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Zanket
science forum beginner

Joined: 08 Jul 2006
Posts: 21

Posted: Wed Jul 12, 2006 1:11 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

In both the post below and the other one (same day), you clearly assume that
an event horizon exists at r = 2M. It is invalid to assume such, while
evaluating something that purports to show they don't exist.

In general, it is invalid to assume that something is "so" when someone is
trying to show you that it's "not so", or vice versa. That is not scientific
thinking.

In short, you are just saying the equivalent of "GR is right. Therefore you're
wrong." You are not giving a logical basis for your position.

So, for the sake of this argument, I ask you to suspend your belief that an
event horizon exists at r = 2M. For example, don't say things like:

 Quote: For r<=2M that construction simply cannot be done because there are no such frames.

At least until you have reestablished that an event horizon exists there, by
logically refuting my claim that they do not exist (in a theory consistent
with section 1).

Given that you said:

 Quote: As I said before, such measurements _DO_ approach a limit of c as r->2M (for an object released from rest at r=infinity).

And you agreed that:

"In general relativity, above an event horizon of a black hole, an object
falling freely from rest at infinity passes each altitude at a directly
measured velocity equal to the escape velocity there."

Then to prove me wrong you must invalidate the next statement in the paper:

"If this velocity approached a limit of c then so would escape velocity, in
which case escape velocity would always be less than c and then there would
be no black holes."

Can you do that?

"Tom Roberts" <tjroberts137@sbcglobal.net> wrote in message
news:6PXsg.63700\$Lm5.8131@newssvr12.news.prodigy.com...
 Quote: Zanket wrote: Reader: At and below an event horizon, the directly measured velocity of an object is always less than c. So directly measured free-fall velocity *does* approach a limit of c. Author: That puts the cart before the horse. If the velocity approached a limit of c then so would escape velocity, and then there would be no event horizons. You are quite confused, and have completely hidden the frames relative to which your velocities are measured. Outside the horizon my earlier construction can be used to measure the infalling object's speed relative to a local inertial frame at rest relative to the black hole. As I said before, such measurements _DO_ approach a limit of c as r->2M (for an object released from rest at r=infinity). For r<=2M that construction simply cannot be done because there are no such frames. Because your statements here have hidden important details they are just plain wrong. As is your conclusion -- there _IS_ an event horizon.
Dirk Van de moortel
science forum Guru

Joined: 01 May 2005
Posts: 3019

Posted: Wed Jul 12, 2006 7:49 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

"Zanket" <zanket@gmail.com> wrote in message news:urJrg.339953\$Fs1.306945@bgtnsc05-news.ops.worldnet.att.net...
 Quote: A Flaw of General Relativity, a New Metric and Cosmological Implications http://zanket.home.att.net/

You say:
| "In general relativity, above an event horizon of a black hole,
| an object falling freely from rest at infinity passes each altitude at
| a directly measured velocity equal to the escape velocity there (3).
| If this velocity approached a limit of c then so would escape
| velocity, in which case escape velocity would always be less
| than c and then there would be no black holes."

So you notice that a black hole is defined as something that is
somewhere bounded by places where escape velocity is c.
Then you object that *outside* the boundary the escape
velocity is less than c, so the black hole cannot exist.

Dirk Vdm
Tom Roberts
science forum Guru

Joined: 24 Mar 2005
Posts: 1399

Posted: Thu Jul 13, 2006 4:51 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

Zanket wrote:
 Quote: In both the post below and the other one (same day), you clearly assume that an event horizon exists at r = 2M. It is invalid to assume such, while evaluating something that purports to show they don't exist.

You are discussing the Schwarzschild manifold, and it _IS_ valid to use
all that is already known about it, such as the existence of an event
horizon at r=2M. <shrug>

Basically you have assumed that a particle can always escape, right down
to r=0. You have no justification for that _ASSUMPTION_ at all, and it's
false for this manifold. <shrug>

IOW: for r<2M there is no such thing as "escape velocity" because it is
impossible for a timelike object to escape. The speed of the infalling
object has a limit of c relative to any locally inertial frame, but for
r<2M the construction I gave before does not work because it is
impossible for an inertial frame to be at rest relative to the black hole.

IOW: this discussion is not in a vacuum, it is in the context of GR and
the Schwarzschild manifold, and all the properties of that manifold.

 Quote: In general, it is invalid to assume that something is "so" when someone is trying to show you that it's "not so", or vice versa. That is not scientific thinking.

When you are discussing arithmetic, it _is_ valid to use 1+1=2. When you
are discussing Schwarzschild spacetime, it _IS_ valid to use all that is

 Quote: So, for the sake of this argument, I ask you to suspend your belief that an event horizon exists at r = 2M.

Do you "suspend your belief" that 1+1=2? Why ask me to "suspend belief"
for a concept equally well established?

 Quote: In short, you are just saying the equivalent of "GR is right. Therefore you're wrong." You are not giving a logical basis for your position.

No. _YOU_ need to give a basis for your assumption that an object can
escape from any point down to r=0. The usual way to do this would be to
find a timelike path from such a point to r=infinity -- why haven't you
done so? That's a rhetorical question, because such paths simply do not
exist. Indeed, in the region r<2M there is no future-pointing timelike
path for which r increases at all.

 Quote: As I said before, such measurements _DO_ approach a limit of c as r->2M (for an object released from rest at r=infinity). And you agreed that: "In general relativity, above an event horizon of a black hole, an object falling freely from rest at infinity passes each altitude at a directly measured velocity equal to the escape velocity there."

Yes. Given my other caveats.

 Quote: Then to prove me wrong you must invalidate the next statement in the paper: "If this velocity approached a limit of c then so would escape velocity, in which case escape velocity would always be less than c and then there would be no black holes."

The first part is correct: "this velocity" [#] does indeed approach a
limit of c [@], and so does escape velocity [#]. But this does NOT imply
"there would be no black holes".

[#] Relative to the succession of locally inertial frames
I discussed before. They only exist for r>2M.

[@] as r->2M of course. You seem to be a bit confused about
what this means. It means that as r gets closer to 2M (from
above), the velocity of the infalling test particle approaches
c; for a specified value of |c-velocity| that is arbitrarily
small, one can find a value of r that is >2M and |c-velocity|
is less than the specified value.

In the region r>2M, escape velocity is always < c, and I suppose there
is no black hole in that region <shrug>. But there is most definitely a
black hole in the manifold, and for r<=2M the concept "escape velocity"
simply does not apply -- see above for how this affects this discussion.

Tom Roberts
Zanket
science forum beginner

Joined: 08 Jul 2006
Posts: 21

Posted: Thu Jul 13, 2006 8:12 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

 Quote: Then you object that *outside* the boundary the escape velocity is less than c, so the black hole cannot exist.

No, I object that above the boundary the escape velocity approaches a limit
of c. Big difference. Look at the curve of Einstein's escape velocity
equation, eq. 4 in fig. 2. Does it approach a limit of c above the boundary
(at r / R = 1) as r tends to zero? No. It approaches c, but it does not
approach a limit of c. Eq. 6 in fig. 2 approaches a limit of c. An equation
does not apply beyond its limit.

"Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com> wrote
in message news:lnctg.533384\$O31.13075603@phobos.telenet-ops.be...
 Quote: "Zanket" wrote in message news:urJrg.339953\$Fs1.306945@bgtnsc05-news.ops.worldnet.att.net... A Flaw of General Relativity, a New Metric and Cosmological Implications http://zanket.home.att.net/ You say: | "In general relativity, above an event horizon of a black hole, | an object falling freely from rest at infinity passes each altitude at | a directly measured velocity equal to the escape velocity there (3). | If this velocity approached a limit of c then so would escape | velocity, in which case escape velocity would always be less | than c and then there would be no black holes." So you notice that a black hole is defined as something that is somewhere bounded by places where escape velocity is c. Then you object that *outside* the boundary the escape velocity is less than c, so the black hole cannot exist. Dirk Vdm
Dirk Van de moortel
science forum Guru

Joined: 01 May 2005
Posts: 3019

Posted: Thu Jul 13, 2006 10:17 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

"Zanket" <zanket@gmail.com> wrote in message news:qOxtg.126925\$mF2.71443@bgtnsc04-news.ops.worldnet.att.net...

[ Reformatted to undo top-posting.
We don't top-post here. Thanks. ]

 Quote: "Dirk Van de moortel" wrote in message news:lnctg.533384\$O31.13075603@phobos.telenet-ops.be... "Zanket" wrote in message news:urJrg.339953\$Fs1.306945@bgtnsc05-news.ops.worldnet.att.net... A Flaw of General Relativity, a New Metric and Cosmological Implications http://zanket.home.att.net/ You say: | "In general relativity, above an event horizon of a black hole, | an object falling freely from rest at infinity passes each altitude at | a directly measured velocity equal to the escape velocity there (3). | If this velocity approached a limit of c then so would escape | velocity, in which case escape velocity would always be less | than c and then there would be no black holes." So you notice that a black hole is defined as something that is somewhere bounded by places where escape velocity is c. Then you object that *outside* the boundary the escape velocity is less than c, so the black hole cannot exist. No, I object that above the boundary the escape velocity approaches a limit of c.

Apart from your problem with logic (stated before and to which
I will not come back again since you don't seem to understand
anyway), your problem with carefully listening to people who
are kind enough to try to help, and your obvious problem with
noticing that we do not top-post on this group, you also seem to
have a very severe problem with the simple concept of limits.

In context ( http://zanket.home.att.net/ ):
| "Section 1 shows that directly measured free-fall velocity approaches
| a limit of c in a uniform gravitational field. This limit applies
| everywhere since a gravitational field is everywhere uniform locally.
| Then the directly measured free-fall velocity of an object falling
| freely from rest at infinity approaches a limit of c. This was inferred
| by means general relativity allows. In general relativity, above an
| event horizon of a black hole, an object falling freely from rest at
| infinity passes each altitude at a directly measured velocity equal to
| the escape velocity there (3). If this velocity approached a limit of
| c then so would escape velocity, in which case escape velocity
| would always be less than c and then there would be no black holes."

Apart from formally dragging a sloppily worded statement (*),
true everywhere in a uniform (linear) gravitational field, over into a
spherically symmetric and highly non-uniform field, in which the
statement only happens to be true for a well defined limit-set of
locations, in your first (uniform field) situation the sloppy phrase
"approaching a limit of c"
only refers to
"objects at infinity"
and is not in any way referring to location, whereas in your second
(non-uniform) situation the same sloppy phrase
"approaching a limit of c"
primarily refers to
"at locations r greater than but arbitrarily close to 2M"
and
"objects at infinity".

So, you might want to correct the second part of the last sentence
to something like:
"... in which case locally measured escape velocity would always
be less than c above that event horizon (r > 2M)."

When you do that, you might immediately notice that you can cut
your article short and perhaps find another hobby.
But yes, you already showed that you don't understand this part,
and I promised not to come back to this, so you can safely ignore
it.

(*) One example of sloppiness is the phrase:
"... approaches a limit of c."
Either you say:
"it has a limit of c",
or you say:
"it is arbitrarily close to c",
or you say, like a sloppy engineer would:
"it approaches the value of c".

Dirk Vdm
PD
science forum Guru

Joined: 03 May 2005
Posts: 4363

Posted: Fri Jul 14, 2006 5:34 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

Sorcerer wrote:
 Quote: "Dirk Van de moortel" wrote in message news:jpqsg.528975\$bn7.12748973@phobos.telenet-ops.be... [anip] This is PHYSICS, not math or logic, and "proof" is completely irrelevant. -- Humpty Roberts, co-author of relativity FAQs. Never mind the math, check the physics. -- Dork Van de merde, local village idiot. Androcles.

Androcles:
There is no velocity for a round trip, arsehole. Velocity is a vector,
it has both direction and magnitude, not two directions.

PD:
Billy runs around a closed track and crosses the finish line
at the same point he started the race. What is his average *velocity*
during this race?

Androcles
Zero.

PD:
Yes, exactly. And yet you just told me there is "no velocity for a
round trip, a*****le". But you just found one, a*****le.

Now Billy runs around the same closed track at a speed of 8 m/s and
crosses the finish line at the same point he started the race. What is
his average *velocity* during this race, a*****le?

Androcles:
Still zero, you stupid cunt.
You haven't found me wrong yet, imbecile.

PD:
That's right, it is zero.
Now light runs back and forth on a closed circuit at a speed of
299,792,458 m/s and crosses the finish line at the same point it
started the race. What is the average *velocity* during this trip,
a*****le?

Androcles:
It can't, speed is the magnitude of velocity and the velocity is zero.

PD
Sorcerer1
science forum Guru

Joined: 09 Jun 2006
Posts: 410

 Posted: Fri Jul 14, 2006 6:02 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications "PD" wrote in message news:1152898494.481392.98510@35g2000cwc.googlegroups.com... | | Sorcerer wrote: | > "Dirk Van de moortel" wrote | > in message news:jpqsg.528975\$bn7.12748973@phobos.telenet-ops.be... | > | > [anip] Yep. I write [anip] to Dork's messages, if I even bother to read them at all. That's what he does. Androcles.
Zanket
science forum beginner

Joined: 08 Jul 2006
Posts: 21

Posted: Fri Jul 14, 2006 7:53 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

 Quote: You are discussing the Schwarzschild manifold, and it _IS_ valid to use all that is already known about it, such as the existence of an event horizon at r=2M.

It is also valid to see if there is any contradiction about that. If there
was, you would not see it as long as you insist that an event horizon
exists. GR says there is an event horizon there, and it also says that there
is not. Section 2 points out the latter.

 Quote: Basically you have assumed that a particle can always escape, right down to r=0. You have no justification for that _ASSUMPTION_ at all, and it's false for this manifold.

How could you have responded to my justification below, if I didn't give it?

 Quote: IOW: this discussion is not in a vacuum, it is in the context of GR and the Schwarzschild manifold, and all the properties of that manifold.

Yes, and if those properties contradict one another, then there is an
inconsistency.

 Quote: Do you "suspend your belief" that 1+1=2? Why ask me to "suspend belief" for a concept equally well established?

Because theories are open to scrutiny, and they can be inconsistent. "Well
established" does not mean "valid". Can you prove that GR does not
contradict itself regarding the existence of an event horizon?

 Quote: No. _YOU_ need to give a basis for your assumption that an object can escape from any point down to r=0. The usual way to do this would be to find a timelike path from such a point to r=infinity -- why haven't you done so? That's a rhetorical question, because such paths simply do not exist. Indeed, in the region r<2M there is no future-pointing timelike path for which r increases at all.

The usual way is not the only way. You responded to my way, below, so I must
have given a basis. Your basis for "such paths simply do not exist" is
nothing more sophisticated than "GR is right".

 Quote: Then to prove me wrong you must invalidate the next statement in the paper: "If this velocity approached a limit of c then so would escape velocity, in which case escape velocity would always be less than c and then there would be no black holes." The first part is correct: "this velocity" [#] does indeed approach a limit of c [@], and so does escape velocity [#]. But this does NOT imply "there would be no black holes". [#] Relative to the succession of locally inertial frames I discussed before. They only exist for r>2M.

 Quote: [@] as r->2M of course. You seem to be a bit confused about what this means. It means that as r gets closer to 2M (from above), the velocity of the infalling test particle approaches c; for a specified value of |c-velocity| that is arbitrarily small, one can find a value of r that is >2M and |c-velocity| is less than the specified value.

This in no way describes an approach to a limit. One can say the same thing
about any other r, for the escape velocity there. For example: Let r=20M.
According to GR, the particle's directly measured free-fall velocity there
is 0.316c. Let x=0.316c. Then:

It means that as r gets closer to 20M (from above), the velocity of the
infalling test particle approaches x; for a specified value of |x-velocity|
that is arbitrarily small, one can find a value of r that is >20M and
|x-velocity| is less than the specified value.

IOW, you haven't said anything unique to r=2M. You haven't shown an approach
to a limit there. You showed only an approach to a value on the curve, as
proven by my demonstration that the same can be done for any r>2M in GR.

Here is how it really works in GR: At any altitude, the particle's free-fall
velocity approaches a limit of infinity, which is shown by eq. 4 in fig. 2.
At r<=2M, by interpretation, all objects must fall such that no velocity >=
c can be directly measured.

Now I will correct your reasoning above:

 Quote: The first part is correct: "this velocity" [#] does indeed approach a limit of c [@], and so does escape velocity [#]. But this does NOT imply "there would be no black holes".

When escape velocity approaches a limit of c, its equation cannot return a
value >= c. Then there are no event horizons or black holes.

Are you really suggesting that an equation which yields only one curve can
return a value at or beyond its limit?
Tom Roberts
science forum Guru

Joined: 24 Mar 2005
Posts: 1399

Posted: Sat Jul 15, 2006 5:25 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

Zanket wrote:
 Quote: This in no way describes an approach to a limit.

Apparently you do not know what a limit is. It is very simple:

Consider lim(x->1) f(x) for various functions f(x):
f(x)=1 lim(x->1) f(x) = 1
f(x)=x lim(x->1) f(x) = 1
Consider the discontinuous function f(x)={0 if x=1, 1 otherwise}, then
lim(x->1) f(x) = 1, even though f(1)=0

Now for the case at hand, let v(r) be the velocity of an infalling test
particle released from rest at r=infinity, relative to one of my
previous post's locally-inertial frames. r is the Schw. r coordinate. We
have:
lim(r->2M) v(r) = c
Where the limit must be taken from above. Note that v(r) is UNDEFINED
for r<=2M, for the simple reason that those frames do not exist in that
region of the manifold.

 Quote: One can say the same thing about any other r, for the escape velocity there.

No. Only as r approaches 2M does the velocity relative to those frames
approach c. <shrug>

 Quote: For example: Let r=20M. According to GR, the particle's directly measured free-fall velocity there is 0.316c. Let x=0.316c. Then: It means that as r gets closer to 20M (from above), the velocity of the infalling test particle approaches x; for a specified value of |x-velocity| that is arbitrarily small, one can find a value of r that is >20M and |x-velocity| is less than the specified value.

Stipulating your value (which I have not checked), yes. So what?

 Quote: IOW, you haven't said anything unique to r=2M.

The _value_ of the limit is unique to r=2M (as a limit). But sure, one
can take this limit r->R for any value of R>2M. How could it be
otherwise? -- you can take the limit of a function while approaching any
point within its domain -- and there's the point: the limit must be
taken WITHIN THE DOMAIN OF THE FUNCTION. How could it be otherwise? <shrug>

 Quote: You haven't shown an approach to a limit there.

Sure I did. You seem to think there is something magical about the
phrase "approach to a limit" -- there isn't. The examples of limits
above show this (e.g. for f(x)=1, lim(x->K) f(x)=1 for any K).

 Quote: You showed only an approach to a value on the curve,

For a continuous curve THAT'S WHAT A LIMIT IS. The path of that
infalling particle, and the function v(r) used above, are both
continuous in the region r>2M. <shrug>

 Quote: Here is how it really works in GR: At any altitude, the particle's free-fall velocity approaches a limit of infinity,

This is simply not true, as long as the velocity is measured relative to
a locally inertial frame. But you keep forgetting to specify how you are
measuring velocity. Around here that is a very big red flag that the
person does not understand relativity.

This is GR, and relative to any locally inertial frame, no timelike
object can exceed the speed c. Period. Your "infinity" up there is just
plain wrong. You _REALLY_ need to learn the basics.

 Quote: When escape velocity approaches a limit of c, its equation cannot return a value >= c.

And it does not, FOR REGIONS OF THE MANIFOLD IN WHICH IT IS VALID. but
the function v(r) used above is valid only in the region r>2M.

 Quote: Then there are no event horizons or black holes.

You keep repeating this mistake as if pure repetition will somehow make
it true. The existence of horizons (aka black holes) is determined by
the geometry of the manifold, not by your handwaving. And especially not
by handwaving that is simply wrong.

 Quote: Are you really suggesting that an equation which yields only one curve can return a value at or beyond its limit?

No. I'm pointing out that you are making incorrect claims because the
functions that you look at have a limited region of validity, and you
are applying them outside that region.

Remember it is _essential_ to measure speed relative to a locally
inertial frame. And to get the value you want for "escape velocity" you
must use a locally inertial frame that is at rest relative to the black
hole. For r>2M that is fine, and I described how to do it in a previous
post, but for r<=2M such frames simply don't exist, and the v(r) used
above is undefined. <shrug>

This is getting overly repetitious. Don't expect me to continue unless
you come up with something new. Hint: that takes STUDYING.

Tom Roberts
Dirk Van de moortel
science forum Guru

Joined: 01 May 2005
Posts: 3019

Posted: Sat Jul 15, 2006 8:51 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

"Tom Roberts" <tjroberts137@sbcglobal.net> wrote in message news:P__tg.131341\$dW3.50198@newssvr21.news.prodigy.com...
 Quote: Zanket wrote: This in no way describes an approach to a limit. Apparently you do not know what a limit is. It is very simple:

So much was clear from my very first glance at his text :-)

Dirk Vdm
Zanket
science forum beginner

Joined: 08 Jul 2006
Posts: 21

Posted: Sun Jul 16, 2006 4:26 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

 Quote: Apparently you do not know what a limit is. It is very simple: ...

You are right. I am wrong. I looked at the definition of a limit and found
it to be in agreement with you. (See, I do listen.) I did not know that a
curve can have an infinite number of limits. I agree that section 2 was
flawed. Thank you for pointing that out.

 Quote: Here is how it really works in GR: At any altitude, the particle's free-fall velocity approaches a limit of infinity, But you keep forgetting to specify how you are measuring velocity. Around here that is a very big red flag that the person does not understand relativity.

We've been discussing directly measured velocity. I just didn't repeat that
there.

 Quote: This is GR, and relative to any locally inertial frame, no timelike object can exceed the speed c. Period. Your "infinity" up there is just plain wrong. You _REALLY_ need to learn the basics.

I didn't say it reaches >= c. I said it approaches a limit of infinity. The
event horizon functions as a governor to prevent it from reaching >= c. Only
the interpretation that all objects must fall at and below an event horizon
prevents it from reaching >= c.

 Quote: Remember it is _essential_ to measure speed relative to a locally inertial frame. And to get the value you want for "escape velocity" you must use a locally inertial frame that is at rest relative to the black hole. For r>2M that is fine, and I described how to do it in a previous post, but for r<=2M such frames simply don't exist, and the v(r) used above is undefined.

How can a locally inertial frame be at rest relative to a black hole, when
an inertial frame is by definition in free fall? A frame at rest relative to
a body, and not at its center, is noninertially accelerating. To get the
value I want for "escape velocity" I have the free-falling particle (which
free-falls from rest at infinity, and whose frame is presumably inertial; an
inertial frame is local by definition in my paper) directly measure the
velocity of a fixed-altitude object passing by.

If an event horizon can be shown to be inconsistent within GR, then its
existence would be in doubt. Section 2 shows such an inconsistency while
analyzing the region above an event horizon (but see below).

 Quote: This is getting overly repetitious. Don't expect me to continue unless you come up with something new. Hint: that takes STUDYING.

I changed the misusage of "limit" in the paper to "asymptote". The
conclusions remained the same.

I'd like to acknowledge you in the paper for finding my mistake regarding
limits. It seems likely that you wouldn't want to be attributed to a
"handwaving" argument, so please let me know if you do.
Tom Roberts
science forum Guru

Joined: 24 Mar 2005
Posts: 1399

Posted: Sun Jul 16, 2006 6:25 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

Zanket wrote:
 Quote: Tom Roberts wrote: This is GR, and relative to any locally inertial frame, no timelike object can exceed the speed c. Period. Your "infinity" up there is just plain wrong. You _REALLY_ need to learn the basics. I didn't say it reaches >= c. I said it approaches a limit of infinity.

You _still_ don't know what a limit is. Any quantity that "approaches a
limit of infinity" must achieve a value greater than any finite value,
such as c.

 Quote: How can a locally inertial frame be at rest relative to a black hole, when an inertial frame is by definition in free fall?

Go back and re-read where I described it. One can hold the frame at rest
relative to the black hole, and release it just as the infalling
particle reaches it; its clocks must be preset so they will be
synchronized in the locally inertial frame immediately after release,
and the measurement must be made immediately after release (or the
measurement is not done at rest relative to the black hole). The key
point is the synchronization of the clocks used to measure the infalling
particle's speed.

Just using Schw. coordinates to measure a coordinate speed is useless --
there are no limits on such a coordinate speed.

 Quote: If an event horizon can be shown to be inconsistent within GR, then its existence would be in doubt.

Yes. But you have not done so. <shrug>

I have since looked briefly at the article by Crothers that you quote.
He makes the same mistakes you do:
a) confusing coordinates on the manifold with the manifold itself
b) making assumptions and expecting the math to conform to them
c) fantasizing about a new geometrical concept: a point with
nonzero area

He provides nothing new in deriving the exterior Schwarzschild metric.
His insistence on his Ansatz (eq 1,2,3) is ill founded. Yes, the
external manifold obeys it, and yes the interior does not. What he did
not do is consider whether or not the external manifold he found can be
extended inside the horizon, he merely asserts it cannot. As is well
known, this exterior manifold can indeed be extended into the interior,
and then to a second exterior. <shrug>

In short: the Schwarzschild spacetime does not conform to his Ansatz
everywhere, just in the exterior region. His (and your) blind adherence
to the assumptions of that Ansatz is hopeless. The interior of the Schw.
spacetime is not static. Just as you cannot reasonably expect the
universe to obey your personal wishes and dreams, so too you cannot
expect mathematics to do so. <shrug>

So yes, if one requires a manifold that is static and spherically
symmetric, the exterior Schwarzschild manifold is the only solution.
This is well know (see Birkhoff's theorem). But that manifold can be
uniquely extended into the region r<2M, and out to another exterior. All
claims that this region "does not exist" or "is a point" are just plain
wrong. The interior is _DIFFERENT_, not "non existent". <shrug>

Tom Roberts
Dirk Van de moortel
science forum Guru

Joined: 01 May 2005
Posts: 3019

Posted: Sun Jul 16, 2006 6:48 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

"Zanket" <zanket@gmail.com> wrote in message news:KMtug.137595\$mF2.99686@bgtnsc04-news.ops.worldnet.att.net...
 Quote: Apparently you do not know what a limit is. It is very simple: ...

[snip]

 Quote: I changed the misusage of "limit" in the paper to "asymptote". The conclusions remained the same.

You also seem to have a very severe problem with the simple
concept of asymptotes.

Dirk Vdm
Zanket
science forum beginner

Joined: 08 Jul 2006
Posts: 21

Posted: Tue Jul 18, 2006 4:36 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

 Quote: You _still_ don't know what a limit is. Any quantity that "approaches a limit of infinity" must achieve a value greater than any finite value, such as c.

OK, I rephrase: It would reach c, were it not for the interpretation that
all objects at and below an event horizon must fall.

 Quote: Go back and re-read where I described it. One can hold the frame at rest relative to the black hole, and release it just as the infalling particle reaches it; its clocks must be preset so they will be synchronized in the locally inertial frame immediately after release, and the measurement must be made immediately after release (or the measurement is not done at rest relative to the black hole). The key point is the synchronization of the clocks used to measure the infalling particle's speed.

I think this measurement technique is unnecessary. For one, we on Earth
measure free-fall velocity without using that technique, and those
measurements are not meaningless. The most you could say is that they are
inaccurate. For another, Taylor and Wheeler do not mention that measuring
technique for the same scenario, in their book Exploring Black Holes. Also
the experimental confirmation of the clock postulate shows that this
technique is unnecessary. See
http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html: "[The
postulate] tells us that noninertial objects only age and contract by the
same gamma factor as that of their MCIF [momentarily comoving inertial
frame]. So, any measurements we make in a noninertial frame that use clocks
and rods, will be identical to measurements made in our MCIF."

Regardless, anyone who insists on using that technique can assume that it is
applied. My paper isn't wrong just because it doesn't mention it. It's good
enough to say the "velocity as directly measured at each altitude".

 Quote: Just using Schw. coordinates to measure a coordinate speed is useless -- there are no limits on such a coordinate speed.

The analysis in section 2 is wholly above an event horizon, where there is a
limit on such a coordinate speed.

 Quote: If an event horizon can be shown to be inconsistent within GR, then its existence would be in doubt. Yes. But you have not done so.

Not that you have shown. <shrug>

Thanks for pointing out that I misused "limit". But your issue went away
when I corrected it to "asymptote".

 Quote: I have since looked briefly at the article by Crothers that you quote. He makes the same mistakes you do:

I don't recall quoting Crothers.

 Quote: But that manifold can be uniquely extended into the region r<2M, and out to another exterior. All claims that this region "does not exist" or "is a point" are just plain wrong. The interior is _DIFFERENT_, not "non existent".

You contradict yourself. All such claims cannot be wrong if its existence
can be in doubt, as you agreed it can.
Zanket
science forum beginner

Joined: 08 Jul 2006
Posts: 21

Posted: Tue Jul 18, 2006 4:45 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

 Quote: You also seem to have a very severe problem with the simple concept of asymptotes.

How so?

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