Black holes - relative or absolute? 
Author Message
 Black holes - relative or absolute?
Black holes arise in GR in situations where classical physics would
result in escape velocities higher than the speed of light. To an
escape velocity of c corresponds a difference in gravitational
potential of 0.5 c^2.

The gravitational potential decreases further if one approaches the
center of a star. If a spherical object has a constant density, then
the gravitational potential at the center is 1.5 times the one of the
surface. In the case of real stars the factor is much higher than 1.5
because of the much higher density near the center.

At least a classical consideration leads to the conclusion that a
visible star does somehow contain a black hole if the escape velocity
is higher than c at its center. But as far as I understand GR, also
this theory suggests, that light cannot escape from below this
black-hole-radius of the non-black-hole.

This problem results from a more general question: are black holes
absolute or are they relative (i.e. observer-dependent)?

Wolfgang Gottfried G. (0:003.6)
http://www.***.com/



Sat, 22 Jun 2002 03:00:00 GMT
 Black holes - relative or absolute?

Quote:

> Black holes arise in GR in situations where classical physics would
> result in escape velocities higher than the speed of light. To an
> escape velocity of c corresponds a difference in gravitational
> potential of 0.5 c^2.

> The gravitational potential decreases further if one approaches the
> center of a star. If a spherical object has a constant density, then
> the gravitational potential at the center is 1.5 times the one of the
> surface. In the case of real stars the factor is much higher than 1.5
> because of the much higher density near the center.

> At least a classical consideration leads to the conclusion that a
> visible star does somehow contain a black hole if the escape velocity
> is higher than c at its center. But as far as I understand GR, also
> this theory suggests, that light cannot escape from below this
> black-hole-radius of the non-black-hole.

> This problem results from a more general question: are black holes
> absolute or are they relative (i.e. observer-dependent)?

> Wolfgang Gottfried G. (0:003.6)
> http://members.lol.li/twostone/E/paradoxGR.html

There are no absolutes in physics or sciences in general.  Black holes are
just a case in point.  They are explained by general relativity in that one
can determine properties about them.  We also find objects orbiting other
stars or located in the centers of galaxies that exhibit, to the best of our
observational knowledge, some of the properties ascribed to black holes by GR.
So, one can conclude, within context of current theory, that said objects are
black holes.

This is not an absolute.  It simply is an interpretation of observation in
context of current theory.

GR is known to be a limited theory, and it is hoped a more inclusive one will
eventually be developed.  But, as a theory, it is a good one from a science
standpoint because it makes predictions which have since been verified.  The
degree of that success has given confidence in its applications to other
observations to interpret them.

--

Gheens Science Center and Rauch Planetarium
http://www.louisville.edu/planetarium
University of Louisville



Sat, 22 Jun 2002 03:00:00 GMT
 Black holes - relative or absolute?




Quote:
> This problem results from a more general question: are black holes
> absolute or are they relative (i.e. observer-dependent)?

They are absolute. If an event is inside of event horizon for one
observer then it is inside for every observer.

Mikko


Sat, 22 Jun 2002 03:00:00 GMT
 Black holes - relative or absolute?

Quote:



> > This problem results from a more general question: are black holes
> > absolute or are they relative (i.e. observer-dependent)?

> They are absolute. If an event is inside of event horizon for one
> observer then it is inside for every observer.

> Mikko

Are you sure?

(this is an extra transmission from black hole)



Sat, 22 Jun 2002 03:00:00 GMT
 Black holes - relative or absolute?

Quote:

> Black holes arise in GR in situations where classical physics would
> result in escape velocities higher than the speed of light. To an
> escape velocity of c corresponds a difference in gravitational
> potential of 0.5 c^2.

Attempting to model GR using "gravitational potential" can only be
done in weak field regions. Near a black hole this is never the case.
In general the gravitational field has too many degrees of freedom to
be modeled by a simple scalar (or even vector) potential.

Quote:
> The gravitational potential decreases further if one approaches the
> center of a star. If a spherical object has a constant density, then
> the gravitational potential at the center is 1.5 times the one of the
> surface. In the case of real stars the factor is much higher than 1.5
> because of the much higher density near the center.

I haven't checked your "1.5", but this sort of thing certainly occurs
within the approximation that the star is "small".

Quote:
> At least a classical consideration leads to the conclusion that a
> visible star does somehow contain a black hole if the escape velocity
> is higher than c at its center. But as far as I understand GR, also
> this theory suggests, that light cannot escape from below this
> black-hole-radius of the non-black-hole.

I don't unserstand what you are tying to say. I suppose that in
Newtonian gravitation one could imagine a star such that at its
center its escape velocity exceeds c but at its surface does not.
But this is nowhere close to a black hole in GR -- in Newtonian
gravitation there is nothing special about the speed c. And if one
considered the same star with the same mass density in GR one
would obtain a completely different situation -- since the Nettonian
escape velocity exceeds c at the center, I suspect that the entire
star would be forced to collapse into a black hole; but I am not
sure and have made no computations, this is only a guess.

Newtonian gravitation is woefully inadequate to describe a black
hole.

Quote:
> This problem results from a more general question: are black holes
> absolute or are they relative (i.e. observer-dependent)?

In GR, if an event is inside the event horizon of a black
hole to one observer, it is to all observers. Observers are merely
representations of different coordinates, and the tensors of GR
are coordinate independent, as are the relationships among them.
Also: if a given object is a black hole to one observer (i.e. has
an event horizon [aka a "closed trapped surface"]) then it is so
to all.

GR has more "absolute" aspects to it than does SR, but it is not an
"absolute" theory in the sense that Newtonian mechanics presumes an
absolute space and time.

        I put "absolute" in quotes, because not all of the usual
        aspects of the word apply here.




Sat, 22 Jun 2002 03:00:00 GMT
 Black holes - relative or absolute?

Quote:

> Black holes arise in GR in situations where classical physics would
> result in escape velocities higher than the speed of light. To an
> escape velocity of c corresponds a difference in gravitational
> potential of 0.5 c^2.

That's not the right way to think of it at all.  The defining feature of a
black hole is an event horizon which acts as a "one way gate": objects
(and light) can pass through it in only one direction.  The simplest way
of thinking about this (in the simplest case, a nonrotating black hole
with mass m) is to visualize the light cones shearing over with decreasing
radius until at radius r = 2m, one side is vertical, and for 0 < r < 2m,
even radially -outgoing- light must fall in.  Specifically:

 ds^2 = -dt^2 + (dr + sqrt(2m/r) dt)^2 + r^2 (du^2 + sin(u)^2 dv^2)
                                         ^^^^^^^^^^^^^^^^^^^^^^^^^^

      = -(1-2m/r) dt^2 - 2 sqrt(2m/r) dt dr

                        + dr^2 + r^2 (du^2 + sin(u)^2 dv^2)
                          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Here, one can take the ONB of Lemaitre observers (freely infalling
observers who "start from rest at r = infty") as

 e_t = d/dt - sqrt(2m/r) d/dr

 e_r = d/dr

 e_u = 1/r d/du

 e_v = csc(u)/r d/dv

In the tr plane, you can draw the light cones by first drawing the basis
vectors for say -5m < t < 5m and 0 < r < 5m.  Note the the vector e_r is
horizontal, pointing in the direction of increasing r, but the e_t vector
has constant height 1 but is sheared over toward r = 0.  You can then draw
the light cones using these vectors the same way you would use the vectors
d/dt, d/dr to draw light cones in Minkowski spacetime.  I can't illustrate
that in ASCII but you should figure out how to do this.  If you have
trouble, looking at Geroch, General Relativity from A to B might help.

Quote:
> The gravitational potential decreases further if one approaches the
> center of a star. If a spherical object has a constant density, then
> the gravitational potential at the center is 1.5 times the one of the
> surface.

You are no doubt referring to the Schwarzschild incompressible fluid
solution, which can be matched along surfaces r = r0, r0 suffiently
greater than 2m, to the Schwarzschild vacuum just discussed.  However, the
Painleve coordinates given above are suitable for matching to a Friedmann
dust with E^3 hyperslices (Oppenheimer-Snyder collapse); you should use
the original "static" coordinates of Schwarzschild to match to a fluid.

However, "Gravitational potential" has no meaning in gtr. You probably
mean the acceleration of fluid particles, which causes their world lines
to be nongeodesics.  This acceleration does indeed to decrease to zero at
the center of the fluid drop, but the pressure increases to a maximum, and
the curvatures R^t_(wtw) etc. are negative and decrease to a mininum (a
maximum in modulus) at r = 0.  The gravitational time dilation relative to
the gravitational time dilation at the surface also increases to a maximum
at r = 0.  But the ratio of the time dilation at the center to the time
dilation at the surface (both relative to clocks at r = infty) is not 3:2.

Quote:
> In the case of real stars the factor is much higher than 1.5 because
> of the much higher density near the center.

> At least a classical consideration leads to the conclusion that a
> visible star does somehow contain a black hole if the escape velocity
> is higher than c at its center.

The Schwarzschild model is oversimplified, but ordinary stars do not
contain black holes at their center.  (Think about it: would hydrostatic
equilibrium be possible if there were was a black hole at the center of a
fluid drop?)

Quote:
> This problem results from a more general question: are black holes
> absolute or are they relative (i.e. observer-dependent)?

I think the best short answer is that according to gtr, black holes are
most definitely not observer dependent in the sense you mean.  The event
horizon is a real phenomenom and there is no question about whether any
given event is inside or outside it, in any spacetime containing a black
hole.

(But see my post on the Vaidya solution, on my relativity pages, for a
cautionary note about the ontological nature of event horizons as compared
with apparent horizons--- you might think you are outside the horizon when
actually it has unexpectedly expanded out beyond your location, even
though you can still hover motionless above the hole by firing your rocket
engines.  You only find out what has happened when some time later (by
your clocks) a collapsing spherical shell of radiation (moving at the
speed of light, so you can have no warning that it is coming) falls past
your location, after which you find you can no longer keep yourself from
falling into the hole, i.e., the new apparent horizon is -outside- your
present location, and you are doomed.  See Hawking and Ellis for a related
discussion, and see also Frolov and Novikov; the full citations are in my
reading list.)

This is not to deny that the physical phenomena experienced by various
observers during a close encounter with a black hole depend very much on
the details of their motion relative to the hole.  For example an
"ultrarelativistic observer" experiences a near encounter with a black
hole as something like an "impulsive" gravitational plane wave.  But this
does not contradict what I just said about every event either being inside
or outside (or on) the event horizon.

Chris Hillman

Home Page: http://www.math.washington.edu/~hillman/personal.html



Sat, 22 Jun 2002 03:00:00 GMT
 Black holes - relative or absolute?

Quote:




> > > This problem results from a more general question: are black holes
> > > absolute or are they relative (i.e. observer-dependent)?

> > They are absolute. If an event is inside of event horizon for one
> > observer then it is inside for every observer.

> > Mikko

> Are you sure?

Yes, according to gtr every event is either inside, on, or outside the
event horizon.  There are other types of horizons, of course, such as the
"cosmological horizon" in the de Sitter vacuum (with nonzero lambda).  
Several recent preprints study various properties of the Schwarzschild-de
Sitter solution which models a black hole sitting in a de Sitter vacuum
instead of a Minkowksi vacuum.  For realistic models, the event horizon of
the hole is a sphere which is much, much, MUCH smaller than the
cosmological horizon, but if you look at what happens when the event
horizon is almost as large as (very close to) the cosmological horizon,
you can expect interesting effects involving Hawking-Unruh radiation
between the two horizons, which are at different "temperatures".  See the
recent preprint coauthored by Hawking.

Chris Hillman

Home Page: http://www.math.washington.edu/~hillman/personal.html



Sat, 22 Jun 2002 03:00:00 GMT
 Black holes - relative or absolute?
===== all previous comments deleted =====

It seems to me that all of the repliers have missed what the original
questioner is after. I suggest that we consider the following "gedanken"
experiment.

Suppose we have a neutron star somewhere. Let's suppose that, at present, it is
NOT a black hole but that its mass is NEAR to black hole mass.

Suppose our neutron star is sitting somewhere in a gaseous nebula or dust
cloud, so that additional mass is slowly raining down on it. Eventually, its
total mass increases until it becomes a black hole (I suppose; I don't really
know).

Here is my question, which I think captures the intent of the original
questioner. As this object makes the transition from neutron star to black
hole, does the "event horizon" suddenly appear at its SURFACE, so that the
entire object becomes a black hole at once? Or does the "event horizon" appear
as a tiny spherical shell at the object's center, which then slowly expands
outward, toward the neutron star surface, as the additional mass continues
raining down?

My new sig says it all:

---
Stanley Sramek
Inactive physics PhD with expertise in nothing
Houston, Texas



Sun, 23 Jun 2002 03:00:00 GMT
 Black holes - relative or absolute?

|Here is my question, which I think captures the intent of the original
|questioner. As this object makes the transition from neutron star to
|black hole, does the "event horizon" suddenly appear at its SURFACE,
|so that the entire object becomes a black hole at once?

Nothing seems at all to be 'sudden' to the *observer* that is far from
the black hole.

|Or does the "event horizon" appear as a tiny spherical shell at the
|object's center, which then slowly expands outward, toward the neutron
|star surface, as the additional mass continues raining down?

As the neutron star gains so much mass that the escape velocity equals
the speed of light, it appears to become an ever deeper, darker, blacker
body.  At some point it becomes so black that you cannot see it.  

How minimally massive can a black hole be?



Sun, 23 Jun 2002 03:00:00 GMT
 Black holes - relative or absolute?

|The Schwarzschild model is oversimplified, but ordinary stars do not
|contain black holes at their center.  (Think about it: would hydrostatic
|equilibrium be possible if there were was a black hole at the center of a
|fluid drop?)

Very good point!!



Sun, 23 Jun 2002 03:00:00 GMT
 Black holes - relative or absolute?


Quote:
>I haven't checked your "1.5", but this sort of thing certainly occurs
>within the approximation that the star is "small".

1.5 is correct, for uniform density; let the radius be a, then the
potential at the surface is -GM/a and the increase going from the
surface to a radius r is
              / r                                / r
delta phi = G |   M(r') r^-2 dr' = 4/3 pi rho G  |   r' dr' =
              / a                                / a

          = 1/2 (4/3 pi rho G) [r^2 - a^2]
(where M(r) = 4/3 pi rho r^3, and r is the density) which is clearly
just half GM/a at r=0. The only approximation here is that gravitation
is Newtonian!

Quote:
>I don't unserstand what you are tying to say.

As I understand it, he's saying that phi might be of order c^2
somewhere inside a star, and deducing from that that stars might
contain black holes. Ignoring the fact that this isn't the proper
relativistic way of doing things, it is true that a real star, obeying
hydrostatic equilibrium, might have a higher phi(r=0) than is implied
by the uniform-density calculation. But, as Chris Hillman points out,
a star with a central black hole would *not* obey the hydrostatic
equilibrium condition; it would collapse. So it's not possible to use
hydrostatic equilibrium arguments to deduce a central black hole in a
star. Therefore stars are not, in fact, hiding black holes.

Martin
--
Martin Hardcastle             Department of Physics, University of Bristol
`Innocent light-minded men, who think that astronomy can be learnt by
looking at the stars without knowledge of mathematics, will become birds...'
Please replace the xxx.xxx.xxx in the header with bristol.ac.uk to mail me



Sun, 23 Jun 2002 03:00:00 GMT
 Black holes - relative or absolute?


Quote:
> Black holes arise in GR in situations where classical physics would
> result in escape velocities higher than the speed of light. To an
> escape velocity of c corresponds a difference in gravitational
> potential of 0.5 c^2.

You made an assumption that the speed of light is independent from the
gravitational potential. The denser the medium the lower the speed of
light.

Quote:
> The gravitational potential decreases further if one approaches the
> center of a star. If a spherical object has a constant density, then
> the gravitational potential at the center is 1.5 times the one of the
> surface. In the case of real stars the factor is much higher than 1.5
> because of the much higher density near the center.

An other assumption: constant density. Earth has a few denser regions
toward the center, would not you expect the same from the stars?

Quote:
> At least a classical consideration leads to the conclusion that a
> visible star does somehow contain a black hole if the escape velocity
> is higher than c at its center. But as far as I understand GR, also
> this theory suggests, that light cannot escape from below this
> black-hole-radius of the non-black-hole.

> This problem results from a more general question: are black holes
> absolute or are they relative (i.e. observer-dependent)?

Non of that. The answer is: there are no black holes.

Quote:
> Wolfgang Gottfried G. (0:003.6)
> http://members.lol.li/twostone/E/paradoxGR.html

Speed of light represents the density, a basic property of the medium
in which the wave of photons progresses. The speed of light will change
with the density of the medium - decreases with higher density - but
the process will go, there is no 'turning back or falling into the
black hole' or 'event horizon'. The high gradient of density causes the
light to turn near the large mass objects, but it never goes "black".
--
Aladar
http://www2.3dresearch.com/~alistolmar

Sent via Deja.com http://www.deja.com/
Before you buy.



Sun, 23 Jun 2002 03:00:00 GMT
 Black holes - relative or absolute?


Quote:


> > Black holes arise in GR in situations where classical physics would
> > result in escape velocities higher than the speed of light. To an
> > escape velocity of c corresponds a difference in gravitational
> > potential of 0.5 c^2.

> You made an assumption that the speed of light is independent from the
> gravitational potential. The denser the medium the lower the speed of
> light.

> > The gravitational potential decreases further if one approaches the
> > center of a star. If a spherical object has a constant density, then
> > the gravitational potential at the center is 1.5 times the one of
the
> > surface. In the case of real stars the factor is much higher than
1.5
> > because of the much higher density near the center.

> An other assumption: constant density. Earth has a few denser regions
> toward the center, would not you expect the same from the stars?

> > At least a classical consideration leads to the conclusion that a
> > visible star does somehow contain a black hole if the escape
velocity
> > is higher than c at its center. But as far as I understand GR, also
> > this theory suggests, that light cannot escape from below this
> > black-hole-radius of the non-black-hole.

> > This problem results from a more general question: are black holes
> > absolute or are they relative (i.e. observer-dependent)?

> Non of that. The answer is: there are no black holes.

> > Wolfgang Gottfried G. (0:003.6)
> > http://members.lol.li/twostone/E/paradoxGR.html

> Speed of light represents the density, a basic property of the medium
> in which the wave of photons progresses. The speed of light will
change
> with the density of the medium - decreases with higher density - but
> the process will go, there is no 'turning back or falling into the
> black hole' or 'event horizon'. The high gradient of density causes
the
> light to turn near the large mass objects, but it never goes "black".
> snoop
> So gravity has no effecton how light travels!!!!!!!!!!!

Sent via Deja.com http://www.deja.com/
Before you buy.


Mon, 24 Jun 2002 03:00:00 GMT
 Black holes - relative or absolute?

Quote:





> > > Black holes arise in GR in situations where classical physics
would
> > > result in escape velocities higher than the speed of light. To an
> > > escape velocity of c corresponds a difference in gravitational
> > > potential of 0.5 c^2.

> > You made an assumption that the speed of light is independent from
the
> > gravitational potential. The denser the medium the lower the speed
of
> > light.

> > > The gravitational potential decreases further if one approaches
the
> > > center of a star. If a spherical object has a constant density,
then
> > > the gravitational potential at the center is 1.5 times the one of
> the
> > > surface. In the case of real stars the factor is much higher than
> 1.5
> > > because of the much higher density near the center.

> > An other assumption: constant density. Earth has a few denser
regions
> > toward the center, would not you expect the same from the stars?

> > > At least a classical consideration leads to the conclusion that a
> > > visible star does somehow contain a black hole if the escape
> velocity
> > > is higher than c at its center. But as far as I understand GR,
also
> > > this theory suggests, that light cannot escape from below this
> > > black-hole-radius of the non-black-hole.

> > > This problem results from a more general question: are black holes
> > > absolute or are they relative (i.e. observer-dependent)?

> > Non of that. The answer is: there are no black holes.

> > > Wolfgang Gottfried G. (0:003.6)
> > > http://members.lol.li/twostone/E/paradoxGR.html

> > Speed of light represents the density, a basic property of the
medium
> > in which the wave of photons progresses. The speed of light will
> change
> > with the density of the medium - decreases with higher density - but
> > the process will go, there is no 'turning back or falling into the
> > black hole' or 'event horizon'. The high gradient of density causes
> the
> > light to turn near the large mass objects, but it nevergoes "black".

 snoop
 So gravity has no effecton how light travels!!!!!!!!!!!
Quote:

> Sent via Deja.com http://www.deja.com/
> Before you buy.

Please, give a brief description of gravity. What is it in your
understanding?
--
Aladar
http://www2.3dresearch.com/~alistolmar

Sent via Deja.com http://www.deja.com/
Before you buy.



Mon, 24 Jun 2002 03:00:00 GMT
 Black holes - relative or absolute?
Wouldn't a black hole at the center of a fluid drop blow the drop
apart from the energy of infalling matter?

What would, say, a 4 Ms black hole surrounded by a 100 Ms ball of
gas look like? How long would it last, and would much of the gas
end up in the BH?

Mass falling into a black hole doesn't always end there, and it does
take a finite time for it to "enter" the black hole.

If, say, Eta Carinae was a black hole at it's core, could we tell?

Quote:


> |The Schwarzschild model is oversimplified, but ordinary stars do not
> |contain black holes at their center.  (Think about it: would hydrostatic
> |equilibrium be possible if there were was a black hole at the center of a
> |fluid drop?)

> Very good point!!



Mon, 24 Jun 2002 03:00:00 GMT
 
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