OPEN QUESTION
(I refer here to my posting chain titles in this sci.physics.relativity Google Group:
"Analytic GR solutions of S2-star orbits and precession 732” per revolution", "Re: Analytic GR solutions of S2-star orbits and precession 732” per revolution")

PROBLEM OF PHYSICS FOUND WHICH HAS TO BE SOLVED PROPERLY:

Coordinate Time Axis Points to Past Direction in Interior of Schwarzschild Black Hole (0 < r < 2*MG/c^2).

Proper Time Axis Points to Future Direction in Interior of Schwarzschild Black Hole (0 < r < 2*MG/c^2).

Best Regards,
Hannu Poropudas
Kolamäentie 9E,
90900 Kiiminki / Oulu,
Finland

On 5/3/23 5:58 AM, Hannu Poropudas wrote:
> PROBLEM OF PHYSICS FOUND WHICH HAS TO BE SOLVED PROPERLY:

The solution is trivial.

> Coordinate Time Axis Points to Past Direction in Interior of
> Schwarzschild Black Hole (0 < r < 2*MG/c^2).

Only when you choose such coordinates. Instead, choose coordinates in
which the time axis is future pointing. Your imaginary "problem" is
solved. Of course in this region the singularity is in the future of
every point. Note also that your coordinate "r" is TIMELIKE, and a
suitable future-pointing time axis is -d/dr (d = partial derivative). Of
course many other coordinate systems are possible, and some don't even
have a time axis (e.g. Kruskal coordinates).

> Proper Time Axis Points to Future Direction in Interior of
> Schwarzschild Black Hole (0 < r < 2*MG/c^2).

For any object, anywhere and anywhen, its proper time axis is always
future pointing. That's part of what "proper time" means.

Tom Roberts

Hannu Poropudas wrote:

> revolution", "Re: Analytic GR solutions of S2-star orbits and precession
> 732” per revolution")
>
> PROBLEM OF PHYSICS FOUND WHICH HAS TO BE SOLVED PROPERLY:

lets remember a few bearded *_sandal_wearing_Arabs_* with no flying
experience, piloted a huge Boeing Jet complete with circus maneuvers at
high speed then crashed into the Pentagon. ( so they reported )

USA/UK/Germany/France should be thrown out of the UN for being terror org.

A day after the commemoration of *_the_Odessa_massacre_2014_*, the
*_Nazis_in_Washington_* are *_evil_creatures_*.

CIA Terrorism Central planned, directed and supplied the materiel for the
terrorist attack just as they have done with every single attack on
Russian soil since the start of the *_US-NATO_proxy_war_*. #CrystalBall

I think Putin will be responding soon, the WEF *_global_young_leader_*
_traitor_ should have retaliated a long time ago.

On 5/3/2023 11:53 AM, Tom Roberts wrote:

> For any object, anywhere and anywhen, its proper time axis is always
> future pointing. That's part of what "proper time" means.
>
I once heard an interesting description long ago that at the event
horizon, the time axis and the r axis switch behaviors. That is, outside
time is always into the future and never the past, nor can it be stopped
but you have freedom in 3 space dimensions. Inside the horizon, the "r"
axis is always heading to the singularity and never away from it, nor
can motion along the r axis be stopped. So "r" behaves more like time
than distance. I think the poster claimed that there was freedom of
movement in time. The alternative is that time is time but there are two
timelike dimensions.

Bogus?

keskiviikko 3. toukokuuta 2023 klo 18.56.17 UTC+3 Tom Roberts kirjoitti:
> On 5/3/23 5:58 AM, Hannu Poropudas wrote:
> > PROBLEM OF PHYSICS FOUND WHICH HAS TO BE SOLVED PROPERLY:
> The solution is trivial.

NO

> > Coordinate Time Axis Points to Past Direction in Interior of
> > Schwarzschild Black Hole (0 < r < 2*MG/c^2).
> Only when you choose such coordinates. Instead, choose coordinates in
> which the time axis is future pointing. Your imaginary "problem" is
> solved. Of course in this region the singularity is in the future of
> every point. Note also that your coordinate "r" is TIMELIKE, and a
> suitable future-pointing time axis is -d/dr (d = partial derivative). Of
> course many other coordinate systems are possible, and some don't even
> have a time axis (e.g. Kruskal coordinates).

NO, I think that this your mentioned mathematics (=only trick of mathematics?)
is of NO USE in this case of REAL General Relativity problem of Schwarzschild metrics.

I think that this solution could be perhaps my speculative "time-wave"
interpretation, which I mentioned in my recent posting chain "Megacycles"
in sci.geo.geology Google Group ?

What could this speculative "time-wave" be in case of black hole and its surroundings?
My speculation: It consists two parts: one part time is flowing to past
and second part time is flowing to future. And there are hundreds of thousands of
such couples around singularity of black hole (instead of singularity
I have "creation stone of the Universe") and its surroundings ?

Please take a look two analytic General Relativity solutions of
S2-star orbits ( SgrA* Black Hole) mine from above mentioned posting chain.
(Maple 9 program codes (two solutions are primitive functions in parametric form)
and they can be copy pasted into Maple and run in Maple programs and
see this REAL GR PROBLEM.)

> > Proper Time Axis Points to Future Direction in Interior of
> > Schwarzschild Black Hole (0 < r < 2*MG/c^2).
> For any object, anywhere and anywhen, its proper time axis is always
> future pointing. That's part of what "proper time" means.

YES

>
> Tom Roberts

Hannu Poropudas

On Wednesday, May 3, 2023 at 3:21:45 PM UTC-7, Volney wrote:
> On 5/3/2023 11:53 AM, Tom Roberts wrote:
>
> > For any object, anywhere and anywhen, its proper time axis is always
> > future pointing. That's part of what "proper time" means.
> >
> I once heard an interesting description long ago that at the event
> horizon, the time axis and the r axis switch behaviors. That is, outside
> time is always into the future and never the past, nor can it be stopped
> but you have freedom in 3 space dimensions. Inside the horizon, the "r"
> axis is always heading to the singularity and never away from it, nor
> can motion along the r axis be stopped. So "r" behaves more like time
> than distance. I think the poster claimed that there was freedom of
> movement in time. The alternative is that time is time but there are two
> timelike dimensions.
>
> Bogus?

This is only a coordinate property of the standard Schwarzschild coordinates,
so partially bogus. The "r" coordinate inside the horizon *is* timelike and
the "t" one *is* spacelike, so there is "freedom of movement" but it's
ordinary movement in space. This space is of infinite extent but it cannot be
explored arbitrarily because the singularity approaching in finite time.

The "r" and "t" are just letters that happen to coincide with
the opposite-causality coordinate letters labelling the outside due to an
accident of the method of derivation of this solution (same formula works
with the same letters so it looks like a causality "switch" has occurred).

--
Jan

On Thursday, 4 May 2023 at 08:56:34 UTC+2, JanPB wrote:
> On Wednesday, May 3, 2023 at 3:21:45 PM UTC-7, Volney wrote:
> > On 5/3/2023 11:53 AM, Tom Roberts wrote:
> >
> > > For any object, anywhere and anywhen, its proper time axis is always
> > > future pointing. That's part of what "proper time" means.
> > >
> > I once heard an interesting description long ago that at the event
> > horizon, the time axis and the r axis switch behaviors. That is, outside
> > time is always into the future and never the past, nor can it be stopped
> > but you have freedom in 3 space dimensions. Inside the horizon, the "r"
> > axis is always heading to the singularity and never away from it, nor
> > can motion along the r axis be stopped. So "r" behaves more like time
> > than distance. I think the poster claimed that there was freedom of
> > movement in time. The alternative is that time is time but there are two
> > timelike dimensions.
> >
> > Bogus?
> This is only a coordinate property of the standard Schwarzschild coordinates,

While, on the other hand, your time dilation idiocy is
only a coordinate property of the standard Einstein/Minkowski
coordinates.

Volney wrote:

> On 5/3/2023 11:53 AM, Tom Roberts wrote:
>> For any object, anywhere and anywhen, its proper time axis is always
>> future pointing. That's part of what "proper time" means.
> I once heard an interesting description long ago that at the event
> horizon, the time axis and the r axis switch behaviors. That is, outside
> time is always into the future and never the past, nor can it be stopped
> but you have freedom in 3 space dimensions. Inside the horizon, the "r"
> axis is always heading to the singularity and never away from it, nor
> can motion along the r axis be stopped. So "r" behaves more like time
> than distance. I think the poster claimed that there was freedom of
> movement in time. The alternative is that time is time but there are two
> timelike dimensions. Bogus?

they murdered Solilmani in a foreign country after they asked Iraq to
request his presence in a meeting. OMG, their lies just get worse. We
don't do that? Did his pants burst into flames? lol

On 5/4/2023 11:07 AM, Josue De felice wrote:
> Volney wrote:
>
>> On 5/3/2023 11:53 AM, Tom Roberts wrote:
>>> For any object, anywhere and anywhen, its proper time axis is always
>>> future pointing. That's part of what "proper time" means.
>> I once heard an interesting description long ago that at the event
>> horizon, the time axis and the r axis switch behaviors. That is, outside
>> time is always into the future and never the past, nor can it be stopped
>> but you have freedom in 3 space dimensions. Inside the horizon, the "r"
>> axis is always heading to the singularity and never away from it, nor
>> can motion along the r axis be stopped. So "r" behaves more like time
>> than distance. I think the poster claimed that there was freedom of
>> movement in time. The alternative is that time is time but there are two
>> timelike dimensions. Bogus?
>
> they murdered Solilmani in a foreign country after they asked Iraq to
> request his presence in a meeting. OMG, their lies just get worse. We
> don't do that? Did his pants burst into flames? lol

So what "direct involvement" is dangerous to whom and why, Crazy Ivan?

On 5/4/23 12:31 AM, Hannu Poropudas wrote:
> keskiviikko 3. toukokuuta 2023 klo 18.56.17 UTC+3 Tom Roberts
> kirjoitti:
>> On 5/3/23 5:58 AM, Hannu Poropudas wrote:
>>> PROBLEM OF PHYSICS FOUND WHICH HAS TO BE SOLVED PROPERLY:
>> The solution is trivial.
>
> NO

Yes. You simply do not understand this.

>>> Coordinate Time Axis Points to Past Direction in Interior of
>>> Schwarzschild Black Hole (0 < r < 2*MG/c^2).
>> Only when you choose such coordinates. Instead, choose coordinates
>> in which the time axis is future pointing. Your imaginary "problem"
>> is solved. Of course in this region the singularity is in the
>> future of every point. Note also that your coordinate "r" is
>> TIMELIKE, and a suitable future-pointing time axis is -d/dr (d =
>> partial derivative). Of course many other coordinate systems are
>> possible, and some don't even have a time axis (e.g. Kruskal
>> coordinates).
>
> NO, I think that this your mentioned mathematics (=only trick of
> mathematics?) is of NO USE in this case of REAL General Relativity
> problem of Schwarzschild metrics.

THINK about what you just said. The metric is a TENSOR, and is thus
completely independent of any coordinates. Moreover, one is free to
select any coordinate system one likes. This is not "only a trick of
mathematics", this is an essential aspect of GR, which is inherently
based on the differential geometry of semi-Riemannian manifolds.

The usual Schwarzschild coordinates on Schwarzschild spacetime apply in
two DISJOINT regions, with a singular region in which they don't apply
at all (here G=c=1):
2M<r: the region outside the horizon; r is spacelike, t is
timelike, and d/dt is future pointing
0<r<2M: the region inside the horizon; t is spacelike, r is
timelike, and -d/dr is future pointing
r=2M: these coordinates are singular, and therefore useless
These are facts about THIS COORDINATE SYSTEM, and are not properties of
the manifold itself.

It took physicists many decades to learn to distinguish
coordinate-specific properties from properties of the manifold itself.
You seem to never have learned that essential lesson about differential
geometry and GR.

> My speculation: [... complete nonsense displaying a serious lack of
> understanding of basic GR]

Tom Roberts

On Thursday, 4 May 2023 at 21:26:52 UTC+2, Tom Roberts wrote:
> On 5/4/23 12:31 AM, Hannu Poropudas wrote:
> > keskiviikko 3. toukokuuta 2023 klo 18.56.17 UTC+3 Tom Roberts
> > kirjoitti:
> >> On 5/3/23 5:58 AM, Hannu Poropudas wrote:
> >>> PROBLEM OF PHYSICS FOUND WHICH HAS TO BE SOLVED PROPERLY:
> >> The solution is trivial.
> >
> > NO
> Yes. You simply do not understand this.
> >>> Coordinate Time Axis Points to Past Direction in Interior of
> >>> Schwarzschild Black Hole (0 < r < 2*MG/c^2).
> >> Only when you choose such coordinates. Instead, choose coordinates
> >> in which the time axis is future pointing. Your imaginary "problem"
> >> is solved. Of course in this region the singularity is in the
> >> future of every point. Note also that your coordinate "r" is
> >> TIMELIKE, and a suitable future-pointing time axis is -d/dr (d =
> >> partial derivative). Of course many other coordinate systems are
> >> possible, and some don't even have a time axis (e.g. Kruskal
> >> coordinates).
> >
> > NO, I think that this your mentioned mathematics (=only trick of
> > mathematics?) is of NO USE in this case of REAL General Relativity
> > problem of Schwarzschild metrics.
> THINK about what you just said. The metric is a TENSOR, and is thus
> completely independent of any coordinates.

Samely as it is completely unmeasurable.

torstai 4. toukokuuta 2023 klo 22.26.52 UTC+3 Tom Roberts kirjoitti:
> On 5/4/23 12:31 AM, Hannu Poropudas wrote:
> > keskiviikko 3. toukokuuta 2023 klo 18.56.17 UTC+3 Tom Roberts
> > kirjoitti:
> >> On 5/3/23 5:58 AM, Hannu Poropudas wrote:
> >>> PROBLEM OF PHYSICS FOUND WHICH HAS TO BE SOLVED PROPERLY:
> >> The solution is trivial.
> >
> > NO
> Yes. You simply do not understand this.

NO, real space-time is not full 4-dimensional due time dimension
is different kind that space dimensions.

> >>> Coordinate Time Axis Points to Past Direction in Interior of
> >>> Schwarzschild Black Hole (0 < r < 2*MG/c^2).
> >> Only when you choose such coordinates. Instead, choose coordinates
> >> in which the time axis is future pointing. Your imaginary "problem"
> >> is solved. Of course in this region the singularity is in the
> >> future of every point. Note also that your coordinate "r" is
> >> TIMELIKE, and a suitable future-pointing time axis is -d/dr (d =
> >> partial derivative). Of course many other coordinate systems are
> >> possible, and some don't even have a time axis (e.g. Kruskal
> >> coordinates).
> >
> > NO, I think that this your mentioned mathematics (=only trick of
> > mathematics?) is of NO USE in this case of REAL General Relativity
> > problem of Schwarzschild metrics.
> THINK about what you just said. The metric is a TENSOR, and is thus
> completely independent of any coordinates. Moreover, one is free to
> select any coordinate system one likes. This is not "only a trick of
> mathematics", this is an essential aspect of GR, which is inherently
> based on the differential geometry of semi-Riemannian manifolds.
>
> The usual Schwarzschild coordinates on Schwarzschild spacetime apply in
> two DISJOINT regions, with a singular region in which they don't apply
> at all (here G=c=1):
> 2M<r: the region outside the horizon; r is spacelike, t is
> timelike, and d/dt is future pointing
> 0<r<2M: the region inside the horizon; t is spacelike, r is
> timelike, and -d/dr is future pointing
> r=2M: these coordinates are singular, and therefore useless
> These are facts about THIS COORDINATE SYSTEM, and are not properties of
> the manifold itself.
>
> It took physicists many decades to learn to distinguish
> coordinate-specific properties from properties of the manifold itself.
> You seem to never have learned that essential lesson about differential
> geometry and GR.

Full 4-dimensional manifold mathematics problem is this:

Real space-time is not full 4-dimensional due time dimension
is different kind that space dimensions.

>
> > My speculation: [... complete nonsense displaying a serious lack of
> > understanding of basic GR]

I think that new physics starts in many cases with somehow rough speculations
and
then we continue investigations with experimental observations about these
rough speculations that could they (or some modifications of them) correspond
somehow to REAL (old or new) physical properties of the Universe ?

First is situation such that we don't properly understand how to formulate
new rough speculations correctly or exactly and this is the case here
with the time dimension (we don't understand properly deep nature of time dimension)?

Situation with new knowledge has been so in history of physics many times ?

>
> Tom Roberts

Hannu Poropudas

On 5/5/23 1:14 AM, Hannu Poropudas wrote:
> torstai 4. toukokuuta 2023 klo 22.26.52 UTC+3 Tom Roberts kirjoitti:
>> You simply do not understand this.
>
> NO, real space-time is not full 4-dimensional due time dimension is
> different kind that space dimensions.

That is VERY naive. The Lorentzian manifolds of GR have dimension (3+1),
not 4. This is very basic, and the fact that you do not understand it
indicates that you do not really understand GR, despite your many
attempts to write about it around here (which I ignore due to their
clear and obvious ignorance and naivete).

> Real space-time is not full 4-dimensional due time dimension is
> different kind that space dimensions.

Hmmm. First, spacetime is a MODEL, and is not "real". Second, the
Lorentzian manifolds of GR are SEMI-RIEMANNIAN, not Riemannian.

> I think that new physics starts in many cases with somehow rough
> speculations [...]

Yes. But it does NOT start from a position of ignorance. EVERY physicist
who has created a viable new theory has demonstrated a masterful
understanding of the then-current physics, both theoretical and
experimental. So if you want to create some new theory, first STUDY GR
and learn its fundamentals, details, and experiments. There is no
shortcut.

Tom Roberts

On Saturday, 6 May 2023 at 17:59:26 UTC+2, Tom Roberts wrote:

> Yes. But it does NOT start from a position of ignorance. EVERY physicist
> who has created a viable new theory has demonstrated a masterful
> understanding of the then-current physics, both theoretical and
> experimental.

Your idiot guru, on the other hand, was unable
to understand even basic definitions, and thus
created The Shit.

On 5/3/23 5:21 PM, Volney wrote:
> I once heard an interesting description long ago that at the event
> horizon, the time axis and the r axis switch behaviors.

This is only for the traditional Schwarzschild coordinates on Schw.
spacetime. Note that those coordinates are valid in two disjoint regions
of the manifold, and are not valid on the horizon. Note also that one
can choose any coordinates one likes, and there are other coordinate
systems that are continuous at the horizon and do not "switch" like
that. This is an artifact of the coordinates, not any aspect of the
Schw. manifold itself.

Bottom line: 'r' and 't' are just LABELS, and the "switch" you mention
is merely due to the way the coordinates happened to be labeled.

> That is, outside time is always into the future and never the past,
> nor can it be stopped but you have freedom in 3 space dimensions.
> Inside the horizon, the "r" axis is always heading to the singularity
> and never away from it, nor can motion along the r axis be stopped.
> So "r" behaves more like time than distance. I think the poster
> claimed that there was freedom of movement in time. The alternative
> is that time is time but there are two timelike dimensions.

This is garbled, with puns on "time" (sometimes it means a timelike
axis, sometimes it means the t coordinate).

For the usual Schw. coordinates on Schw. spacetime:
Outside the horizon:
d/dt is a future pointing timelike coordinate axis
d/dr is spacelike, as are d/dtheta and d/dphi
Inside the horizon:
-d/dr is a future pointing timelike coordinate axis
d/dt is spacelike, as are d/dtheta and d/dphi
At the horizon:
these coordinates are invalid and cannot be used

Note there is no relationship between (r,t) inside and (r,t) outside,
except: a) they use the same symbols, and b) d/dt is a Killing vector.
Yes, inside the horizon it is unusual for the timelike coordinate 'r' to
multiply the usual spherically-symmetric angular functions of theta and
phi. Note also that outside the horizon Schw. spacetime is both
stationary and static, but inside it is not even stationary.

stationary = there is a timelike Killing vector
static = stationary and there is a 3-d space
orthogonal to the timelike Killing vector

Tom Roberts

On Sunday, 7 May 2023 at 18:04:58 UTC+2, Tom Roberts wrote:
> On 5/3/23 5:21 PM, Volney wrote:
> > I once heard an interesting description long ago that at the event
> > horizon, the time axis and the r axis switch behaviors.
> This is only for the traditional Schwarzschild coordinates on Schw.
> spacetime. Note that those coordinates are valid in two disjoint regions
> of the manifold, and are not valid on the horizon.

Sure - note that your idiot gurus are unable
to create a consistent set of coordinates
in their Shit.

lauantai 6. toukokuuta 2023 klo 18.59.26 UTC+3 Tom Roberts kirjoitti:
> On 5/5/23 1:14 AM, Hannu Poropudas wrote:
> > torstai 4. toukokuuta 2023 klo 22.26.52 UTC+3 Tom Roberts kirjoitti:
> >> You simply do not understand this.
> >
> > NO, real space-time is not full 4-dimensional due time dimension is
> > different kind that space dimensions.
> That is VERY naive. The Lorentzian manifolds of GR have dimension (3+1),
> not 4. This is very basic, and the fact that you do not understand it
> indicates that you do not really understand GR, despite your many
> attempts to write about it around here (which I ignore due to their
> clear and obvious ignorance and naivete).
> > Real space-time is not full 4-dimensional due time dimension is
> > different kind that space dimensions.
> Hmmm. First, spacetime is a MODEL, and is not "real". Second, the
> Lorentzian manifolds of GR are SEMI-RIEMANNIAN, not Riemannian.
> > I think that new physics starts in many cases with somehow rough
> > speculations [...]
>
> Yes. But it does NOT start from a position of ignorance. EVERY physicist
> who has created a viable new theory has demonstrated a masterful
> understanding of the then-current physics, both theoretical and
> experimental. So if you want to create some new theory, first STUDY GR
> and learn its fundamentals, details, and experiments. There is no
> shortcut.
>
> Tom Roberts

How to modify the corollary of the Birkhoff theorem if
we cut singularity at r = 0 away and put in place of it
"H-M's creation stone of the Universe" ?

I think that mathematically the Swarzschild solution is good if we
cut singularity at r = 0 away in case of inside the event horizon,
but how to take into account this "H-M's creation stone of the Universe"
in place of this singularity at r = 0 ?

Maybe it could be mathematically calculate as at r = 0 we have
infinite mass and only think that there is something uncountable
time coordinate related infinity which we do not understand properly at the moment???

Let us see the corollary of the Birkhoff theorem
(COPY and my added comments *...* below):

Birkhoff theorem

"A spherically symmetric gravitational field in empty space must be static,
with a metric given by the Schwarzschild solution.

The Birkhoff theorem may be applied, not only to the gravitational field
outside a body, but also to the field inside an empty spherical cavity at
the center of a spherically symmetric (but not necessarily static) body.

In this case the metric is again given by the Schwarzscild solution, but
since the point r = 0 is here in empty space (*in my speculation this singularity
is replaced by the "creation stone of the Universe"*), there can be no singularity,
so the integration constant MG must vanish. (*This is not true in my mentioned
speculation.*)

The Birkhoff theorem thus has the corollary that the metric inside an empty
spherical cavity at the center of a spherically symmetric system must be
equivalent to the flat-space Minkowski metric eta_uv.
(*This is not true in my mentioned speculation.*)

Its (*Corollary of the Birkhoff theorem*) importance arises from the fact
that the Birkhoff theorem is a local theorem, not depending on any conditions
on the metric for r -> infinity (aside from spherical symmetry), so that space
must be flat in a spherical cavity at the center of a spherically symmetric system,
(*This is not true in my mentioned speculation.*), even if the system is infinite
- even, in fact, if the system is the whole universe."

Reference:

Weinberg Steven, 1972.
Gravitation and Cosmology:
Principles and Applications of
the General Theory of Relativity.
John Wiley & Sons, Inc.
Printed in the United States of America.
657 pages, pp. 335-338, (Birkhoff theorem).

Best Regards,
Hannu Poropudas

On 5/8/23 1:40 AM, Hannu Poropudas wrote:
> How to modify the corollary of the Birkhoff theorem if we cut
> singularity at r = 0 away and put in place of it "H-M's creation
> stone of the Universe" ?

I have no idea what that is. But it doesn't really matter....

> Birkhoff theorem "A spherically symmetric gravitational field in
> empty space must be static, with a metric given by the Schwarzschild
> solution.

That is NOT Birkhoff's theorem. Don't make up straw-man versions of
standard theorems.

Note: the Wikipedia page is poorly written and misstates
the theorem in a similar way. So does Weinberg in
_Gravitation_and_Cosmology_.

Note, for instance, that Schwarzschild spacetime is a counterexample to
your misstated "theorem" above -- it is a spherically symmetric vacuum
manifold, but it is NOT static inside the horizon (it is not even
stationary there).

Note the REAL Birkhoff's theorem discusses the metric in a vacuum region
outside a spherically-symmetric body, which necessarily means there is
no horizon in the manifold, and only the exterior Schw. metric applies
(in the vacuum region) -- that is static.

Bottom line: General Relativity is complicated and subtle; details matter.

Tom Roberts

On 5/7/2023 12:04 PM, Tom Roberts wrote:
> On 5/3/23 5:21 PM, Volney wrote:
>> I once heard an interesting description long ago that at the event
>> horizon, the time axis and the r axis switch behaviors.
>
> This is only for the traditional Schwarzschild coordinates on Schw.
> spacetime. Note that those coordinates are valid in two disjoint regions
> of the manifold, and are not valid on the horizon. Note also that one
> can choose any coordinates one likes, and there are other coordinate
> systems that are continuous at the horizon and do not "switch" like
> that. This is an artifact of the coordinates, not any aspect of the
> Schw. manifold itself.
>
> Bottom line: 'r' and 't' are just LABELS, and the "switch" you mention
> is merely due to the way the coordinates happened to be labeled.

So r and t inside cannot be the same as r and t outside?

My thought experiment goes like this: A spaceship outside the hole
defines r as being directly at a (Schwarzschild) black hole, it has a
display for r, and has an ideal clock on board measuring and displaying
what is defined as t. The rocket goes directly towards the black hole,
directly towards the singularity. What happens with the displayed r and
t as the ship approaches the hole? What happens when they cross the
event horizon? Are r and t now something different? Can the spaceship
move around in t in the plus and minus directions before r reaches the
singularity and all is obliterated?

I understand an observer at infinity never sees the spaceship crossing
the horizon, I have no problem with that. I'm wondering what the
spaceship experiences.
>
>> That is, outside time is always into the future and never the past,
>> nor can it be stopped but you have freedom in 3 space dimensions.
>> Inside the horizon, the "r" axis is always heading to the singularity
>> and never away from it, nor can motion along the r axis be stopped.
>> So "r" behaves more like time than distance. I think the poster
>> claimed that there was freedom of movement in time. The alternative
>> is that time is time but there are two timelike dimensions.
>
> This is garbled, with puns on "time" (sometimes it means a timelike
> axis, sometimes it means the t coordinate).

Yes I learned much of this by reading web pages and usenet posts so my
terminology won't be standard, sorry.
>
> For the usual Schw. coordinates on Schw. spacetime:
> Outside the horizon:
>    d/dt is a future pointing timelike coordinate axis
>    d/dr is spacelike, as are d/dtheta and d/dphi
> Inside the horizon:
>    -d/dr is a future pointing timelike coordinate axis

Yes meaning you're heading to the singularity no matter what, no r away
from the singularity. Is it just timelike or is it really like the time
coordinate outside the hole? (sorry for not asking the question properly)

>    d/dt is spacelike, as are d/dtheta and d/dphi

Can the spaceship fly around in +/- t, at least for a while? What would
that even mean?

Can I do Lorentz trasformations to analyze (local) motion in/near the
spaceship?

> At the horizon:
>    these coordinates are invalid and cannot be used

What happens upon crossing? Does the clock explode? :-)
>
> Note there is no relationship between (r,t) inside and (r,t) outside,
> except: a) they use the same symbols, and b) d/dt is a Killing vector.
> Yes, inside the horizon it is unusual for the timelike coordinate 'r' to
> multiply the usual spherically-symmetric angular functions of theta and
> phi. Note also that outside the horizon Schw. spacetime is both
> stationary and static, but inside it is not even stationary.
>
>     stationary = there is a timelike Killing vector
>     static = stationary and there is a 3-d space
>              orthogonal to the timelike Killing vector

I will try to read up on that, I hope I can understand.

On 5/9/2023 1:32 PM, Tom Roberts wrote:
> On 5/8/23 1:40 AM, Hannu Poropudas wrote:
>> How to modify the corollary of the Birkhoff theorem if we cut
>> singularity at r = 0 away and put in place of it "H-M's creation stone
>> of the Universe" ?
>
> I have no idea what that is. But it doesn't really matter....

I sort of do. Long ago (20+ years) Hannu had a daughter who colored
drawings like any little kid does. Hannu would post details of these as
being colored quarks or something, conflating crayon colors with quark
"color".

The kid must be all grown up now. But the drawings still reveal the
secrets to the universe, apparently.

Volney wrote:

> On 5/7/2023 12:04 PM, Tom Roberts wrote:
>>     stationary = there is a timelike Killing vector static =
>>     stationary and there is a 3-d space
>>              orthogonal to the timelike Killing vector
>
> I will try to read up on that, I hope I can understand.

I love these people so very much. You suck dicks on this planet, america.
You became a shithole of stinking *_criminal_liars_* and *_terrorists_*.

*_Katusha_in_40_languages_*
https://bi%74%63%68%75te.com/video/FUgPTOmVF9CL

On Tuesday, 9 May 2023 at 22:38:12 UTC+2, Volney wrote:
> On 5/9/2023 1:32 PM, Tom Roberts wrote:
> > On 5/8/23 1:40 AM, Hannu Poropudas wrote:
> >> How to modify the corollary of the Birkhoff theorem if we cut
> >> singularity at r = 0 away and put in place of it "H-M's creation stone
> >> of the Universe" ?
> >
> > I have no idea what that is. But it doesn't really matter....
> I sort of do. Long ago (20+ years) Hannu had a daughter who colored

And do you still believe that 9 192 631 770 ISO idiocy
is some "Newton mode"? You're such an amazing idiot,
stupid Mike, even considering the standards of your
moronic religion.

tiistai 9. toukokuuta 2023 klo 23.38.12 UTC+3 Volney kirjoitti:
> On 5/9/2023 1:32 PM, Tom Roberts wrote:
> > On 5/8/23 1:40 AM, Hannu Poropudas wrote:
> >> How to modify the corollary of the Birkhoff theorem if we cut
> >> singularity at r = 0 away and put in place of it "H-M's creation stone
> >> of the Universe" ?
> >
> > I have no idea what that is. But it doesn't really matter....
> I sort of do. Long ago (20+ years) Hannu had a daughter who colored
> drawings like any little kid does. Hannu would post details of these as
> being colored quarks or something, conflating crayon colors with quark
> "color".
>
> The kid must be all grown up now. But the drawings still reveal the
> secrets to the universe, apparently.

H-M (Hanna-Maria) was that 5 years old little kid who draw
for example the nice drawing of colored black hole in the year 1992.

I have put these old H-M's drawings to be PUBLIC in my
Facebook page "Hannu Poropudas" and I have presently
called these old drawings as "axioms of astrophysics".

Please take a look those old color drawings of H-M.
(Unfortunately operator of Facebook has turned some
drawings upside down, but when you copy them you can
turn them back on right seeing.)

Hannu Poropudas

black holes do not exist. bh represent a measurement uncertainty of a telescope.

On 5/3/2023 10:31 PM, Hannu Poropudas wrote:
> keskiviikko 3. toukokuuta 2023 klo 18.56.17 UTC+3 Tom Roberts kirjoitti:
>> On 5/3/23 5:58 AM, Hannu Poropudas wrote:
[...]
> Please take a look two analytic General Relativity solutions of
> S2-star orbits ( SgrA* Black Hole) mine from above mentioned posting chain.
> (Maple 9 program codes (two solutions are primitive functions in parametric form)
> and they can be copy pasted into Maple and run in Maple programs and
> see this REAL GR PROBLEM.)

What about the great attractor?