An Alternative to a singularity?

[Jeffocal]

Originally Posted by modest

Clocks at the center of a collapsing star would tick slower than clocks on the surface, and clocks at the surface would again tick slower than clocks further out.
~modest

I disagree with your conclusion that the clocks would tick slower on a surface of a collapsing star than the ones further out because the gravitational force and therefore the time dilation would be strongest at it' surface. Both the clocks*at the center and at an infinite distance would slow to a complete stop relative to the surface of a mass as it collapsed through its event horizon because relativity tells us that the differential gravitational forces they would experience at those points in space would be infinite.

However, the contraction is not related to the time dilation between the reference frames on its surface and an external one. It is related to the fact that Einstein's theories indicate that the contraction of a stars surface must be measured relative to the external reference frames in which it is contracting. But as mentioned earlier Einstein's theories indicate time would become infinitely dilated or stop in the reference frames that were at its center or at an infinite from a collapsing star as it nears its critical circumference. Therefore, because motion is not possible in a reference frame or an environment where time has stopped, the collapse of a star's surface cannot continue beyond the critical circumference.

This contradicts the assumption that a star can continue to collapse beyond its critical circumference to form an event horizon.

A more serious and what I believe to be a fatal flaw in the argument for the existence of an event horizon is the fact that the laws of physics for those on a surface of a collapsing star as it passed through an event horizon would be different than for those that are not. The laws of motion would not apply to either of thoes reference fames relative to the other because each would view time in the others to have stopped.

[modest]

Originally Posted by Jeffocal

I disagree with your conclusion that the clocks would tick slower on a surface of a collapsing star than the ones further out because the gravitational force and therefore the time dilation would be strongest at it' surface.

The field strength is stronger on the surface than further out. A stronger field means more dilation (as in: slower clock). Clocks on the surface (where the field is stronger) are then slower than clocks further out (where the field is weaker).

EDIT: Sorry, it's not the strength of the field that determines gravitational time dilation, but the value of gravitational potential. Clocks on the surface (where potential is less [considering it as negative]) are then slower than clocks further out (where potential is greater).

Originally Posted by Jeffocal

Both the clocks*at the center and at an infinite distance would slow to a complete stop relative to the surface of a mass as it collapsed through its event horizon because relativity tells us that the differential gravitational forces they would experience at those points in space would be infinite.

Your previous quote disagreed that clocks on the surface are slower than clocks further out and your quote here says clocks on the surface do tick slower than clocks further out.

Some specific numbers are calculated by 2 different methods in this post:

Some numberic examples of gravitational time dilation in and arround Sol

And this one:

Re: Some numberic examples of gravitational time dilation in and arround Sol

You can also think of time dilation as the inverse of redshift (wavelength being the inverse of frequency where photons make great clocks). As a photon travels from the center of a collapsing mass to the surface it climbs out of a gravity well and is redshifted. This means the frequency of the photon is greater at the center and less at the surface... time ticks slower (as revealed by the photon) at the center vs. the surface.

Any time you climb uphill fighting the force of gravity your proper time gets larger relative to a clock which you leave behind. This is a fundamental aspect of general relativity by the equivalence principle. If you consider a rocket accelerating then clocks on the nose of the rocket tick faster than on the floor (by the engine). For the person on the floor of the rocket to reach the nose he must climb uphill against the force of acceleration.

To think of this graphically (and rather simply) you can plot the gravitational potential of a homogeneous ball:

-source

Points on the curve that have a steeper slope have clocks that run slower than points on the curve which have less slope. The "strength of the field" *is* the slope of the curve of potential. Edit: Again, sorry, Time dilation is a function of potential not field strength! So, the further down on that plot the slower clocks run. The slope of the curve has nothing to do with it but rather how far up and down the curve it is. Sorry

So, yes, clocks at the center of a mass where the field is strongest run slower than clocks on the surface where the field is weaker. EDIT: and, again, it's not the strength of the field but the value of gravitational potential. This is most easily shown mathematically with the equation for time dilation as a function of gravitational potential (U):

where U is:

-source

You might also notice the first sentence in the wiki for gravitational time dilation:

Gravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the lower the gravitational potential [where it is taken to be negative] (closer to the center of a massive object), the more slowly clocks run.

I don't know what else to do to convince you of this. Do you have a link explaining or agreeing with what you're thinking?

~modest

[Jeffocal]

Originally Posted by modest

Your previous quote disagreed that clocks on the surface are slower than clocks further out and your quote here says clocks on the surface do tick slower than clocks further out.

~modest

Ya I guess I am a bit but hope we can work through it

However if you agree with my other statement that

Both the clocks*at the center and at an infinite distance would slow to a complete stop relative to the surface of a mass as it collapsed through its event horizon because relativity tells us that the differential gravitational forces they would experience at those points in space would be infinite.

Then the arguments I have presented are still valid. Could you please elaborate on any logical inconsistency which may invalidate them. Because if they are logically consistent within the confines of relativity then the assumption made by physicist that an event horizon is form when a star collapse is invalid.

[modest]

Originally Posted by Jeffocal

Ya I guess I am a bit but hope we can work through it

That's a good approach

Originally Posted by Jeffocal

However if you agree with my other statement that

Both the clocks*at the center and at an infinite distance would slow to a complete stop relative to the surface of a mass as it collapsed through its event horizon because relativity tells us that the differential gravitational forces they would experience at those points in space would be infinite.

No, I would disagree. The person on the surface of the collapsing star should see clocks at the center as time dilated and running slower than his own. Looking at clocks further out away from the star he would find them running faster than his own. The further a clock is from the center of the collapsing star, the faster it ticks.

~modest

[modest]

Jeff, I'm sorry, I've been moving through this thread on autopilot. I've been saying that gravitational time dilation is greater or less depending on the "strength of the field". That's not true at all. It is directly proportional to gravitational potential regardless of field strength.

The force of gravity is change in potential. If you're in an area of space where potential changes quickly then a person will feel a large gravitational force. As a person gets farther away from a mass the gravitational potential and the field strength both change, but it is most certainly the value of potential which determines time dilation.

It was probably very confusing that I mixed those up. I see now what you were saying that a person in the center of the mass would feel no gravitational force—the field strength would be zero while the field strength would be very large on the surface. If time dilation were a function of field strength then you'd most certainly be correct in your conclusions.

But, time dilation is a function of gravitational potential and the person at the center of the star has greater potential [where potential (U) is considered positive] than the person on the surface. The farther from the center of the star, the less the potential and the slower clocks run. EDIT: "...the faster they run." I can't keep my clocks straight!

So, I think that was the problem. You were thinking that time dilation was a function of field strength (the force of gravity) and I was saying the same without thinking about it—it's most certainly not the case.

~modest

[Jeffocal]

Originally Posted by modest

But, time dilation is a function of gravitational potential and the person at the center of the star has greater potential [where potential (U) is considered positive] than the person on the surface. The further from the center of the star, the less the potential and the slower clocks run.

~modest

Thanks

However you will have to explain to me using only the concepts of relativity why the center of a star is consider to have greater gravitational potential than its surface because until then I will stick to the conclusion both the clocks*at the center and at an infinite distance would slow to a complete stop relative to the surface of a mass as it collapsed through its event horizon because relativity tells us that the differential gravitational forces they would experience at those points in space would be infinite.

Please try to explain it to me in terms of the relativistic properties the star internal gravitational potential not relative to anything outside of it.
Thanks Jeff

Source: The Imagineer’s Chronicles

[modest]

Originally Posted by Jeffocal

Thanks

However you will have to explain to me using only the concepts of relativity why the center of a star is consider to have greater gravitational potential than its surface because until then I will stick to the conclusion both the clocks*at the center and at an infinite distance would slow to a complete stop relative to the surface of a mass as it collapsed through its event horizon because relativity tells us that the differential gravitational forces they would experience at those points in space would be infinite.

Please try to explain it to me in terms of the relativistic properties the star internal gravitational potential not relative to anything outside of it.

No problem. First, I should add that I edited that post right before you replied to it. I meant to say:

But, time dilation is a function of gravitational potential and the person at the center of the star has greater potential [where potential (U) is considered positive] than the person on the surface. The further from the center of the star, the less the potential and the faster clocks run.

rather than slower.

But, yeah, gravitational potential energy can either be negative or positive. In Newtonian mechanics it is considered negative and called phi (), or V. In general relativity it is considered positive and called U. It doesn't really matter which way you do it, it's just important to keep straight which sign you're using.

Probably the easiest way for me to convince you that potential is greatest at the center of the object and decreases to zero at infinity is to quote a good source:

This is the expression of gravitational potential for a point inside solid sphere. The potential at the center of sphere is obtained by putting r = 0,

This may be an unexpected result. The gravitational field strength is zero at the center of a solid sphere, but not the gravitational potential. However, it is entirely possible because gravitational field strength is rate of change in potential, which may be zero as in this case.

The plot of gravitational potential for uniform solid sphere is shown here as we move away from the center.



Gravitational potential due to rigid body

So, if you look at that blue line it is most negative (in general relativity we would say it is "most positive") at r=0, the center of the solid sphere. That's the point where time dilation would be greatest and clocks would run slowest. The higher up the blue line goes on the graph the less time dilation we have and the faster clocks run.

The field strength which is the slope of that blue line at any given point is not the same as the potential. The value of potential at a point on the line is given by how far up and down on the graph the point is. In particular, at r=0 (the center of the sphere) the slope is zero meaning the field strength is zero, but the potential is not zero.

You'll find that result is fully derived on that web page: Gravitational potential due to rigid body. We would say, then, that gravitational potential is zero at infinity and increases as one gets closer to a massive body. It continues to increase inside the body and is largest at the center of the mass. The larger the potential, the slower clocks tick.

~modest

[Jeffocal]

Originally Posted by modest

But, time dilation is a function of gravitational potential and the person at the center of the star has greater potential [where potential (U) is considered positive] than the person on the surface. The further from the center of the star, the less the potential and the faster clocks run.

rather than slower.
~modest

Ya but I believe that is only true if you are observing it from the perspective of someone who is outside of stars surface. However relativity says that the laws of physics must be the same for all observers. If you assume the person at the center of the star has relativity greater potential than the person on its surface I think to keep the laws the same for both an observer who is at its center as for one on it surface one would have to say that an observer on the surface of a star would have a relativity greater potential than one at the center.

It appears to me many have misused or misunderstood Einstein's basic concepts to justify the existence of things like an event horizon.

[modest]

Everyone can use the same physics (general relativity) and everyone concludes that the clock on the surface runs faster than the clock at the center using that physics—including the people in those positions.

The laws of physics being the same for everyone does not mean everyone will have the same potential any more than it would mean everyone feels the same acceleration or everyone is the same distance from some given mass. The physics that everyone uses can be considered:



while different observers have different values of U.

I do, however, agree with you to an extent about the event horizon. Because Schwarzschild was the first to make an exact solution to GR and his metric broke down at the event horizon many people took the horizon to be a kind of physical boundary in space. This is not really the case with GR, but just an effect of Schwarzschild coordinates. In other words: GR doesn't break down at the horizon, Schwarzschild's metric does (because it's static).

~modest

[Pluto]

G'day from the land of ozzzz

This paper maybe of interest to the topic. The ABS is explains the point without further writting.

[astro-ph/9910408] Non-occurrence of trapped surfaces and Black Holes in spherical gravitational collapse: An abridged version
Non-occurrence of trapped surfaces and Black Holes in spherical gravitational collapse: An abridged version

Authors: Abhas Mitra (BARC, Theory Division)
(Submitted on 22 Oct 1999 (v1), last revised 5 Dec 2000 (this version, v5))

Abstract: We have shown in that for arbitrary EOS and radiation transport properties, (even) the idealized spherical gravitational collapse DOES NOT lead to the formation of trapped surfaces: 2GM(r,t)/R <=1. Hence all singularity theorems of Hawking, Penrose and Geroch, built on the assumption of formation of trapped surfaces, get invalidated! And this inequality, demands that M->0 if indeed R->0. We have shown that the final state corresponds to a zero mass BH state and, this state would occur only after infinite proper time indicating that GR is indeed the only naturally singularity free theory for isolated bodies (as was cherished by Einstein). This M->0 state would materialize after the body radiates its entire initial mass-energy. Thus there is no event horizon at any finite R or M, and, therefore all the great theoretical confusions like whether there could be (i) White Holes, (ii) whether t (R) becomes spacelike (timelike) inside the EH (iii) Loss of information in gravitational collapse, and (iv) validity of cosmic censorship conjecture get resolved. At any finite proper time, the collapsed object would be either static (z<2) or may appear static (R almost frozen) though, in extreme cases, internally, in terms of proper radial length, it might be collapsing at a speed ~c! We call the latter as Eternally Collapsing Objects.

later 2006 he writes this paper.


Sources of Stellar Energy, Einstein- Eddington Timescale of Gravitational Contraction and Eternally Collapsing Objects
[astro-ph/0608178] Sources of Stellar Energy, Einstein- Eddington Timescale of Gravitational Contraction and Eternally Collapsing Objects


Authors: Abhas Mitra

(Submitted on 8 Aug 2006 (v1), last revised 3 Sep 2006 (this version, v3))

Abstract: We point out that although conventional stars are primarily fed by burning of nuclear fuel at their cores, in a strict sense, the process of release of stored gravitational energy, known as, Kelvin - Helmholtz (KH) process is either also operational albeit at an arbitrary slow rate, or lying in wait to take over at the disruption of the nuclear channel. In fact, the latter mode of energy release is the true feature of any self-gravity bound object including stars. We also highligh the almost forgotten fact that Eddington was the first physicist to introduce Special Relativity into the problem and correctly insist that, actually, total energy stored in a star is not the mere Newtonian energy but the total mass energy (E = M c^2). Accordingly, Eddington defined an ``Einstein Time Scale'' of Evolution where the maximum age of the Sun turned out to be t_E = 1.4. 10^{13} yr. We extend this concept by introducing General Relativity and show that the minimum value of depletion of total mass-energy is t_E =infty not only for Sun but for and sufficiently massive or dense object. We propose that this time scale be known in the name of ``Einstein - Eddington''. We also point out that, recently, it has been shown that as massive stars undergo continued collapse to become a Black Hole, first they become extremely relativistic Radiation Pressure Supported Stars. And the life time of such relativistic radiation pressure supported compact stars is indeed dictated by this Einstein -Eddington time scale whose concept is formally developed here. Since this observed time scale of this radiation pressure supported quasistatic state turns out to be infinite, such objects are called Magnetospheric Eternally Collapsing Objects (MECO).

My question to this is what is the state or phase of matter in these star cores to be able to store gravitational radiation?