Speed of light enough to escape black holes ?

[silvercrow]

I wad thinking since black holes are so dense ... lights speed would get slow significantly , so isn't it that if you are at light speed ( 3 x 10^8 m/s ) then you might come out of a black hole ?
Its the same concept we learn in 10 grade !
Am i right ?

 

[Chronos]

No, the escape velocity of a black hole is c - by definition.

 

[silvercrow]

But light doesn't escape because it slows down ? :p

 

[NWH]

I believe this is more of a General Relativity question?

 

[Chronos]

Yes, it cannot escape the event horizon.

 

[Drakkith]

But light doesn't escape because it slows down ? :p

That is an easy way to remember it, though technically it's that there are simply no paths through spacetime that lead out from beyond the event horizon. However if you don't have a basic understanding of General Relativity just remember that light is "pulled" back in.

 

[mfb]

That is an easy way to remember it, though technically it's that there are simply no paths through spacetime that lead out from beyond the event horizon.

In other words, once you are inside, all directions are "towards" the center. There is no "outwards" direction for your flashlight.

 

[RUTA]

But light doesn't escape because it slows down ? :p

The "escape velocity" analogy isn't a good one. When an object is ejected/launched radially at escape velocity its speed is reduced as measured by local observers along its path until at infinity it has slowed to zero speed. However, light always moves a c as measured by observers locally. And, light does not leave the Schwarzschild radius even though according to the escape velocity analogy it should get to infinity.

 

[cosmik debris]

I wad thinking since black holes are so dense ... lights speed would get slow significantly , so isn't it that if you are at light speed ( 3 x 10^8 m/s ) then you might come out of a black hole ?
Its the same concept we learn in 10 grade !
Am i right ?

Light, climbing out of a gravitational well, doesn't slow down, it loses energy. This increases the wavelength (reduces the frequency). At the horizon it's frequency is zero.

 

[pervect]

Light, climbing out of a gravitational well, doesn't slow down, it loses energy. This increases the wavelength (reduces the frequency). At the horizon it's frequency is zero.

Not really. Light emitted outward exactly at the time someone crosses the event horizon will simply "hang" at the event horizon, not loosing or gaining energy.

Someone else falling into the black hole on the same trajectory can see the light left there, an image of the previous traveller.

No physical observer can hover at the event horizon. Any physical observer passing through the event horizon , using their own local clocks and rulers ,will measure the speed of any trapped light there to be equal to "c", just as they would measure the speed of any other light to be "c" (with the same conditions, the measurement must be a local one).

The above requires exact timing. If you consider a bunch of photons emitted over a period of time from an infalling object, (more realistic), as time advances a smaller and smaller number of the photons will be close enough to the exact time to be close to the event horizon. Those that are emitted "too late" will fall into the central singularity. Those emitted "too early" will escape to infinity.

Reference: see for example http://casa.colorado.edu/~ajsh/singularity.html#r=1, Hamilton's website on black hole's. Hamilton is a physics professor with several published papers on black holes.

At this instant, as we pass through the horizon into the Schwarzschild bubble, we see all the other persons who passed through this location before us also pass through the horizon into the bubble.

 

[harrylin]

In other words, once you are inside, all directions are "towards" the center. There is no "outwards" direction for your flashlight.

That is a bit difficult for me to picture. What I do understand is how Einstein calculated light bending in a gravitational field with the Huygens construction; such gravitational lensing is a true physicists approach. However, considering that method, it is not clear to me why perfectly "outwards" should not be possible. What exactly prevents this possibility in terms of that approach?

 

[PAllen]

That is a bit difficult for me to picture. What I do understand is how Einstein calculated light bending in a gravitational field with the Huygens construction; such gravitational lensing is a true physicists approach. However, considering that method, it is not clear to me why perfectly "outwards" should not be possible. What exactly prevents this possibility in terms of that approach?

Actually (let's pretend supermassive black hole with minimal tidal forces after crossing horizon; as usual, ideal SC geometry), after you cross the horizon, up until you crunch, you can point your flashlight any direction, and locally see its light move away from you at c in any direction (assuming, further, you are inertial). So, locally (as required by definition of semi-riemannian manifold), everything still looks Minkowski sufficiently locally.

However, if you define radial position in terms of circumference of a circle about the singularity / 2 pi, what happens is: your radial coordinate is decreasing much faster than the outgoing light (which is also moving - slowly - in the decreasing r direction). Note, that if someone falls in shortly after you, you can continue sending them light signals until you reach the horizon. To you, they are outgoing light signals, meeting this later infaller who is futher from the singularity than you. In terms of r coordinate, everything is ingoing, but at different rates.

A key point is that a line of constant r (as defined above) is a spacelike curve inside the horizon. Thus, a light like path must decrease in r with increase in its affine parameter.

[Upshot: I would qualify mfb's statement: all timelike or light like directions inside the horizon point in a decreasing r coordinate direction; outgoing r directions exist, but they are spacelike.]

 

[harrylin]

Actually (let's pretend supermassive black hole with minimal tidal forces after crossing horizon; as usual, ideal SC geometry), after you cross the horizon, up until you crunch, you can point your flashlight any direction, and locally see its light move away from you at c in any direction (assuming, further, you are inertial). So, locally (as required by definition of semi-riemannian manifold), everything still looks Minkowski sufficiently locally.

OK... that I understand. Now, the Huygens method is non-local, as pictured from a distant frame far in space. So, I guess that my question boils down to asking how to transform that description into a description based on such a non-local frame.

However, if you define radial position in terms of circumference of a circle about the singularity / 2 pi, what happens is: your radial coordinate is decreasing much faster than the outgoing light (which is also moving - slowly - in the decreasing r direction). Note, that if someone falls in shortly after you, you can continue sending them light signals until you reach the horizon. To you, they are outgoing light signals, meeting this later infaller who is futher from the singularity than you. In terms of r coordinate, everything is ingoing, but at different rates.

A key point is that a line of constant r (as defined above) is a spacelike curve inside the horizon. Thus, a light like path must decrease in r with increase in its affine parameter.

[Upshot: I would qualify mfb's statement: all timelike or light like directions inside the horizon point in a decreasing r coordinate direction; outgoing r directions exist, but they are spacelike.]

Thanks, but that isn't a Huygens construction - not even a "non-local" description. If someone can translate the above into a non-local description, that would be very helpful for me and no doubt many others. I guess that I put my finger on the Schwartzschild singularity issue.

Aren't clocks supposed to stop at the Schwartzschild radius and should thus also the frequency of light emitted from that point be zero? How can frequency be anything less than zero?

When searching a little about this question I found this:

http://casa.colorado.edu/~ajsh/schwp.html

(I only read the first half)

as well as this:

http://blogs.discovermagazine.com/badastronomy/2007/06/19/news-do-black-holes-really-exist/

That makes sense to me.
There is also an interesting discussion included which I did not yet fully read; post 10 provides a slight correction in phrasing by the author.

 

[PAllen]

OK... that I understand. Now, the Huygens method is non-local, as pictured from a distant frame far in space. So, I guess that my question boils down to asking how to transform that description into a description based on such a non-local frame.

I don't know anything about this Huygen's method. It is not used in any texts I have or papers I've read on gravitational lensing (at least by that name). I've studied methods that simply follow null paths in SC coordinates.

Thanks, but that isn't a Huygens construction - not even a "non-local" description. If someone can translate the above into a non-local description, that would be very helpful for me and no doubt many others. I guess that I put my finger on the Schwartzschild singularity issue.

.
The r coordinate I've described is simply the Schwarzschild coordinate r coordinate - I've given its physical definition. In contrasting the local inertial frame observation that you can point a flashlight in any direction, of flash a bulb and get a spherical wave front, with the global statement that all timelike or null paths (inside the EH) progress toward the singularity, you must define some such global coordinate. I don't know of any simpler coordinate for this purpose than SC r coordinate.

Aren't clocks supposed to stop at the Schwartzschild radius and should thus also the frequency of light emitted from that point be zero? How can frequency be anything less than zero?

This false belief has been refuted numerous times on these forums. It's all about relativity. A distant or external hovering observer sees infalling clocks slow and their emitted light redshift, as they approach the horizon. The infalling observer sees no such thing. Their clock proceeds normally right up to the singularity, and they see external clocks also proceeding at a normal rate (slower or faster depending on the exact infall trajectory, but with a strictly finite Doppler factor).

One way of explaining this asymmetry is simply noting that ingoing light has no trouble decreasing r coordinate to the singularity; while outgoing light has increasing 'difficulty' escaping as the EH is approached, up until not escapting at all if emitted at the EH (or inside). Personally, I do see this [freezing of clocks as viewed external to EH] as purely an gravitational optical effect [on outgoing light], somewhat analogous to Lene Hau's freezing light in a BEC.

 

[Naty1]

I wa thinking since black holes are so dense ...lights speed would get slow significantly...

What do you mean by this? It appears you may be thinking of a black hole, inside the event horizon, as dense matter??...so 'light would slow' as, for example, in glass or fiber optic cable??

That is NOT what is believed to be inside a BH event horizon...all the mass that caused the original BH to form is crushed from existence and resides at the singularity.

There is a good discussion about spacetime geometry inside a black hole here:

http://www.jimhaldenwang.com/black_hole.htmIn summary here is what you get inside a black hole horizon...all the way to the singularity at the center of the BH:

[r = 2M is the Schwarzschild radius, the location of the BH horizon]

[In GR] It is the coordinate with the minus sign that determines the meaning of “timelike. ... inside the event horizon, r is the timelike coordinate, not t. In GRT, the paths of material particles are restricted to timelike world lines. ... According to GR, inside a black hole, time is defined by the r coordinate, not the t coordinate. It follows that the inevitability of moving forward in time becomes, inside the black hole, the inevitability of moving toward r = 0. This swapping of space and time occurs at r = 2M. Thus, r = 2M marks a boundary, the point where space and time change roles. For the observer inside this boundary, the inevitability of moving forward in time means that he must always move inward toward the center of the black hole at r = 0.

 

[harrylin]

I don't know anything about this Huygen's method. It is not used in any texts I have or papers I've read on gravitational lensing (at least by that name). I've studied methods that simply follow null paths in SC coordinates. [..]

It was the method that Einstein famously used to calculate the light bending by the Sun. On this forum I elaborated on that several times, with a link to the paper. Here once more: https://en.wikisource.org/wiki/The_...erihelion-motion_of_the_paths_of_the_Planets..

This false belief [of http://casa.colorado.edu/~ajsh/schwp.html] has been refuted numerous times on these forums.

That would mean that the only references that I found elsewhere are wrong according to refutations on this forum. In case you or someone else remembers any of such refutations that give a correct "distant" perspective instead, a link to it would be great!

It's all about relativity. A distant or external hovering observer sees infalling clocks slow and their emitted light redshift, as they approach the horizon. The infalling observer sees no such thing. [..]

Yes, that is obvious (well, to me it is) and not in question!

One way of explaining this asymmetry is simply noting that ingoing light has no trouble decreasing r coordinate to the singularity; while outgoing light has increasing 'difficulty' escaping as the EH is approached, up until not escapting at all if emitted at the EH (or inside). Personally, I do see this as purely an gravitational optical effect, somewhat analogous to Lene Hau's freezing light in a BEC.

According to the second link that I gave, it is an unrealistic assumption that there would be anything to emit light "at or inside" the EH; seeing the there provided arguments, that made perfect sense to me.

 

[PAllen]

In reference to the quote in #15, while this description is often given, it is not quite accurate IMO. The switching places of r and t in SC coordinates is primarily a coordinate effect that disappears in a number of well behaved coordinate systems for this geometry. The change of role for t is exclusively the result of defining it so that fixing r,theta,phi and varying t labels points on spheres of fixed surface area (each distinguished by a different t). Since a path inside the EH that does not progress toward the singularity is spacelike, t labels points on the spacelike path, so it becomes spacelike.

Instead, consider Lemaitre coordinates. Here, you have a radial coordinate that remains spacelike all the way to the singularity, and a time coordinate that remains timelike all the way to the singularity. This is achieved by allowing the radial coordinate to be non-static (effectively describing a collapsing space). Specifically, fixing radial and angular coordinates and varying Lemaitre time coordinate produces a path connecting spheres of decreasing surface area.

The key physical statement about interior SC geometry is just that all timelike and null paths reach the singularity.

 

[PAllen]

It was the method that Einstein famously used to calculate the light bending by the Sun. On this forum I elaborated on that several times, with a link to the paper. Here once more: https://en.wikisource.org/wiki/The_...erihelion-motion_of_the_paths_of_the_Planets..

Well then I've just not heard it called Huygen's, and don't see much difference between it and other methods.

That would mean that the only references that I found elsewhere are wrong according to refutations on this forum. In case you or someone else remembers any of such refutations using the "distant" perspective that I'm after, a link to it would be great!

The statement I was responding to was:

"Aren't clocks supposed to stop at the Schwartzschild radius and should thus also the frequency of light emitted from that point be zero? How can frequency be anything less than zero?"

The key point being that the understanding: "Only from the point of view of an external observer"
is missing. The reputable sources have this understanding.

Yes, that is obvious (well, to me it is) and not in question!

According to the second link that I gave, it is an unrealistic assumption that there would be anything to emit light "at or inside" the EH; seeing the there provided arguments, that made perfect sense to me.

You mean the arguments described in Discover magazine? The classical portion of these have been raised and refuted many times. External observers are seeng a frozen image - that is all. They can deduce that the object has reached the singularity. Specifically, they can compute when to send a signal such that the infaller will receive it an instant before reaching the singularity. The argument about Hawking radiation is more speculative because there is no complete theory of quantum gravity. Most other researcher's analyzing the same situation come to opposite conclusions (that horizon [or quantum analog thereof] forms in finite external time when quantum corrections are taken into account). However, this is an active, disputed area. For the purposes of this forum and thread, I am only discussing classical GR, classical EM.

 

[harrylin]

[..] The key point being that the understanding: "Only from the point of view of an external observer" is missing. The reputable sources have this understanding.

This is matter of context; the understanding that you say to be missing was specified in my post:

"the Huygens method is non-local, as pictured from a distant frame far in space. So, I guess that my question boils down to asking how to transform [your local] description into a description based on such a non-local frame. [..] If someone can translate the above into a non-local description, that would be very helpful for me and no doubt many others. I guess that I put my finger on the Schwartzschild singularity issue.
Aren't clocks supposed to stop at the Schwartzschild radius and should thus also the frequency of light emitted from that point be zero? How can frequency be anything less than zero?"

So, once more: In case you or someone else remembers any post that gives a reasonable answer from that same perspective, a link to it would be very helpful.

You mean the arguments described in Discover magazine? The classical portion of these have been raised and refuted many times. External observers are seeng a frozen image - that is all.

That is quite what I understood from it (without contemplating what distant observers actually "see"; surely distant observers will not see anything after a while).

They can deduce that the object has reached the singularity. Specifically, they can compute when to send a signal such that the infaller will receive it an instant before reaching the singularity. The argument about Hawking radiation is more speculative because there is no complete theory of quantum gravity. Most other researcher's analyzing the same situation come to opposite conclusions (that horizon [or quantum analog thereof] forms in finite external time when quantum corrections are taken into account). However, this is an active, disputed area. For the purposes of this forum and thread, I am only discussing classical GR, classical EM.

That's fine to me; this is also not the forum for quantum gravity!

 

[PAllen]

Ok, then how much of what you're looking for is addressed or not addressed by the following observation I made:

"They can deduce that the object has reached the singularity. Specifically, they can compute when to send a signal such that the infaller will receive it an instant before reaching the singularity. "

Even though they won't get a reply, the distant observer knows when to send a signal that will be received by a given infaller:

- at moment of crossing horizon
- at an any point between horizon and singularity

None of these signals involve waiting for infinite time to pass [before sending them]. Further, the infaller can flash a radio burst on receiving each of these signals. It just so happens that the bursts (that propagate away from the infaller in all directions, in their frame) never escape the horizon. The whole assemblage (infaller, out going signal sphere) is moving towards the singularity [in terms of SC r coordinate, and in terms of termination world lines and null paths on the singularity].

 

[robinpike]

Light, climbing out of a gravitational well, doesn't slow down, it loses energy. This increases the wavelength (reduces the frequency). At the horizon it's frequency is zero.

So where does the energy of the light go? Is it still in the black hole?

 

[mfb]

It is part of the gravitational field. The black hole won't lose much energy by emitting a high-energetic photon close to the Schwarzschild radius.

 

[harrylin]

Ok, then how much of what you're looking for is addressed or not addressed by the following observation I made:

"They can deduce that the object has reached the singularity. Specifically, they can compute when to send a signal such that the infaller will receive it an instant before reaching the singularity. "

Even though they won't get a reply, the distant observer knows when to send a signal that will be received by a given infaller:

- at moment of crossing horizon
- at an any point between horizon and singularity

None of these signals involve waiting for infinite time to pass [before sending them]. Further, the infaller can flash a radio burst on receiving each of these signals. It just so happens that the bursts (that propagate away from the infaller in all directions, in their frame) never escape the horizon. The whole assemblage (infaller, out going signal sphere) is moving towards the singularity [in terms of SC r coordinate, and in terms of termination world lines and null paths on the singularity].

I think that it doesn't really address the OP's question (corrected as in post #3) from a distant perspective.

In particular, that doesn't explain from that perspective what the frequency of light can be, if anything, that is emitted from "inside" (and why), nor why apparently many people think that in the lifetime of our universe anything can get beyond that horizon.

 

[PAllen]

I think that it doesn't really address the OP's question (corrected as in post #3) from a distant perspective.

In particular, that doesn't explain from that perspective what the frequency of light can be, if anything, that is emitted from "inside" (and why), nor why people think that in the lifetime of our universe anything can get beyond that horizon.

I don't understand why it doesn't address both questions.

1) Locally, light emitted inside the horizon can be any frequency, and everything is perfectly normal, locally. What frequency it would be if it could escape is meaningless because it can't. What frequency it would be observed at by any world line (inside) that interacts with it is well defined and a function of the source and emitter world lines and intervening curvature, just like anywhere else in the universe (Doppler).

2) Why people think matter crosses the horizon has been addressed by my example of: I send a signal at 3PM today and know (per GR) that it will be received by a specific infaller as it crosses a 2-sphere exactly 1/4 the surface area of the apparent horizon. These issue have also been addressed in numerous long threads. You can reject this conclusion of classical GR only by rejecting classical GR (which you are free to do). Also note that, in GR (and SR, for that matter) simultaneity is a matter of convention. Using a different simultaneity convention than that used to construct SC coordinates (that matches this convention far from the BH) - for example, using Lemaitre t=<constant> simultaneity - one can talk about specific places inside the horizon that an infaller is 'now'. It is perfectly normal that the image you see of the infaller is older than 'now' (in this case, from some moment before it crossed the horizon).

I honestly think that if Lemaitre coordinates had been discovered before SC coordinates, 99% of BH misunderstanding would never have occurred. It is almost always due to attributing physical significance to coordinate artifacts.

 

[harrylin]

I don't understand why it doesn't address both questions.

1) Locally, light emitted inside the horizon can be any frequency, and everything is perfectly normal, locally. [..] What frequency it would be observed at by any world line (inside) that interacts with it is well defined and a function of the source and emitter world lines and intervening curvature, just like anywhere else in the universe (Doppler).

According to me, a worldline cannot observe. Anyway, I still wonder why the emission frequency would be positive and real (from a distant perspective of course) instead of imaginary as with the approximate solution:
- http://en.wikipedia.org/wiki/Schwarzschild_radius#Other_uses_for_the_Schwarzschild_radius

2) Why people think matter crosses the horizon has been addressed by my example of: I send a signal at 3PM today and know (per GR) that it will be received by a specific infaller as it crosses a 2-sphere exactly 1/4 the surface area of the apparent horizon. These issue have also been addressed in numerous long threads.

I have followed some of those threads without participating: the parts that I saw exactly avoided addressing such issues as this one. And it looks as if you formulated it better (more precisely) last time:

"They can deduce that the object has reached the singularity. Specifically, they can compute when to send a signal such that the infaller will receive it an instant before reaching the singularity. [..] "

If you transform that description of yours to our distant ECI frame, I suspect that you will find that to our reckoning, those signals of us will reach that person shortly before t=∞ so that "an instant before reaching the singularity" transforms to "perhaps after the end of this universe". But if that is wrong, please clarify why.

I honestly think that if Lemaitre coordinates had been discovered before SC coordinates, 99% of BH misunderstanding would never have occurred. It is almost always due to attributing physical significance to coordinate artifacts.

That may be well the case. I think that there will be even much less misunderstanding if you or someone else would be so kind to express those events in "earth coordinates", which would clarify if in theory this topic relates to something that can ever happen. But as this is the fourth consecutive post in which I ask this, I'll leave it at this if it still doesn't get addressed.

Thanks,
Harald

 

[PAllen]

According to me, a worldline cannot observe. Anyway, I still wonder why the emission frequency would be positive and real (from a distant perspective of course) instead of imaginary as with the approximate solution:
- http://en.wikipedia.org/wiki/Schwarzschild_radius#Other_uses_for_the_Schwarzschild_radius

To me, a detector (which follows a world line) is the only thing that can observe. Coordinate labels and simultaneity are abstractions, not observables. So any detector that can observe light emitted inside the EH observes red or blueshift following normal GR rules. The general GR rule is to parallel transport the emitter 4-velociy to the receiver world line along the light path followed. Then express the transported emitter 4 velocity and local light path tangent vector in the local frame basis of the reception event, and use SR doppler formula. This formulation covers every combination of kinematic and curvature and cosmological contribution to redshift in one general method.

The concept of a gravitational redshift 'field' as in that wikipedia formula is a special case that applies only to static space time. It is doubly nonsensical to apply it across the event horizon:
1) There are no emitter and receiver possible from the inside to outside the EH. Therefore it is applied outside its domain of validity.

2) You can't even write an alternative equivalent formula for inside the horizon because the region inside the horizon is not static, so there is no such thing, even approximately, of a gravitational potential. The concept of gravitational redhsift factored out separately from general redshift as I described above is possible only for static spacetime.

One final key point: for emitter outside EH and receiver inside EH, you can compute the red/blue shift using the standard method I describe and get a perfectly normal result - because there is a light path from emitter to receiver in this case. The result cannot be summarized into a redhift as a function of position for the very reason above: the light path goes from a static region of spacetime to a non-static region.

I'm sorry if all of these realities of GR are ignored in wikipedia level treatments, but I can assure you they were well understood by 1960.

I have followed some of those threads without participating: the parts that I saw exactly avoided addressing such issues as this one. And it looks as if you formulated it better (more precisely) last time:

"They can deduce that the object has reached the singularity. Specifically, they can compute when to send a signal such that the infaller will receive it an instant before reaching the singularity. [..] "

If you transform that description of yours to our distant ECI frame, I suspect that you will find that to our reckoning, those signals of us will reach that person shortly before t=∞ so that "an instant before reaching the singularity" transforms to "perhaps after the end of this universe". But if that is wrong, please clarify why.

There is no such thing as a global frame in GR. There are local frames and global coordinate systems. So your statement asks for something GR states does not exist.

The best you can do in GR is define a family non-intersecting spacelike 3-surfaces of simultaneity that you parametrize with a timelike parameter. SC coordinates do this in a way that covers only the exterior region of a BH. Lemaitre and Kruskal coordinates do this in a way that covers the whole spacetime. Each provides a specific (and different) answer to what events inside the horizon are simultaneous with a given event outside.

Each of these coordinate systems (Lemaitre and Kruskal) provide a finite well defined answer to 'when', for an outside observer, a signal reaches a given inside detector.

Short answer: your question reflects fundamental misunderstanding of GR; corrected in the only way I know, your conclusion is wrong.

That may be well the case. I think that there will be even much less misunderstanding if you or someone else would be so kind to express those events in "earth coordinates", which would clarify if in theory this topic relates to something that can ever happen. But as this is the fourth consecutive post in which I ask this, I'll leave it at this if it still doesn't get addressed.

Thanks,
Harald

As above, GR says this question is wrongly formulated - there is no preferred definition of global Earth coordinates. There are at least two common global coordinates that answer this question - each differently. SC coordinates don't answer it for the trivial reason they don't cover enough of spacetime. (Note: SC coordinates provide two separate coordinate patches, one for interior region, one for exterior. If you want a simultaneity convention between spacetime regions, you need a single coordinate patch that includes both regions. Thus SC coordinates are simply inadmissable for answering your question).

[EDIT: Perhaps this coordinate free description will help ... or not; we'll see. You can't treat causally connected events as simultaneous. The relations of backward and forward going light cones defines the causal structure of spacetime. In the SC geometry, every event outside the EH is in the causal past of a set of events inside the EH. The causal future of any internal event includes only internal events. For a given event, anywhere, you can choose to consider any event between its past and future light cones as simultaneous with it. For an outside event, this means there are a set of interior events in its future light cone that cannot be considered simultaneous. Any interior event 'before' this future light cone can be considered simultaneous with the chosen external event. Thus not only is it possible to choose interior events simultaneous with external event, there are infinite possible choices. Similarly, given an internal event, there is a set of external events in its past light cone; any external event outside of this past light cone is a possible choice for a simultaneous external event]

 

[PAllen]

But as this is the fourth consecutive post in which I ask this, I'll leave it at this if it still doesn't get addressed.

Thanks,
Harald

Just FYI: I feel I and others have have answered all of these questions multiple times in multiple ways, in multiple threads. It seems to me you simply reject the answers but are not willing to say, straight out, that you reject GR.

 

[pervect]

OK... that I understand. Now, the Huygens method is non-local, as pictured from a distant frame far in space. So, I guess that my question boils down to asking how to transform that description into a description based on such a non-local frame.

I don't have any idea what you're asking for here either.

Space time is curved, like the surface of the Earth. You can make maps of it, like you can make maps of the Earth's surface. But they won't / can't be to scale except for small regions (frames). The metric describes how the particular part of the map is distorted. To oversimplify greatly, the closer the metric is to unity, the less the distortion.

http://casa.colorado.edu/~ajsh/schwp.html

(I only read the first half)

Considering that Hamilton spends a good part of his time describing a journey into a black hole, (complete with visuals), do you really think it's an accurate reading of him to say that he supports your "time stops at the event horizon, so we don't have to worry about what comes after" idea?

(That was semi-rhetorica., I can say that I certainly don't, and I would be surprised if you did if you thought about it a bit more. Though I've been surprised in this manner before, alas.)

 

[harrylin]

[..] There is a good discussion about spacetime geometry inside a black hole here:
http://www.jimhaldenwang.com/black_hole.htm

In summary here is what you get inside a black hole horizon...all the way to the singularity at the center of the BH [..]

Interesting summary! I had not seen that post which you wrote simultaneously to me.

In particular, by chance (because you did not directly respond to me) it gives an answer from the "distant" perspective that I asked for:

"In the subsequent analysis, we will often consider the perspective of an observer who is at rest at "infinity," that is, very far away from the black hole."

Thanks!

 

[PAllen]

Interesting summary! I had not seen that post which you wrote simultaneously to me.

In particular, by chance (because you did not directly respond to me) it gives an answer from the "distant" perspective that I asked for:

"In the subsequent analysis, we will often consider the perspective of an observer who is at rest at "infinity," that is, very far away from the black hole."

Thanks!

This article looks pretty good, but there is at least one historical blunder. Lemaitre fully resolved the SC coordinate singularity in 1932 with his Lemaitre coordinates. Bergmann's 1942 textbook (I have a copy) already refers to resolution of this 'problem' using a slightly later approach by Robertson (of Robertson-Walker fame). So, at the University textbook level, the problem was considered solved by 1942.

What occurred in 1950 was the first hint that the SC geometry can by geodesically completed into a two world sheet geometry connected by a wormhole bridge; and that the eternal black hole is completed into a prior eternal white hole. None of these geoemetric features apply to a BH that arises from collapse matter - they only apply to the mathematical eternal BH. This effort, begun by J.L. Synge in 1950, reached fruition in the work of Martin Kruskal and George Szekeres, in 1960.