holes are thought to rotate, if the star that ends up as a BH is spinning and conservation laws says that angular momentum is preserved, then the BH needs to be spinning to.

 

From concepts drawn of rotating black holes, it is shown that a singularity, spinning rapidly, can become a ring-shaped object. This results in two event horizons, as well as an ergosphere, which draw closer together as the spin of the singularity increases. When the outer and inner event horizons merge, they shrink toward the rotating singularity and eventually expose it to the rest of the universe.

http://en.wikipedia.org/wiki/Naked_singularity

[ManOfSteel]

Thanks very much. That'll be all (for now at least ).