Can a Sun be a Black Hole?

[luc]

That is, could a star be so massive that its own light could not escape its gravity? If so, then could this explain "black holes" as stars which are simply so massive that light cannot escape them?

I do not know the mass that is required to trap light nor the mass that a star typically can reach before it collapses into a black hole. Perhaps someone who does could give a definitive answer.

[InfiniteNow]

Originally Posted by luc

That is, could a sun be so massive that its own light could not escape its gravity? If so, then could this explain "black holes" as suns that are simply so large that light cannot escape them?

I do not know the mass that is required to trap gravity nor the mass that a sun typically can reach before it collapses into a black hole. Perhaps someone who does could give a definitive answer.

Hi Luc,

By "sun" I presume you mean "star?" If so, that's exactly where most blackholes come from.

Here's a great link which covers many aspects of blackhole formation:

Curious About Astronomy? Black Holes and Quasars


I encourage you to check it out.

Also, per your question on mass, you must also consider radius. Obviously, the same mass spread out over a greater distance will be less dense. To better understand this relationship, and where the boundaries are for when this happens, you might look into the Chandrasekhar Limit.

Chandrasekhar limit - Wikipedia, the free encyclopedia


Enjoy. If you have more questions, then ask. There are people here who know much more about this stuff than I do, and they are all really quite helpful.

[Moontanman]

Originally Posted by luc

That is, could a star be so massive that its own light could not escape its gravity? If so, then could this explain "black holes" as stars which are simply so massive that light cannot escape them?

I do not know the mass that is required to trap light nor the mass that a star typically can reach before it collapses into a black hole. Perhaps someone who does could give a definitive answer.

No, many stars have more than enough mass to be black holes (1.4X our Sun) but the production of energy through fusion prevents them from collapsing into a black hole. The more mass a star has the quicker is burns it's fuel and explodes. A truly massive star (something like 100 solar masses) would immediately explode as it formed. The remnants of a star after it's fusion has stopped can contract into a black hole if enough mass is left after the super nova. (1.4 solar masses)

[InfiniteNow]

Good point, Moontanman. I'd almost forgetten how the outward pressure created by all of the nuclear reactions balance against the inward pressure from the force of gravity within a star. Bravo, sir.

[KALSTER]

Is there any way that the remnants of a supernova form a neutron star, but with a small enough radius for the event horizon to be above the surface (I mean the predetermined radius at which the escape velocity would equal C)? What about if the next level of collapse is a quark star? Basically what I am asking is if a black hole necessarily has to have a singularity at its core?

[modest]

Originally Posted by KALSTER

Is there any way that the remnants of a supernova form a neutron star, but with a small enough radius for the event horizon to be above the surface (I mean the predetermined radius at which the escape velocity would equal C)? What about if the next level of collapse is a quark star? Basically what I am asking is if a black hole necessarily has to have a singularity at its core?

You are correct, there is no need for a black hole to have a singularity at the center. Any density material can make a black hole (according to the Schwarzschild definition) so long as the radius is large enough. CraigD does a good job of explaining that in this post.

~modest

[KALSTER]

Thanks Modest, that was an interesting read. I am sorry if this is too off topic, but I don't quite understand this part:

Originally Posted by modest

Originally Posted by CraigD
“As I understand Relativity, you only have zero motion relative to something when both you and it are not accelerating. Both a clock stationary to a point on Earth and one in Geostationary orbit are accelerating centripetally.”

I can't believe I did that. Talk about 2D thinking. Thank you for pointing this out.

My input values were grossly rounded - earth's mass and radius, etc. (bad and lazy modest). What equation did you use for an orbiting speed? V = (GM/R)^1/2?
I feel challenged now and think I will graph these parameters in Mathematica.
Thank you for the review Craig.
-modest

As I have it; a geosynchronous satellite would be accelerating relative to the earth, but not relative to a clock on the spot the satellite is in synch with, so no velocity time dilation. Am I wrong with this and how?

Anyway, back to the topic.
Did you guys ever resolve the issue that a homogeneous cloud of gas the size of one AU would have an event horizon, but that the gas would coalesce under its own gravity? If it would coalesce, would it not then be compressed beyond the quark star limit and then collapse into a singularity?

Edit:Oh sorry, I confused a geosynchronous orbit with a geostationary orbit.

[Moontanman]

Originally Posted by KALSTER

Anyway, back to the topic.
Did you guys ever resolve the issue that a homogeneous cloud of gas the size of one AU would have an event horizon, but that the gas would coalesce under its own gravity? If it would coalesce, would it not then be compressed beyond the quark star limit and then collapse into a singularity?

:

Anything can in theory collapse into a black hole if there is no resistance to gravity. The earth could collapse into a black hole if not for the resistance of electrons, protons and neutral particles to compression. A gas cloud with sufficient mass and not capable of nuclear reactions could indeed collapse into a black hole. I'm confused by your use of event horizon. In my understanding of this term in regard to a black hole an event horizon is the point near a mass where light can no longer escape. A quark star that collapses past the point of light being able to escape is no longer a quark star, it is then a black hole.

[KALSTER]

Originally Posted by Moontanman

Anything can in theory collapse into a black hole if there is no resistance to gravity. The earth could collapse into a black hole if not for the resistance of electrons, protons and neutral particles to compression. A gas cloud with sufficient mass and not capable of nuclear reactions could indeed collapse into a black hole.

I understand and agree with this bit.

Originally Posted by Moontanman

I'm confused by your use of event horizon. In my understanding of this term in regard to a black hole an event horizon is the point near a mass where light can no longer escape.

I agree with this also. The event horison is the border at which the escape velocity equals C, farther away from the mass it decreases and closer to it, it gets larger. I was referring to a link Modest provided where CraigD showed that a gas cloud with evenly spread density and a radius of 1 AU would present an event horizon, meaning one could never escape it.

An excerpt from CraigD's post:

"I can’t imagine any natural process that would allow such a black hole to form, but if one could somehow entice about 50 million solar masses into a sphere about the radius of the Earth’s orbit without them coalescing into something super-dense or singularity-ish, you’d have a black hole with no terrible tidal forces anywhere, and an average density less than that of water."

I was enquiring as to the possibility of normally gravitated matter being able to exhibit an event horizon without collapsing into a singularity, like possibly having a quark star at its centre.

[modest]

Originally Posted by KALSTER

Thanks Modest, that was an interesting read. I am sorry if this is too off topic, but I don't quite understand this part:

As I have it; a geosynchronous satellite would be accelerating relative to the earth, but not relative to a clock on the spot the satellite is in synch with, so no velocity time dilation. Am I wrong with this and how?

In the correct rotating reference frame, any clock on earth is motionless relative to a geosynchronous satellite. However, this does noting to set velocity time dilation equal between them. In a rotating frame points of different distance from the center have different acceleration. So, they have some relative time dilation merely by the fact they're rotating - which is true for any two spots on the frame that don't have the same r. This has been proven very conclusively (even apart from earth's orbit):

Bailey et al., “Measurements of relativistic time dilation for positive and negative muons in a circular orbit,” Nature 268 (July 28, 1977) pg 301. Bailey et al., Nuclear Physics B 150 pg 1–79 (1979).

The distance someone on earth's equator travels in a day (the distance of being rotated around the earth) is significantly less than the distance a geosynchronous satellite travels in a day. The satellite has a larger orbit, making a larger circle, traveling a larger distance, with a greater overall velocity. Its clocks then should run slower than earth's clocks by velocity alone.

Originally Posted by KALSTER

Anyway, back to the topic.
Did you guys ever resolve the issue that a homogeneous cloud of gas the size of one AU would have an event horizon, but that the gas would coalesce under its own gravity? If it would coalesce, would it not then be compressed beyond the quark star limit and then collapse into a singularity?

The problem which we didn't get into is rather complicated. We were using the Schwarzschild metric which does a good job of defining where the event horizon is and how much mass is behind it. There are three possible distance variables in that metric that have to be used to consider the density in a black hole. There is R, the size of the gravitating body. There is r, the distance you're considering from the center of that body, and there's r_s, which is the location of the event horizon.

The case of R < r_s is a black hole and that's good to know, but it doesn't describe the density behind R. In fact, the Schwarzschild metric never makes sense for r < R. It's a vacuum solution and it just can't be used to describe the inside of a star or planet or anything else. So, you can't use that metric to describe the density of a black hole - it just can't be done.

There are other possible metrics that would work, such as the Lemaitre metric, but I haven't looked into that. The conventional wisdom is that any density material can make a black hole so long as the radius is large enough.

To answer your question directly: I believe it would (and must) collapse into a singularity - no matter its density. Any time you put enough mass behind the Schwarzschild radius that mass will collapse into a singularity - it has a singularity in its future. As it is collapsing (for a while) it has non-infinite density - but it will collapse into an infinitely dense singularity.

//EDIT
As an aside, does this describe our universe? Is the density of the universe such that it will eventually collapse into a singularity? Is the actual radius of the universe smaller than the gravitational radius / Schwarzschild radius? If so, we are in a black hole right now Food for thought.
//EDIT

Originally Posted by KALSTER

Edit:Oh sorry, I confused a geosynchronous orbit with a geostationary orbit.

Everything in this post applies to any geosynchronous orbit, including a geostationary orbit and your question is a good one. The answer is not exactly intuitive.

~modest