The Paradoxical Nature of Black Holes

[PaulS1950]

The become one bigger black hole - like when galaxies merge.

[King, North TX]

The become one bigger black hole - like when galaxies merge.

 

Has such a thing ever been witnessed, or is this speculation?

[StringJunky]

Has such a thing ever been witnessed, or is this speculation?

 

http://www.wired.com/wiredscience/2009/10/black-hole-collision/

 

 

It's worth clicking the link to get the lowdown on what you are looking at and how it was made.

Edited May 1, 2010 by StringJunky

[Slinkey]

Except that in it's own reference frame, it isn't contracted at all.

 

Indeed. Now apply that to the EH. As you move towards the EH it is contracted in the direction of your movement and as your velocity increases the BH becomes more and more pancake shaped. If you could reach light speed it would become an infinitely thin pancake.

 

Falling towards a BH isn't just like falling towards a planet although even when you fall towards a planet, like Earth, it also is contracted in the direction of your movement, but because you are travelling at a tiny fraction of c this effect is negligible.

[King, North TX]

...

 

It's worth clicking the link to get the lowdown on what you are looking at and how it was made.

 

Wow.

 

Thank You.

[pioneer]

Along the lines of the paradoxical nature of blackholes, is the singularity from which the universe began. This would be expected to have extreme space-time contraction similar to the grand daddy of all blackholes. The paradox is connected to the initial phase of the universe, called the Planck Epoch, which lasts about 10-43sec.

 

The question I have is, from what reference is the Planck epoch based? Is it measured within the extreme space-time contraction of the initial universe; sort of a black hole reference (more or less). Or is this based on our earth reference? Each will give a different output scenario.

 

If the 10-43 is in the universal (black hole) reference, since time is highly dilated there, it would actually appear to take much longer in our reference. The extremely fast event would be like falling into a black hole or appear to take an extremely long time, such that we might still see it , especially if it is assumed space-time could expand faster than C.

 

If the Planck epoch is based on our earth reference, or what we would see from the earth, then because of the extreme time dilation, the local reference on the singularity, be more like 10-46 .....10-53 sec range, since this faster time, when time dilated, would look like 10-43 in earth reference. At that higher speed, does this phenomena occur at a speed we are not yet able to speculate about?

 

Knowing something about the paradox of black holes tells us about the paradox of the creation of the universe where we have extreme space-time contraction and something occurring at the fastest speed of 10-43 seconds, both at the same time.

[Slinkey]

Pioneer,

 

As we are inside the Universe by definition it will be from our reference frame. Unless you are outside the Universe there is no other reference frame for the Universe.

[Royston]

I realize this is an old thread, and three pages long, (so sorry if this has already been covered) but there's only a paradox if you ignore one of the main tenets of general relativity i.e coordinates do not have an immediate metrical significance.

 

IOW, there is nothing physical about a coordinate singularity, which is what you get for a stationery observer, who's radial distance is [math]O_d>>R_s[/math]. Where [math]R_s[/math] is the Schwarzschild radius. A transformation of coordinates can eliminate infinite redshift et.c. I think confusion arises when special relativity is applied to general relativistic situations, there's bound to be inconsistencies as SR doesn't cope with gravity.

[FooFiFum]

I believe Blach Holes are rather like onions. For instance, they can not possibly include an infinite singularity which would require they reach a Planck Density first. Plank density excludes gravitational force, but black holes accumulate mass and gravity. Accordingly, not one of them has ever achieved Planck Density, let alone an infinite singularity.

 

What they DO achieve is mass acceleration as mass moves towards the center of the BH. This acceleration has three parameters. First, mass acceleration can approach. but never achieve c. Second, mass and asociated gravity increases as mass approaches c. Third, time, as calculated by an external observer approaches zero for all mass accelerating towards the BH. Sort of like converting acceleration to both mass and time dilation.

 

So, how do we account for ever increasing event horizon diameters? I believe there is nothing special about the event horizon. It is simply the onion layer at which light achieves either orbit or adds thermal energy to the BH mass. Because light CAN travel at c, it CAN pass all the mass that is accelerating towards the center.

 

I have NO idea how the various outer shells of added mass might appear to increase their distance from the center as the event horizon for light expands.

 

Just meandering ponderings....

[Slinkey]

I realize this is an old thread, and three pages long, (so sorry if this has already been covered) but there's only a paradox if you ignore one of the main tenets of general relativity i.e coordinates do not have an immediate metrical significance.

 

IOW, there is nothing physical about a coordinate singularity, which is what you get for a stationery observer, who's radial distance is [math]O_d>>R_s[/math]. Where [math]R_s[/math] is the Schwarzschild radius. A transformation of coordinates can eliminate infinite redshift et.c. I think confusion arises when special relativity is applied to general relativistic situations, there's bound to be inconsistencies as SR doesn't cope with gravity.

 

Royston,

 

It appears that I am not alone in my reservations about BHs. Luminaries in the field of physics such as Lawrence Krauss also have reservations.

 

"Physicist Lawrence Krauss and Case Western Reserve colleagues think they have found the answer to the paradox. In a paper accepted for publication in Physical Review D, they have constructed a lengthy mathematical formula that shows, in effect, black holes can't form at all. The key involves the relativistic effect of time, Krauss explains. As Einstein demonstrated in his Theory of General Relativity, a passenger inside a spaceship traveling toward a black hole would feel the ship accelerating, while an outside observer would see the ship slow down. When the ship reached the event horizon, it would appear to stop, staying there forever and never falling in toward oblivion. In effect, Krauss says, time effectively stops at that point, meaning time is infinite for black holes. If black holes radiate away their mass over time, as Hawking showed, then they should evaporate before they even form, Krauss says. It would be like pouring water into a glass that has no bottom. In essence, physicists have been arguing over a trick question for 40 years."

http://news.sciencemag.org/sciencenow/2007/06/21-01.html?rss=1

 

I only found this article today (hence why I have come back to this discussion), so I don't know what has happened in the intervening time and whether Krauss has been refuted or not, but, obviously, I agree with him.

[IM Egdall]

So if black holes cannot form, how come there is so much compelling observational evidence for them (albeit indirect)? You know, like accretion discs, jets, extreme motion of neighboring stars, X-ray emissions, quasars, etc. Can Krauss explain what produces these phenomena if black holes don't exist?

Edited January 17, 2011 by I ME

[Slinkey]

So if black holes cannot form, how come there is so much compelling observational evidence for them (albeit indirect)? You know, like accretion discs, jets, extreme motion of neighboring stars, X-ray emissions, quasars, etc. Can Krauss explain what produces these phenomena if black holes don't exist?

 

Science doesn't work like that. It is not necessary to have an alternative hypothesis in order to show that an existing hypothesis is incorrect.

 

The observations we have indicate something very heavy there, of that there is little doubt. However, whether the gravitating body is a black hole is another question which, if Krauss is right, is not shown by any current theory.

 

According to the BH hypothesis it is an object where at the Event Horizon the escape velocity is equal to the velocity of light. This means accretion disks, jets, x-ray emissions and the effects we association with quasars, are produced outside the EH because if they were produced at the EH (or inside) they could not escape into space. So, you could argue that these effects are not conclusive evidence of a BH and could be the result of an extremely heavy body which is not a BH.

 

As to the observed movement of stars in the vicinity. What details do we have about the actual orbits? ie. what is the smallest orbital radius of an observed object there? Anyone know?

[IM Egdall]

Yes, but a new theory must still explain all known observations to be viable.

 

I found my notes but can't find the link. They say that there are observable differences between black holes and other compact massive objects. Infalling matter collides with the object at relativistic speeds, leading to high-energy emissions. Thermonuclear "burning" may occur on the surface as material builds up. This produces irregular flares of X-rays and others. The lack of flare-ups is evidence the object is a black hole because there is no surface onto which matter can collect.

 

Does Krauss's theory explain this?

Edited March 3, 2011 by I ME

[Slinkey]

Yes, but a new theory must still explain all known observations to be viable.

 

As I understand it, Krauss didn't produce a new theory. He explained why the "old" one didn't explain black holes. As I said, science doesn't need a new theory to show that an old one is wrong.

 

I found my notes but can't find the link. They say that there are observable differences between black holes and other compact massive objects. Infalling matter collides with the object at relativistic speeds, leading to high-energy emissions. Thermonuclear "burning" may occur on the surface as material builds up. This produces irregular flares of X-rays and others. The lack of flare-ups is evidence the object is a black hole because there is no surface onto which matter can collect.

 

With respect you'd have to show me the link for me to comment. However, I will ask, how do we see x-rays coming from a BH? This is because matter is colliding at relativistic speeds. We see x-rays but these weren't x-rays when they were created they were far more energetic nearer to the event horizon.

 

Does Krauss's theory explain this?

 

As I said, Krauss showed how the old theory doesn't lead to BHs. Thus the old theory doesn't explain what you have said either.

[IM Egdall]

As I understand it, Krauss didn't produce a new theory. He explained why the "old" one didn't explain black holes. As I said, science doesn't need a new theory to show that an old one is wrong.

 

 

 

With respect you'd have to show me the link for me to comment. However, I will ask, how do we see x-rays coming from a BH? This is because matter is colliding at relativistic speeds. We see x-rays but these weren't x-rays when they were created they were far more energetic nearer to the event horizon.

 

 

 

As I said, Krauss showed how the old theory doesn't lead to BHs. Thus the old theory doesn't explain what you have said either.

 

Oh, I think I get what you are trying to tell me. Krauss is claiming there is a flaw in the old theory (general relativty); so it does not really predict black holes with event horizons as everyone had thought Is this the jist of it?

[Slinkey]

Oh, I think I get what you are trying to tell me. Krauss is claiming there is a flaw in the old theory (general relativty); so it does not really predict black holes with event horizons as everyone had thought Is this the jist of it?

 

That's what the article says, yes.

[csmyth3025]

...As to the observed movement of stars in the vicinity. What details do we have about the actual orbits? ie. what is the smallest orbital radius of an observed object there? Anyone know?

The following webpage will provide you a nice image and links to research papers and publications which should answer your question:

UCLA Galactic Center Group

 

Chris

[md65536]

Disclaimer: I'm not a real physicist, and I haven't read all the replies, but I wanted to chip in a couple cents.

 

First: How can you possibly see something that's frozen in time? In the first post, you admit that you can't, but then suppose that you can -- that's just asking for problems when you assume something that's known to be unreal.

 

What exactly do you expect to see? If the clock is sending out a signal at frequency more than one million megahertz, yet it appears to be completely frozen for you, how much time do you think it will be between signals that you receive? Answer: Infinity much, that's how much. Similarly, if you are shining light on it and it is reflecting that light, then the light that it reflects in say a second of its own time would need to be stretched out into an infinite amount of your time. It would need to receive and reflect an infinite amount of light in its own frame, for you to see its reflection.

 

 

Second: If you do not observe that the matter of the clock has been absorbed by the BH, then you won't see the same matter evaporate out of it (you'd never know it was the same matter but you could measure its mass to be assured that it is never observed evaporating more mass than it is observed to have). However, if the BH evaporates, eventually it won't be a BH any more (it will become a normal boring dense mass?), at which point you could see the clock fall into it.

 

I think what you'd see is that as the BH evaporates, the event horizon shrinks???, and the clock is allowed to move closer and slowly forward through time as it follows the EH that is shrinking away from it??????

[Iggy]

http://news.sciencemag.org/sciencenow/2007/06/21-01.html?rss=1

 

I only found this article today (hence why I have come back to this discussion), so I don't know what has happened in the intervening time and whether Krauss has been refuted or not, but, obviously, I agree with him.

 

Here is their paper,

 

Observation of Incipient Black Holes and the Information Loss Problem

 

I read it. It's very interesting. The authors tied up some loose ends the following year,

 

Quantum Radiation from Quantum Gravitational Collapse

 

And here is a rebuttal,

 

Pre-Hawking Radiation from a Collapsing Shell

 

where they report that quantum effects make the collapse time finite to an observer at infinity so that a horizon is formed and pre-Hawking radiation is not a solution to the information loss paradox.

 

Edited to add:

 

Slinkey, this looks like a good background on the time it takes to fall into a black hole as viewed from far away in general relativity: Falling Into and Hovering Near A Black Hole.

 

It mentions a similar question to yours but having to do with a closed universe which only exists for a finite time (rather than the finite time of an evaporating black hole)

Edited March 26, 2011 by Iggy

[csmyth3025]

As I understand it, the Milky Way's central massive object is constrained by recent observations and analysis as follows:

The mass of Sagittarius A* has been estimated in two different ways. (1) Two groups—in Germany and the U.S.—monitored the orbits of individual stars very near to the black hole and used Kepler's laws to infer the enclosed mass. The German group found a mass of 4.31 ± 0.38 million solar masses^[1] while the American group found 4.1 ± 0.6 million solar masses.^[2] Given that this mass is confined inside a 44 million km diameter sphere, this yields a density ten times higher than previous estimates. (2) More recently, measurement of the proper motions of a sample of several thousand stars within approximately one parsec from the black hole, combined with a statistical technique, has yielded both an estimate of the black hole's mass, and also of the distributed mass in this region. The black hole mass was found to be consistent with the values measured from individual orbits; the distributed mass was found to be 1.0 ± 0.5 million solar masses.^[8] The latter is believed to be composed of stars and stellar remnants.

(ref. http://en.wikipedia....sive_black_hole )

 

The radius of a 44 million km diameter sphere is 22 million km. This is a little over 1/3 the average distance of Mercury to our sun. Even if we assume that the indicated mass fills the entire volume of this limiting sphere, the escape velocity would be about 220,000 km/s (about 73% c)

(ref. http://www.wolframal...E36+kg&x=6&y=10 )

 

Is it the argument of this thread that there is some as yet unknown mechanism by which such an object will not gravitationally collapse to a smaller size (a sphere about 23 million km in diameter)* that will produce an escape velocity greater than c?

*(ref. http://www.wolframal...5E36+kg&x=6&y=9 )

Chris

[Iggy]

Is it the argument of this thread that there is some as yet unknown mechanism by which such an object will not gravitationally collapse to a smaller size (a sphere about 23 million km in diameter)* that will produce an escape velocity greater than c?

 

It does indeed collapse to a smaller size, but this takes essentially an infinite amount of time for that to happen from our perspective due to time dilation. While it is slowly collapsing, getting closer and closer to forming an event horizon, it is also very slowly (from our perspective again) evaporating by emitting pre-Hawking radiation which lowers its mass. The argument would be that it loses mass quicker than it is able to form an event horizon, so that you never really have a true black hole.

 

It would be almost indistinguishable from a true black hole from our perspective.

[csmyth3025]

It does indeed collapse to a smaller size, but this takes essentially an infinite amount of time for that to happen from our perspective due to time dilation. While it is slowly collapsing, getting closer and closer to forming an event horizon, it is also very slowly (from our perspective again) evaporating by emitting pre-Hawking radiation which lowers its mass. The argument would be that it loses mass quicker than it is able to form an event horizon, so that you never really have a true black hole.

 

It would be almost indistinguishable from a true black hole from our perspective.

I may be misundertanding some basic concepts here. As far as I know, a free falling body in a homogenous gravitational field is in an inertial frame of reference in every way identical to the inertial frame of reference of a distant observer. The clocks of both of these observers wiil show the same elapsed time. Am I mistaken about this?

 

Chris

[Iggy]

I may be misundertanding some basic concepts here. As far as I know, a free falling body in a homogenous gravitational field is in an inertial frame of reference in every way identical to the inertial frame of reference of a distant observer. The clocks of both of these observers wiil show the same elapsed time. Am I mistaken about this?

 

Chris

 

If each clock is free falling then each is in a locally inertial frame, but if they have different gravitational potential then they run at different rates from gravitational time dilation. Further from a mass a clock runs faster and closer to the mass it runs slower. A good and verified example is that the atomic clocks on GPS satellites run faster than identical clocks on the ground.

 

http://users.datarealm.com/herrmann/time.htm

[csmyth3025]

If each clock is free falling then each is in a locally inertial frame, but if they have different gravitational potential then they run at different rates from gravitational time dilation. Further from a mass a clock runs faster and closer to the mass it runs slower. A good and verified example is that the atomic clocks on GPS satellites run faster than identical clocks on the ground.

 

http://users.datarea...rrmann/time.htm

In the case of GPS satelites, the effects of both General and Special Relativity have, indeed, been demonstrated to a high degree of precision. I can certainly see how the atomic clock on the GPS satelite can be in an approximately inertial frame of reference because it's following the spacetime geodesic dictated by its distance from the Earth's center and its tangental velocity relative to the Earth.

 

The atomic clock on the ground, however, is not in an inertial frame of reference - it's in an accelerated frame of reference. The fact that the device on the ground "feels" gravity (has weight) illustrates this fact.

 

I wonder if any experiments have been performed that compare the atomic clock rates of two (or more) atomic clocks on satelites orbiting at different altitudes (11,000 and 22,000 km, for instance).

 

I'll have to think about this for a while. I'm not ready to abandon the strong equivalence principle yet.

 

Chris

[csmyth3025]

It does indeed collapse to a smaller size, but this takes essentially an infinite amount of time for that to happen from our perspective due to time dilation. While it is slowly collapsing, getting closer and closer to forming an event horizon, it is also very slowly (from our perspective again) evaporating by emitting pre-Hawking radiation which lowers its mass. The argument would be that it loses mass quicker than it is able to form an event horizon, so that you never really have a true black hole.

 

It would be almost indistinguishable from a true black hole from our perspective.

Iggy,

 

I have to retract my pevious speculation about objects in circular orbits being in an inertial freame of reference indentical to that of a distant observer. I ran across this passage in Wikipedia's article on gravitational time dilation:

Outside a non-rotating sphere A common equation used to determine gravitational time dilation is derived from the Schwarzschild metric, which describes spacetime in the vicinity of a non-rotating massive spherically-symmetric object. The equation is:

 

, where

• t₀ is the proper time between events A and B for a slow-ticking observer within the gravitational field,
• t_f is the coordinate time between events A and B for a fast-ticking observer at an arbitrarily large distance from the massive object (this assumes the fast-ticking observer is using Schwarzschild coordinates, a coordinate system where a clock at infinite distance from the massive sphere would tick at one second per second of coordinate time, while closer clocks would tick at less than that rate),
• G is the gravitational constant,
• M is the mass of the object creating the gravitational field,
• r is the radial coordinate of the observer (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate),
• c is the speed of light, and
• r₀ = 2GM / c² is the Schwarzschild radius of M. If a mass collapses so that its surface lies at less than this radial coordinate (or in other words covers an area of less than 4πG²M² / c⁴), then the object exists within a black hole.

Circular orbits

In the Schwarzschild metric, free-falling objects can be in circular orbits if the orbital radius is larger than . The formula for a clock at rest is given above; for a clock in a circular orbit, the formula is instead

 

(ref.

http://en.wikipedia....l_time_dilation )

 

The Schwarzschild radius of any object (even the Earth) can be calculated as shown in the quote above. For Earth, this turns out to be 8.872x10^-3 m (about 0.35 in)

(ref. http://www.wolframal...---.*--&x=5&y=7 )

 

A geostationary orbit has a radius of 42,164 km from the center of the Earth. (4.2164x10^7 m).

(ref. http://en.wikipedia....ionary_altitude )

 

Using these values, one second on the geostationary satellite's clock would be: t_o= t_f (1-(3/2)(8.872x10^-3 m)/(4.2164x10^7 m))^1/2 = ~0.9999999998 seconds on the distant observer's clock. Feel free to check my math, since it's very possible that my calculation isn't correct.

 

By the way, the excellent reference you provided ( http://www.mathpages.../s7-03/7-03.htm ) and the previous sectin of this book ( http://www.mathpages.../s7-02/7-02.htm ) seem to argue in favor of the formation of black holes in a finite time from the distant observer's perspective.

 

Chris