An Alternative to a singularity?

[Jeffocal]

Are we 100 percent sure that a singularity exists in the center of a black hole.

Einstein in his General Theory of Relativity predicted time is dilated or moves slower when exposed to gravitational field than when it is not. Therefore, according to Einstein's theory a gravitational field, if strong enough could stop time.

As a star cools and contacts, the gravitational forces at its surface increase as its circumference decrease. We know this because observations of gravitational forces tell us they are proportional to the square root of the stars mass divided by its circumference.

In 1915, Karl Schwarzschild discovered that according to Einstein's General Theory of Relativity the gravitational field associated with the mass of a star greater than approximately 2.0 times a solar mass would stop the movement of time if it collapsed to a one-dimension point in space. He also defined the critical circumference or boundary in space around this one-dimensional point where the strength of a gravitational field will result in time being infinitely dilated or slowing to a stop.

In other words as a star contacts and its circumference decreases the time dilation on the surface of the mass associated with that stars gravitational field will increase. At a certain point the contraction of that mass will produce a gravitational field strong enough to stop the movement of time. Therefore, critical circumference defined by Karl Schwarzschild is a boundary in space where time stops relative to the space outside of that boundary.

This critical circumference is called the event horizon because an event that occurs on the inside of it cannot have any effect on the environment outside of it.

Many physicists believe the existence of black holes is an inevitable outcome of Einstein's General Theory of Relativity.

However, it can be shown using the concepts developed by Einstein, this may not be true.

In Kip S. Thorne book "Black Holes and Time Warps", he describes how in the winter of 1938-39 Robert Oppenheimer and Hartland Snyder computed the details of a stars collapse into a black hole using the concepts of General Relativity. On page 217 he describes what the collapse of a star would look like, form the viewpoint of an external observer who remains at a fixed circumference instead of riding inward with the collapsing stars matter. They realized the collapse of a star as seen from that reference frame would begin just the way every one would expect. "Like a rock dropped from a rooftop the stars surface falls downward (shrinks inward) slowly at first then more and more rapidly. However, according to the relativistic formulas developed by Oppenheimer and Snyder as the star nears its critical circumference the shrinkage would slow to a crawl to the external observer because of the time dilatation associated with the relative velocity of the star's surface with respect to the external observer. The smaller the star gets the more slowly it appears to collapse because the time dilation predicted by Einstein increases as the speed of the contraction increases until it becomes frozen at the critical circumference.

However, the time measured by the observer who is riding on the surface of a collapsing star will not be dilated because he or she is moving at the same velocity as the surface of that star.

Therefore, the proponents of black holes say the contraction of a star can continue until it becomes a one-dimensional point in space because time has not stopped on its surface even though it has stopped to an observer who in remains at fixed circumference to that star.

But one would have to draw a different conclusion if one viewed time dilation in terms of the gravitational field of a collapsing star instead of in terms of the velocity of the contraction.

Einstein showed that time is dilated by a gravitational field. Therefore, the time dilation on the surface of a star will increase relative to an external observer as it collapses because, as mentioned earlier gravitational forces at its surface increase as its circumference decrease.

This means, as a star nears its critical circumference its shrinkage slows with respect to an external observer who is outside of the gravitation field because the increasing strength of its gravitational field causes a slowing of time on its surface. The smaller the star gets the more slowly it appears to collapse because the gravitational field at its surface increase until time becomes frozen for the external observer at the critical circumference.

Therefore, the observations an external observer would make using conceptual concepts of Einstein's theory regarding time dilation caused by the gravitational field of a collapsing star would be identical to those predicted by Robert Oppenheimer and Hartland Snyder in terms of the velocity of its contraction.

However, Einstein developed his Theory of General Relativity based on the equivalence of all inertial reframes which he defined as frames that move freely under their own inertia neither "pushed not pulled by any force and therefore continue to move always onward in the same uniform motion as they began".

This means that one can view the contraction of a star with respect to the inertial reference frame that, according to Einstein exists in the exact center of the gravitational field of a collapsing star.

(Einstein would consider this point an inertial reference frame with respect to the gravitational field of a collapsing star because at that point the gravitational field on one side will be offset by the one on the other side. Therefore, a reference frame that existed at that point would not be pushed or pulled relative to the gravitational field and would move onward with the same motion as that gravitational field.)

The surface of collapsing star from the view point of an observer who is at the center of the collapse would look according to the field equations developed by Einstein as if the shrinkage slowed to a crawl as the star near its critical circumference because of the increasing strength of the gravitation field at the surface of the star relative to it's center. The smaller the star gets the more slowly it appears to collapse because the gravitational field at its surface increases until time becomes frozen at the critical circumference.

Therefore, because time stops or becomes frozen at the critical circumference for both an observer who is at the center of the clasping mass and one who is at a fixed distance from its surface the contraction cannot continue from either of their perspectives.

However, Einstein in his general theory showed that a reference frame that was free falling in a gravitational field could also be considered an inertial reference frame.

As mentioned earlier many physicists assume that the mass of a star implodes when it reach the critical circumference. Therefore, the surface of a star and an observer on that surface will be in free fall with respect to the gravitational field of that star when as it passes through its critical circumference.

This indicates that point on the surface of an imploding star, according to Einstein's theories could also be considered an inertial reference frame because an observer who is on the riding on the surface of an imploding star will not experience the gravitational forces of the collapsing star.

However, according to the principals of Relativity he will observe the differential gravitational forces caused by an imploding mass with respect to someone who remains at a fixed circumference or is at the center of the collapsing mass. But according to the Einstein theory of relativity, as a star nears its critical circumference an observer who is on the stars surface will perceive the differential magnitude of the gravitational field relative to an observer who is in an external reference frame to be increasing. Therefore, he or she will perceive time as slowing to a crawl with respect to those reference frames that are not on its surface as it approaches the critical circumference. The smaller the star gets the more slowly time appears to move with respect to an external reference frame until it becomes frozen at the critical circumference.

However, the contraction of a stars surface must be measured with respect 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 not on the surface of 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 made by many that the implosion would continue for an observer who was riding on its surface.

Therefore, based on the conceptual principles of Einstein's theories relating to time dilation caused by a gravitational field a collapsing star must maintain a minimum volume which is equal to of greater than the critical circumference defined by Karl Schwarzschild and cannot implode to a one dimensional point or a singularity as many physicists believe.

This means either the conceptual ideas developed by Einstein are incorrect or the field equations many physicists used to predict the existence of a singularity are incomplete because the theoretical predications regarding its existence are contradictory.

Only observations can determine which one is correct because both are based on the validity of the concepts presented in Einstein's theories and the mathematical equations he developed.

Source: The Imagineers chronicals

[modest]

Hi Jeff, welcome to Hypography.

You can't tell the difference gravitationally between a point mass (a singularity in this case) and a spherically symmetric ball from a point outside the ball. This is true not only in Schwarzschild's metric, but GR in general. It's called Birkhoff's theorem. So, from outside a black hole (assuming the mass is spherically symmetric) it's impossible to determine if there is a singularity versus some lower density configuration of the matter.

Schwarzchild's metric does not predict a singularity. Because the metric is static (it only works for observers who are not moving) it breaks down at the event horizon—the point where things can no longer be static. It's possible to change up the metric a bit and describe the interior of the horizon which is done with Kruskal–Szekeres coordinates which then show that inside the horizon all future paths lead to a true singularity (rather than the coordinate singularity in Schwarzchild's metric).

Originally Posted by Jeffocal

The surface of collapsing star from the view point of an observer who is at the center of the collapse would look according to the field equations developed by Einstein as if the shrinkage slowed to a crawl as the star near its critical circumference because of the increasing strength of the gravitation field at the surface of the star relative to it's center. The smaller the star gets the more slowly it appears to collapse because the gravitational field at its surface increases until time becomes frozen at the critical circumference.

No, the field is strongest (greatest gravitational potential) at the center of the mass. Gravitational time dilation is proportional to gravitational potential where potential is taken to be positive, greatest at the center of the object, and decreases to zero at infinity. With smaller potential comes faster clocks. You can use the following where U is potential:



So clocks will tick faster on the surface of the collapsing star as considered from the center.

There's a good page on this topic (the geometry inside a black hole) here:

Schwarzschild Geometry

~modest

[Jeffocal]

Originally Posted by modest

You can't tell the difference gravitationally between a point mass (a singularity in this case) and a spherically symmetric ball from a point outside the ball.
~modest

I believe the contradictions mentioned in the origin article would not only apply to the size of mass or "ball" but also on its ability to pass through what physicist call an event horizon.

Therefore, the theoretical predications regarding existence of an event horizon would also be contradictory based on the conceptual principles of Einstein's theories relating to time dilation caused by a gravitational field because the arguments presented in the origin article indicate that a collapsing star must maintain a minimum volume which is equal to of greater than the critical circumference or event horizon defined by Karl Schwarzschild.

[modest]

Originally Posted by Jeffocal

I believe the contradictions mentioned in the origin article would not only apply to the size of mass or "ball" but also on its ability to pass through what physicist call an event horizon.

Did you read the link on Birkhoff's theorem? From outside a spherically symmetric mass (like a star) there are no gravitational effects if the mass were to shrink or grow. It doesn't matter gravitationally if the mass is that of a low-density star or an infinitely dense singularity. If a person outside a black hole wanted to consider a black hole as a shell of mass where all the mass is stuck at the event horizon never being able to pass through because of time dilation then that's fine. By Birkhoff's theorem there is no way of distinguishing that from a singularity.

So, what is the contradiction? The person outside sees objects falling in a black hole become more and more time dilated and more and more redshifted until the object gets infinity close to the horizon and disappears (reaching infinite redshift). What does that contradict?

~modest

[Jeffocal]

Originally Posted by modest

Did you read the link on Birkhoff's theorem?
~modest

Yes I did however, I believe that Birkhoff's theorem contradicts the basic concepts of Relativity because as was mentioned in the original article I think relativity allows one to define the time dilation associated with the gravitational forces on the surface of collapsing mass in terms of an inertial reference frame at its center.

"Someone who was on that surface would the observe the differential gravitational forces caused by an imploding mass with respect to someone who remains at a fixed circumference or is at the center of the collapsing mass. But according to the Einstein theory of relativity, as a star nears its critical circumference an observer who is on the stars surface will perceive the differential magnitude of the gravitational field relative to an observer who is in an external reference frame to be increasing. Therefore, he or she will perceive time as slowing to a crawl with respect to those reference frames that are not on its surface as it approaches the critical circumference. The smaller the star gets the more slowly time appears to move with respect to an external reference frame until it becomes frozen at the critical circumference.

However, the contraction of a stars surface must be measured with respect 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 not on the surface of 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."

I believe this contradicts the assumption made by many that the implosion would continue for an observer who was riding on its surface.

[Pluto]

G'day from the land of ozzzzzz

With this link I'm not trying to prove a point, I just thought that this paper is interesting.

[0904.3520] Time is not the problem
Time is not the problem

Authors: Olaf Dreyer
(Submitted on 22 Apr 2009)

Abstract: Attempts to quantize general relativity encounter an odd problem. The Hamiltonian that normally generates time evolution vanishes in the case of general relativity as a result of diffeomorphism invariance. The theory seems to be saying that time does not exist. The most obvious feature of our world, namely that time seems to progress and that the world changes accordingly becomes a problem in this presumably fundamental theory. This is called the problem of time. In this essay we argue that this problem is the result of an unphysical idealization. We are caught in this "problem of time" trap because we took a wrong turn in the early days of relativity by permanently including a split of geometry and matter into our physical theories. We show that another possibility exists that circumvents the problem of time and also sheds new light on other problems like the cosmological constant problem and the horizon problem in early universe cosmology.

[Jeffocal]

The problem may not be with time but with the relativistic concept of a space-time dimension.

We agree that One of the most persistent observations regarding time is that it is not perceive as matter or space but as an irreversible physical, chemical, and biological change in physical space.

Why then do physicist's assume that it can interact with the physical properties of space when there is no observational evidence for that assumption.

Defining time only in terms of a measure of the sequential ordering of the causality of an event would provide an unambiguous definition of time that is more consistent with both physical and mathematical observations than defining it in terms of the physical properties of a dimension.

Source: the Imagineer's Chronicles

[Pluto]

G'day from the land of ozzzzzzz

Time cannot interact, it measures the interaction.

[Jeffocal]

The fact that time is only measure an interaction may be a clue as to why "Attempts to quantize general relativity encounter an odd problem" because a measurement by definition is continuous.

Maybe instead of trying to quantize relativity we should try to relativize the quantum properties of mass and energy because a continuous medium can not be made up of quantized parts but can be divided into them.

Source: The Imagineer's Chronicles

[modest]

Originally Posted by Jeffocal

Yes I did however, I believe that Birkhoff's theorem contradicts the basic concepts of Relativity

It is derived directly from relativity.

Originally Posted by Jeffocal

because as was mentioned in the original article I think relativity allows one to define the time dilation associated with the gravitational forces on the surface of collapsing mass in terms of an inertial reference frame at its center.

Well, you don't define time dilation, you solve for it. Nonetheless, yes you can solve the difference in proper time between the center and the collapsing surface. The equation I gave earlier would work fine for that (although it is a first order approximation). Where the OP goes wrong is thinking that the field is stronger on the surface of the collapsing star than at the center and therefore clocks tick slower on the surface vs. the center. The opposite is true. 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. There's no contradiction in that.

~modest