Scripsit JanPB
Daryl McCullough wrote:

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").

Well, inside r=2m d/dt is neither future nor past-pointing; it is
spacelike! Be sure not to confuse "time" with "the coordinate
direction that for whatever reason is notated t".

A true "time reversal" never changes the metric; it is just a matter
of chosing the opposite square root for timelike intervals.

Confusingly, the components in the Eddington-Finkelstein basis do
change upon t--t.

Even in the Eddington-Finkelstein metric, d/dt becomes spacelike
inside r=2m.

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?

That's always the problem with singularities-in-the-past, isn't it?

Fortunately white holes cannot exist in reality, because they are only
there if they have been around forever, and reality is not that old. :-)

--
Henning Makholm "Det er trolddom og terror
og jeg får en værre
ballade når jeg kommer hjem!"

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. 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.

Your understanding of science is utterly sad.

Henning Makholm wrote:
Scripsit JanPB
Daryl McCullough wrote:

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").

Well, inside r=2m d/dt is neither future nor past-pointing; it is
spacelike! Be sure not to confuse "time" with "the coordinate
direction that for whatever reason is notated t".

Yes, my fault, thanks! I posted a more sensible version on
sci.physics.relativity and forgot about this one.

--
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

Yes, neither the Einstein field equation nor this particular solution of
it dictate in which direction the future lies. So you must make a
choice, and the usual one is that +d/dt in the exterior region is future
pointing. This is merely a convention, and calling -d/dt the future
would be equally valid (but will confuse your readers).

So pick +d/dt in the exterior region to be the future. In a Kruskal
diagram that makes the interior region at the bottom be a white hole,
and the interior at the top be a black hole. All that "white holes are
the time-reversal of black holes" means is that if you took -d/dt as the
direction of the future then the black and white holes would exchange
places in the Kruskal diagram.


To those who claim "time reversal is meaningless", let me point out that
in the real world this is true, but in a mathematical model of the world
time reversal can make sense, and in this particular MODEL it does. Time
reversal has become one of the important symmetries of MODELS in modern
physics. Nobody really knows why it is important, but it is a part of
all modern theories of physics.


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.

You must select a direction to be the future. Until you do that you
don't know which region is the black or white hole; as soon as you
choose then their locations are determined.

This is normal -- you must select all the criteria necessary to make the
model conform as best as possible to the real world. In this case (and
in most cases of manifolds in GR) that includes selecting a direction in
the manifold to correspond to the future. Of course Schw. spacetime is
not a good model of the universe at all, but that's irrelevant to the
issue of selecting a future direction in the model.

[Schw. spacetime IS a good model for the geometry near a
spherically symmetric static object, such as an isolated
planet or star.]

This is no different from a roadmap -- you must select a direction on
the paper to correspond to North in the real world. Of course the map
maker does that for you, but the principle is the same.


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?

It's still Schw. spacetime. Such values of M do not correspond to any
objects we observe in the real world. Indeed, requiring the energy
density to be everywhere non-negative is called the "energy condition"
of GR, and corresponds to this.

Real world black holes are expected to not be primordial (as in Schw.
spacetime), but rather due to the collapse of massive objects. Such
objects with M0 would not collapse, but would "explode" (as you point
out)....


BTW this is related to the ambiguity in extending the exterior Schw.
region across the horizon, and which of the two Eddington-Finkelstein
coordinate charts one selects. One extension goes only backwards in
time, and the other only forwards in time; the first leads from the
white hole, and the latter leads to the black hole.


Tom Roberts

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

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

Well if you run time backwards, all the light that got sucked into the
black hole comes back out. Since the metric is diagonal and its
components are indepedent of time, there is no difference in the line
elements involved in the two cases. Hence the concept of the white
hole. Prior to the discovery of Hawking radiation, white holes were
potential candidates for quasars and other powerful emission sources in
the universe. But Hawking radiation now seems to be the dominant model
for such things and white holes are hardly talked about any more.

In article .com,
Igor wrote:

Well if you run time backwards, all the light that got sucked into the
black hole comes back out. Since the metric is diagonal and its
components are indepedent of time, there is no difference in the line
elements involved in the two cases. Hence the concept of the white
hole. Prior to the discovery of Hawking radiation, white holes were
potential candidates for quasars and other powerful emission sources in
the universe. But Hawking radiation now seems to be the dominant model
for such things and white holes are hardly talked about any more.

Quasars and related phenomena are not thought to have anything to do with
Hawking radiation. The supermassive black holes that are thought to be
involved in these objects have extremely low Hawking temperatures -- that
is, they emit negligible Hawking radiation.

The standard model for quasars et al. is that the supermassive black
holes are accreting matter from their surroundings. As that matter
approaches the black hole, it forms an accretion disk, which heats
up to very high temperatures. The various forms of radiation we see
from these systems comes from that accreting matter -- before it has
crossed the black hole's event horizon, of course.

-Ted




--
[E-mail me at , as opposed to .]

JanPB says...

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 guess I didn't realize that the "direction of time" was a property
of the manifold. I thought it was a matter of initial conditions
for the matter and fields.

If you consider a test particle moving along a radial geodesic,
then the particle's "position" r as a function of proper time s
will satisfy a differential equation

(dr/ds)^2 - A/r + B = 0

where A and B are constants of the motion. (It's interesting
that this looks exactly like the differential equation for
nonrelativistic motion in Newtonian gravity.)

Without solving the equation explicitly, we can immediately
read off the qualitative behavior:

If the test particle starts below the event horizon,
with r 2m, and with dr/ds 0, then r will increase
up to some maximal radius r_max 2m. Then the particle
will "turn around" and dr/ds will be negative as the
particle falls back towards the singularity at r=0.

As I understand it, the region with r 2m, dr/ds 0 is the
"white hole" interior, the region with r 2m is the black
hole exterior, and the region r 2m, dr/ds 0 is the
"black hole" interior.

But I still don't see any physically significant difference
between the white hole interior and the black hole interior.
Yes, dr/ds is positive in one region and negative in the
other region, but that seems purely conventional. As far
as the physics of idealized test particles is concerned,
proper time doesn't have a preferred direction, either.

If instead of a featureless test particle, we used a
macroscopic object (such as a human), then we could
define the positive direction of proper time to be
the direction in which entropy is increasing, but again
that seems to be a property of the initial conditions
of the matter, rather than a property of the manifold.

In any case, it seems mistaken to say that a white hole
is *repulsive*. dr/ds 0 for the white hole interior
region, but (d/ds)^2 r 0 in both regions, suggesting
that the singularity is always "attractive".

--
Daryl McCullough
Ithaca, NY

Daryl McCullough wrote:
JanPB says...
I guess I didn't realize that the "direction of time" was a property
of the manifold.

It isn't really a property of the manifold itself, but rather of the
relationship between the manifold and the physical system is it supposed
to model. This, of course, is the primary difference between math and
physics. Because of that relationship, we normally require any viable
solution to the EFE to be time orientable and not contain closed
timelike loops (trivially satisfied for Schw. spacetime).


I thought it was a matter of initial conditions
for the matter and fields.

The Einstein field equation is symmetric in time, and cannot determine
the direction of the future. This is, of course, no different from
classical mechanics or E&M; the only distinction between past and future
in the theory is the statistical likelihood of running a given system
backwards or forwards in time (c.f. the second law of thermodynamics).

Symmetries of the equations need not be symmetries of a given solution,
and I suppose it is possible to have initial conditions that uniquely
determine the direction of the future, but I know of no such solution to
the EFE. But then, I am not an expert on this.


If you consider a test particle moving along a radial geodesic,
then the particle's "position" r as a function of proper time s
will satisfy a differential equation
(dr/ds)^2 - A/r + B = 0
where A and B are constants of the motion. (It's interesting
that this looks exactly like the differential equation for
nonrelativistic motion in Newtonian gravity.)
Without solving the equation explicitly, we can immediately
read off the qualitative behavior: [...]

In the interior region r2M, r is timelike and you did not handle that
properly. In the white hole region +d/dr is future pointing, in the
black hole region -d/dr is future pointing.


In any case, it seems mistaken to say that a white hole
is *repulsive*. dr/ds 0 for the white hole interior
region,

Remember that r is TIMELIKE there, and increasing r does NOT mean
"coming out". In the white hole region +d/dr is future pointing, and all
viable timelike trajectories must have dr/ds0, because they must
propagate into the future. A glance at a Kruskal diagram shows that all
future-pointing timelike trajectories in this region are indeed coming
out of the white hole.


Tom Roberts

Henning Makholm wrote:

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.

I take it "far future" means "infinite", in t? I have some questions
about this, but, elsewhere... *

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.

That last part seems a bit fanciful. The geodesics merely describe the
trajectory of test particles _if_ they should somehow happen to appear,
it says nothing about whether there _are_ any test particles, still
less requiring the white hole to randomly spit them out as if it were
some kind of quantum process. The only mass implied by this part of
the solution is a mass M (or is that, just possibly, -M, as Daryl
suggests?) associated with the (white hole) singularity.

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.

Aha! _That_ is the best reason I have seen suggested (in my admittedly
very scanty researchs) to justify neglecting the white hole
singularity. The boundary conditions are not met: GR lives.

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.

* I have wondered if black holes may not be better described as models
of processes which never go to completion, rather than static objects,
sub species aeternis.

wrote:
The standard model for quasars et al. is that the supermassive black
holes are accreting matter from their surroundings. As that matter
approaches the black hole, it forms an accretion disk, which heats
up to very high temperatures. The various forms of radiation we see
from these systems comes from that accreting matter -- before it has
crossed the black hole's event horizon, of course.

The remarkable thing is how much energy can be available. Thermonuclear
reactions, such as in atomic and hydrogen bombs, release only a few MeV
per nucleon. The massive objects associated with galaxies and presumably
quasars can have orders of magnitude more kinetic energy per nucleon for
infalling matter.

Tom Roberts