I'm a little bit confused about white holes. Many physics
web pages, including http://casa.colorado.edu/~ajsh/schww.html
and http://en.wikipedia.org/wiki/White_hole
and http://cosmology.berkeley.edu/Education/BHfaq.html#q10
all describe white holes as the time-reversal of black holes.
It's hard for me to know what that could possibly mean, since
the black hole metric is *symmetric* under time-reversal:

ds^2 = -(1-2m/r) dt^2 + 1/(1-2m/r) dr^2 + r^2 dOmega^2

Some comments from these web pages:

"Just as black holes swallow things irretrievably, so also do white
holes spit them out."

"Since a black hole is a region of space from which nothing
can escape, the time-reversed version of a black hole is a
region of space into which nothing can fall."

These statements seem wrong to me. For an eternal black hole,
there is no preferred direction in time, so I don't see how
it makes sense to talk about the time-reversal being a white
hole.

On the other hand, it seems to me that choosing the parameter
m to be *negative* is a perfectly valid solution to Einstein's
field equations (if unrealistic). That solution is equivalent
to reversing *r*, not t. Is there a name for this exotic
spacetime?

With m negative, there is no event horizon, and freefalling
particles are repelled *away* from the singularity at r=0.

--
Daryl McCullough
Ithaca, NY

Daryl McCullough wrote:

I'm a little bit confused about white holes. Many physics
web pages, including http://casa.colorado.edu/~ajsh/schww.html
and http://en.wikipedia.org/wiki/White_hole
and http://cosmology.berkeley.edu/Education/BHfaq.html#q10
all describe white holes as the time-reversal of black holes.
It's hard for me to know what that could possibly mean, since
the black hole metric is *symmetric* under time-reversal:

Suppose we wrote a Gaussian distribution with time as the independent
variable, and suppose we labled the r.h. tail "a black hole" and the
l.h. tail "a white hole". Then we could say "a white hole is a time
reversed black hole", referring to the tails, while the complete
function is time symmetric.

citations supporting this assertion below

My first thought on seeing this, given that I am a crankteroon (1/8
part), was to see the implication that GR is broken (no shame in that,
it happens to all the best theories): it is one thing to throw out an
entire analytic solution when several are available and we don't like
the looks of one; quite another to take a single analytic solution and
truncate it, because we don't care for where it's going.

wrote in
:

The Kruskal-Szerkes extension is the unique maximal analytic extension
of the Schwarzschild exterior geometry.

Tom Roberts wrote in
:

I.Vecchi wrote:

Tom Roberts ha scritto:

I am pointing out that in the Schwarzschild manifold
there is both a black hole and a white hole.

What we are discussing is "the uniqueness of the extension over the
horizon" and the relevant selection criteria .

Yes. Extension of the exterior region of the Schw. manifold.

The complete extension is known, and is called the "Kruskal extension",
and is covered by Kruskal-Szerkes coordinates.

there are at least two ways to extend the solution over the horizon,
correspoinding to two different physical situations, the black hole and
the white hole.

Knowledge of the complete (inextensible) manifold shows that your "two
ways" are merely different regions of a single manifold.

Andrew Hamilton wrote at http://casa.colorado.edu/~ajsh/schww.html:

The Schwarzschild metric admits negative square root as well as positive
square root solutions for the geometry.

The complete Schwarzschild geometry consists of a black hole, a white
hole, and two Universes connected at their horizons by a wormhole.

The negative square root solution inside the horizon represents a white
hole. A white hole is a black hole running backwards in time. Just as
black holes swallow things irretrievably, so also do white holes spit
them out. White holes cannot exist, since they violate the second law
of thermodynamics.

General Relativity is time symmetric. It does not know about the
second law of thermodynamics, and it does not know about which
way cause and effect go. But we do.

Daryl McCullough wrote:
I'm a little bit confused about white holes. Many physics
web pages, including http://casa.colorado.edu/~ajsh/schww.html
and http://en.wikipedia.org/wiki/White_hole
and http://cosmology.berkeley.edu/Education/BHfaq.html#q10
all describe white holes as the time-reversal of black holes.
It's hard for me to know what that could possibly mean, since
the black hole metric is *symmetric* under time-reversal:

ds^2 = -(1-2m/r) dt^2 + 1/(1-2m/r) dr^2 + r^2 dOmega^2

I'll try again as my previous post seems to have disappeared into a
black hole :-) I see this as:

gravitational physics = metric + time orientation.

IOW the metric is not the whole story, one must also make a continuous
choice of whether the timelike coordinate tangent is future- or
past-pointing. If such choice is possible, the manifold is
time-orientable.

In the Schwarzschild BH interior -d/dr is future pointing, in the WH
it's +d/dr.

Extending some geodesics back in time leads towards a horizon across
which they are extendible into an interior region provided the time
orientation is reversed there compared to the usual BH interior. This
changes the physics of the thing into a singularity that pushes things
out.

These statements seem wrong to me. For an eternal black hole,
there is no preferred direction in time,

There is an implicit time orientation in the sense that future occurs
in the direction of decreasing Schwarzschild r coordinate - this is
assumed (silently!) in order to make the infalling geodesics that have
just crossed the horizon continue the portion of the geodesic just
above the horizon.

--
Jan Bielawski

JanPB wrote:

I'll try again as my previous post seems to have disappeared into a
black hole :-) I see this as:

gravitational physics = metric + time orientation.

IOW the metric is not the whole story, one must also make a continuous
choice of whether the timelike coordinate tangent is future- or
past-pointing. If such choice is possible, the manifold is
time-orientable.

In the Schwarzschild BH interior -d/dr is future pointing, in the WH
it's +d/dr.

Extending some geodesics back in time leads towards a horizon across
which they are extendible into an interior region provided the time
orientation is reversed there compared to the usual BH interior. This
changes the physics of the thing into a singularity that pushes things
out.

Und der tyro sprache:

Extending _some_ geodesics ... I take it that means, some geodesics
associated with the same analytical solution which extends other
geodesics inward, not a different analytical solution.

The thing looks more and more like the simple analogue I suggested.
Say for some reason we had a Guassian with a "coordinate system
discontinuity" at 1-sigma, so that we seemed to have a solution in
three pieces. The central piece is symetrical in time as it stands,
and extending it to the right we join it with a "black tail", whereas
extending it to the left we join it to a time reversed version of the
right tail, or a "white tail", all of which tends to obscure that the
overall solution is simply symmetric under time reversal.

These statements seem wrong to me. For an eternal black hole,
there is no preferred direction in time,

I missed this part of Randy's post the first time.

I have expressed the vague presentment in the past that the BH solution
describes an ongoing and incomplete process, rather than an object. We
are prejudiced to thing of a BH like a ball of rock, potentially
eternal and unchanging, whereas the mathematical solution expresses
something changing all the time. Also, I'm not sure I'm so willing to
accept the assertion that infalling objects somehow cross the event
horizon in finite time, because we can construct a time coordinate
which says so.

We have a kind of two-sided Zeno's paradox:

On the obsverse, the runner (supposedly) never reaches the finish line,
because Zeno implicitly constructs a coordinate system with a
singularity at that event. This is analogous to the outside coordinate
system's view of the infalling test body. On the reverse, however,
suppose we watch a runner who _does_ slow down and stop at the finish
line, and Zeno now claims he _did_ cross it, because he shows us a
coordinate system which compresses all remaining time to an instant,
so the runner keeps going in his own time after our infinity is over!

We may counter, that may be true... whatever "after infinity" means...
but the runner evidently hasn't crossed the line _yet_. Now Zeno goes
all relativist on us, and claims the runner's "time" is just as good as
ours.

Zeno is going to catch a beating.

Emprical question: as the external observer watches the infalling clock
approach the horizon, never quite reaching it, is there a point of no
return for _retrieving_ the clock? Is there a point when, given
indefinite amounts of thrust and a willingness to venture indefinitely
close to the horizon, we will be unable to go in and fetch the clock
back out? If there is no such threshold, we have a good reason to say
that Zeno is a sophist.

Daryl McCullough wrote:
I'm a little bit confused about white holes. Many physics
web pages, including http://casa.colorado.edu/~ajsh/schww.html
and http://en.wikipedia.org/wiki/White_hole
and http://cosmology.berkeley.edu/Education/BHfaq.html#q10
all describe white holes as the time-reversal of black holes.
It's hard for me to know what that could possibly mean, since
the black hole metric is *symmetric* under time-reversal:

Any time-reversal is correctly pointed out by Mr. Savain as absurdity
to the utmost level.

ds^2 = -(1-2m/r) dt^2 + 1/(1-2m/r) dr^2 + r^2 dOmega^2

Some comments from these web pages:

"Just as black holes swallow things irretrievably, so also do white
holes spit them out."

"Since a black hole is a region of space from which nothing
can escape, the time-reversed version of a black hole is a
region of space into which nothing can fall."

[...]

On the other hand, it seems to me that choosing the parameter
m to be *negative* is a perfectly valid solution to Einstein's
field equations (if unrealistic). That solution is equivalent
to reversing *r*, not t. Is there a name for this exotic
spacetime?

With m negative, there is no event horizon, and freefalling
particles are repelled *away* from the singularity at r=0.

Your instinct is absolutely correct. Just write the spacetime you have
written down earlier as

ds^2 = c^2 T (1 + K / r) dt^2 - dr^2 / (1 + K / r) - r^2 dO^2

where T and K are both integration constants that can be anything.

SR limit requires (T = 1). So be it. Newtonian limit dictates (K = - 2
G M / c^2). That is fine. You can also argue for a white hole that (K
0). The possibility is endless under the concept of GR.

This is actually my 2nd attempt to answer your post. The previous post
got lost because of the censorship of sci.physics.research where if not
conformed to present religious teachings of SR and GR it would
disappear. So, please don't include the censored group
sci.physics.research in your posting.

Koobee Wublee wrote:

This is actually my 2nd attempt to answer your post. The previous post
got lost because of the censorship of sci.physics.research where if not
conformed to present religious teachings of SR and GR it would
disappear.

It's just an analog of a peer-reviewed journal. And it's not at all
true that conforming to relativity is the criterion. Competence is.
Also, there is no such thing as "religious teachings of SR and GR".
Where people get those fantastic ideas I'll never know.

--
Jan Bielawski

JanPB wrote:
Koobee Wublee wrote:

This is actually my 2nd attempt to answer your post. The previous post
got lost because of the censorship of sci.physics.research where if not
conformed to present religious teachings of SR and GR it would
disappear.

It's just an analog of a peer-reviewed journal. And it's not at all
true that conforming to relativity is the criterion. Competence is.
Also, there is no such thing as "religious teachings of SR and GR".
Where people get those fantastic ideas I'll never know.

Are you serious about the peer review stuff? sci.physics.research is
staffed by one or two screeners who reads all the posts before
publication. If deemed inapproppriate from the teachings of SR and GR,
you can bet your *ss that no publication is the verdict. It is only
peer-to-peer if published. In reality, it is more like dictatorship.
Who qualified the moderators anyway? It is utterly sad that this is
'science'. I can understand the frustrations of Galileo.

Koobee Wublee wrote:
JanPB wrote:
Koobee Wublee wrote:

This is actually my 2nd attempt to answer your post. The previous post
got lost because of the censorship of sci.physics.research where if not
conformed to present religious teachings of SR and GR it would
disappear.

It's just an analog of a peer-reviewed journal. And it's not at all
true that conforming to relativity is the criterion. Competence is.
Also, there is no such thing as "religious teachings of SR and GR".
Where people get those fantastic ideas I'll never know.

Are you serious about the peer review stuff? sci.physics.research is
staffed by one or two screeners who reads all the posts before
publication. If deemed inapproppriate from the teachings of SR and GR,
you can bet your *ss that no publication is the verdict.

No, if it's deemed *incompetent*. Nobody at sci.physics.research is
going to waste anybody's time - for example - on debates regarding
trivial coordinate changes and obviously _mathematically_ false claims.

It is only
peer-to-peer if published. In reality, it is more like dictatorship.
Who qualified the moderators anyway? It is utterly sad that this is
'science'. I can understand the frustrations of Galileo.

Who cares. It's just a Usenet group. I couldn't care less.

--
Jan Bielawski

Daryl McCullough wrote:
I'm a little bit confused about white holes. Many physics
web pages, including http://casa.colorado.edu/~ajsh/schww.html
and http://en.wikipedia.org/wiki/White_hole
and http://cosmology.berkeley.edu/Education/BHfaq.html#q10
all describe white holes as the time-reversal of black holes.
It's hard for me to know what that could possibly mean, since
the black hole metric is *symmetric* under time-reversal:

ds^2 = -(1-2m/r) dt^2 + 1/(1-2m/r) dr^2 + r^2 dOmega^2

IMHO it only refers to deciding whether d/dt is future- or
past-pointing (aka. "time orientation of a Lorentz manifold"). This
flips the positively-time-oriented basis which means the metric tensor
"flips" too (becuse its components don't). Confusingly, the components
in the Eddington-Finkelstein basis do change upon t--t. Extending
certain geodesics back in time into the interior works only if d/dt is
past-pointing, hence the singularity must be repelling.

I always had this problem with white holes in the sense that what
conceivable principle could determine WHAT comes out of them? A piano?
A sperm whale? Ketchup?

--
Jan Bielawski

Scripsit (Daryl McCullough)

all describe white holes as the time-reversal of black holes.
It's hard for me to know what that could possibly mean, since
the black hole metric is *symmetric* under time-reversal:

ds^2 = -(1-2m/r) dt^2 + 1/(1-2m/r) dr^2 + r^2 dOmega^2

Yes, but the metric does not tell you which way time goes. The most
the metric can tell you is something like event A and event B are
connected by a timelike geodesic with length 1 second, but you're not
told whether it is A that comes after B or vice versa.

I order to whether B is in A's future or its past you need to find a
continous path from A to a region of spacetime where you _have_
decided on an arrow of time, and then transport, say, the
future-pointing lightcone along that path to A. Then you'll know
which direction at A is the future.

But in the Schwarzschid metric (which is the one you quote; it is _one
of_ the possible metrics that describe a black hole, but not the only
one) you cannot always find such a continuous path due to the
coordinate singularity at r=2m; thus it is not clear which way time
goes inside r=2m even if you have decided on a flow of time at infinity.

Inside r=2m there are timelike geodesics that end at the r=0 curvature
singularity. Conventionally they are supposed to be oriented such that
the curvature singularity is in the *future* of all events on the
geodesic. That is a black hole. But the metric equally well describes
an interpretation in which the curvature singularity is in the *past*
of all worldlines inside r=2m. That is a white hole.

Other black-hole metrics, such as Kruskal coordinates, make clear how
the outer part of the Schwarzschild metric is actually connected to
two copies of the inner part; one being a black hole and one being a
white hole. Timelike geodesics outside r=2m may approach the event
horizon asymtotically (by coordinates) either in the far future or
in the far past of the Schwarzschild t coordinate. Those geodesics
that approach r=2m for large positive t join up with geodesics in the
_black_ hole after a finite amount of proper time. Conversely,
geodesics that approach r=2m for large negative t join with geodesics
in the _white_ hole; these are the worldlines of test particles that
the white hole spits out unpredictably.

Real-world black holes formed by gravitational collapse do not have a
white hole counterpart, because the Schwarzchild (and Kruskal)
solutions are _vacuum_ solutions, and if you go back in time to look
for the white hole you reach a time before the collapse where the
vacuum did not reach all the way to r=2m and therefore the vacuum
metric did not apply.

On the other hand, it seems to me that choosing the parameter
m to be *negative* is a perfectly valid solution to Einstein's
field equations (if unrealistic). That solution is equivalent
to reversing *r*, not t. Is there a name for this exotic
spacetime?

Not one I know (which doesn't say much), but it's an intriguing
concept. It's not what is usually meant by a white hole, though.

--
Henning Makholm "- Or hast thee (perverted) designs
to attempt (strange, hybrid) procreation
experiments with this (virginal female) self?"