black holes and singularities

Greg Neill wrote:

[...]
The singularity is inevitable for two reasons. First, the
collapse of the matter that formed the black hole exceeded
the electron degeneracy pressure, the last thing that was
preventing the density from growing without limit; there
is nothing known, no known force, that can support the
matter from total collapse past this point.

This last statement can be made stronger. In general
relativity, mass is not the only source of gravity;
pressure contributes as well. So making pressure
stronger -- say, by finding something stronger than
electron degeneracy pressure -- you are doing two
things: increasing resistance to collapse, but also
increasing the effective mass, and therefore the
tendency to collapse. Under most circumstances,
``resistance'' wins. But if you compress matter to
a small enough size, the contribution of any extra
pressure to gravity wins, and nothing can stop the
collapse.

For spherically symmetric matter,this argument depends
on only a few features: positive energy -- i.e., no
gravitational repulsion -- and a requirement that the
speed of sound can't be greater than the speed of
light, which limits the form of allowed pressure.
For non-spherical collapse, there is a similar
proposal called the ``hoop conjecture,'' which has
not yet been proven, but which seems likely to be
true. There are also general theorems of Hawking
and Penrose, with no assumptions about symmetry,
that say that once the gravitational field has reached
a certain strength -- strong enough to form ``trapped
surfaces'' -- the formation of a singularity is
inevitable, though these don't specify any details
about what kind of singularity.

Of course, these results all assume general relativity,
which may not be a good assumption in regions of very
strong curvature -- for instance, approaching a would-be
singularity -- where quantum effects are likely to be
important.

Steve Carlip

In article ,
says...
"Abe" wrote in message
t...
In article ,
says...

The singularity is inevitable for two reasons. First, the
collapse of the matter that formed the black hole exceeded
the electron degeneracy pressure, the last thing that was
preventing the density from growing without limit; there
is nothing known, no known force, that can support the
matter from total collapse past this point.

Ah, OK. So, does this pressure limit occur at exactly the time at which
the event horizon forms?

This would depend upon the starting mass. For
things like neutron stars, its the degeneracy
pressure that keeps them from collapsing further;
the electrons have already been squeezed together
with protons to form neutrons, and the neutrons
are pushed together (no electrostatic force to
keep atom nuclei apart when they're all neutrons).

So in that case, it would be possible (in theory) to form a black hole
without the body passing the pressure threshold?

The question then becomes, in your average star, does this pressure
limit occur before, after, or round about the time the event horizon
forms? If before, then a singularity becomes probable; if after, then
it's anyone's guess.

In article , carlip@no-physics-
spam.ucdavis.edu says...
There are also general theorems of Hawking
and Penrose, with no assumptions about symmetry,
that say that once the gravitational field has reached
a certain strength -- strong enough to form ``trapped
surfaces'' -- the formation of a singularity is
inevitable, though these don't specify any details
about what kind of singularity.

Interesting.... it's this question of inevitability that I'm chasing
here.

Incidentally, what do mean by "what kind of singularity"? Surely
there's only one kind, given that it's a zero-dimensional object?

"Abe" wrote in message
t...

So in that case, it would be possible (in theory) to form a black hole
without the body passing the pressure threshold?

Yes, as I understand it the event horizon can form before
a singularity forms in the interior. I believe that it
is true to always be the case that a naked singularity
will not be observable from outside the event horizon (I
may be missing some pathalogical case).


The question then becomes, in your average star, does this pressure
limit occur before, after, or round about the time the event horizon
forms? If before, then a singularity becomes probable; if after, then
it's anyone's guess.

For an average star the mass is too small for a black
hole to form at the end of life. For the average star
that is massive enough to form a black hole, I believe
that the pressure limit transgression precedes the
formation of the event horizon. The core of the super
nova remnant collapses (exceeding degeneracy pressure)
and as when the density reaches a given threshold, the
event horizon forms. The delay between the two events
is likely very short.

"Abe" wrote in message
t...
Folks,

Before you all scream and kill this thread, please bear with me. I've
found questions like this on this group, but no really satisfactory
answers, so I'm going to try and phrase it right.

Conventional wisdom says that at the centre of your average black hole,
lies a singularity. Every book or article that I've read on this
subject is adamant about this fact.

So, my question would be, *why* the singularity. The presense of one
isn't necesary to form a black hole, all you need is a body of
sufficient density, e.g. if a sun shrinks beyond size x, it forms an
event horizon. So, while the presense of a singularity neccessitates
the presense of a blackhole, the converse isn't true.

Hi - Good question. Have you read 'A Brief History of Time' by Stephen
Hawking? In the chapter 'Black Holes' he broadly explains how the theory of
General Relativity is be applied to gravitationally collased stars. The
main tool is the idea of the light cone, which defines all the possible
paths of a particle or light beam in any particular gravitational field.

It had been recognised that it would be possible to have a field so strong
that none of the light paths starting within a particular radius could
escape the field (i.e. such things as Black Holes could exist). Much of this
early work was done by Robert Oppenheimer before the Second World War. After
the war, his work was not aadvanced much until the 1960s. Between 1965 and
1970 Hawking and Penrose were able to prove that any gravitational field
strong enough to form such a Black Hole would ALSO have to have a
singularity within it. This proof was mathematical (of course), but it was
based on the formulation of General Relativity.

If that assertion is correct, that a singularity isn't neccessary, then
why the assertion that they are always present? Doesn't Occam's Razor
tell us that it's simply a super-dense object of finite, non-zero
volume? Or does theory suggest that once a body reaches that sort of
density, then it can't help but continue collapse to a point mass under
its own gravity?

Correct, the theory suggests that collapse is indeed inevitable.

Of course, that raises a whole host of quantum/classical conflicts, but
those aside, what gives?

I think* that the inevitability is comes around because
IF
the field is enough to produce a Black Hole
THEN
All light cones within the Event Horizon must be tipped in towards the
centre
AND SO
All light and matter must pass through the same point in spacetime.


Hope this helps.

Owen


* I refer you to the original paper (probably Hawking S., Penrose R., The
Singularities of Gravitational Collapse and Cosmology,
Proc.R.Soc.Lond.A314,1970)

On Mon, 15 Mar 2004 00:31:30 +0000, Abe wrote:

In article , carlip@no-physics-
spam.ucdavis.edu says...
There are also general theorems of Hawking and Penrose, with no
assumptions about symmetry, that say that once the gravitational field
has reached a certain strength -- strong enough to form ``trapped
surfaces'' -- the formation of a singularity is inevitable, though
these don't specify any details about what kind of singularity.

Interesting.... it's this question of inevitability that I'm chasing
here.

Incidentally, what do mean by "what kind of singularity"? Surely
there's only one kind, given that it's a zero-dimensional object?

In a rotating (Kerr type) BH, singularity takes a ring form.

--

Gautam Majumdar

Please send e-mails to

"A" == Abe writes:

A Conventional wisdom says that at the centre of your average black
A hole, lies a singularity. Every book or article that I've read on
A this subject is adamant about this fact.

A So, my question would be, *why* the singularity.

There have been a few answers posted already. I don't find any of
them particularly satisfactory in explaining this basic question
(though a couple of danced around it). Let me give it a try.

Assume that general relativity is correct.

A The presense of one isn't necesary to form a black hole, all you
A need is a body of sufficient density, e.g. if a sun shrinks beyond
A size x, it forms an event horizon. So, while the presense of a
A singularity neccessitates the presense of a blackhole, the converse
A isn't true.

A If that assertion is correct, that a singularity isn't neccessary,
A then why the assertion that they are always present? Doesn't
A Occam's Razor tell us that it's simply a super-dense object of
A finite, non-zero volume? Or does theory suggest that once a body
A reaches that sort of density, then it can't help but continue
A collapse to a point mass under its own gravity?

You've actually answered your own question. What prevents an object
from collapsing? There has to be some opposing force that acts
against gravity.

* For the Earth, it's the electrostatic repulsion between its
constituent atoms.

* For the Sun, it's the gas pressure resulting from the intense heat
produced by nuclear reactions in its core.

* For a white dwarf, it's the Fermi pressure resulting from the
degenerate electrons.

* For a neutron star, it's the Fermi pressure resulting from the
degenerate neutrons.

As I think you're aware, though, the Fermi pressure has its limits.
If you try to add more and more mass to a neutron star, at some mass
(thought to be around 3 times the mass of the Sun), the weight of the
star exceeds the opposing force that the neutron Fermi pressure can
produce. (Indeed, as Steve Carlip has explained, pressure is
equivalent to an energy density, so it contributes to gravity and
hastens the collapse.)

Currently, we know of nothing that can produce more pressure than
neutron degeneracy. Thus, in our hypothetical situation of adding
more and more mass to a neutron star, once the neutron star starts to
collapse, there's nothing that can stop it.

*If* general relativity is correct, it has to collapse to a point of
infinite density. (Although, effectively once the event horizon
forms, what happens inside it doesn't matter.) This point is a
singularity because formally the equations break down.

As I think you alluded to, though, the assumption that general
relativity is correct is wrong. At small enough scales, quantum
mechanics must become important. I think the prevailing wisdom is
that, once general relativity and quantum mechanics are married, there
will be some explanation that prevents a infinite density point from
forming.

--
Lt. Lazio, HTML police | e-mail:
No means no, stop rape. | http://patriot.net/%7Ejlazio/
sci.astro FAQ at http://sciastro.astronomy.net/sci.astro.html

"Abe" ha scritto nel messaggio
t...
Folks,

Before you all scream and kill this thread, please bear with me. I've
found questions like this on this group, but no really satisfactory
answers, so I'm going to try and phrase it right.

Conventional wisdom says that at the centre of your average black hole,
lies a singularity. Every book or article that I've read on this
subject is adamant about this fact.

So, my question would be, *why* the singularity. The presense of one
isn't necesary to form a black hole, all you need is a body of
sufficient density, e.g. if a sun shrinks beyond size x, it forms an
event horizon. So, while the presense of a singularity neccessitates
the presense of a blackhole, the converse isn't true.

If that assertion is correct, that a singularity isn't neccessary, then
why the assertion that they are always present? Doesn't Occam's Razor
tell us that it's simply a super-dense object of finite, non-zero
volume? Or does theory suggest that once a body reaches that sort of
density, then it can't help but continue collapse to a point mass under
its own gravity?

Of course, that raises a whole host of quantum/classical conflicts, but
those aside, what gives?

Maybe "Gravastars" could be an answer to your doubts about singolarity...

"Gravastars" is an interesting new class of objects (if they exist...)

You can see a rapid overview at
http://www.space.com/scienceastronom...rs_020423.html

"Emil Mottola of the Los Alamos National Laboratory and Pawel Mazur of the
University of South Carolina suggest that instead of a star collapsing into
a pinpoint of space with virtually infinite gravity, its matter is
transformed into a spherical void surrounded by an extremely durable form of
matter never before experienced on Earth."
"The matter inside a gravastar would be akin to the Bose-Einstein
condensate. It would exist in a vacuum, surrounded by an ultra-thin,
ultra-cold, ultra-dark bubble, hence the name gra (vitational) va (cuum)
star, or gravastar."

I like this theory because I've always hated singularities, they bring too
much entropy in our universe...
..
Luigi Caselli

"Jonathan Silverlight"
schreef in bericht ...
In message , Nicolaas
Vroom writes

"Abe" schreef in bericht
et...
Folks,

Before you all scream and kill this thread, please bear with me. I've
found questions like this on this group, but no really satisfactory
answers, so I'm going to try and phrase it right.

Conventional wisdom says that at the centre of your average black hole,
lies a singularity. Every book or article that I've read on this
subject is adamant about this fact.

Where did you read that ?
Can you give me an url with a text which claims that.

IMO singularities do not exist.
A black hole is something that exists with has a certain radius 0
A singularity is a mathematical construct
which you get when radius r goes to zero.
In that case the force goes to infinity.

"According to general relativity, there must be a singularity of
infinite density and space-time curvature within a black hole".
A Brief History of Time p 88.

In the copy I have Batam edition, published 1989
that is written at page 93. It starts with:
"The work that Roger Penrose and I did between 1965
and 1970 showed that etc"
Next he writes:
"At this singularity the laws of science and our ability to
predict the future would break down"
What does the first part mean ?
Does it mean that the laws of science are invalid
at this singularity ?
But if that is true you have a problem because
than you also can not use GR in order to predict it.

At page 95 (88+2) he writes:
"W. Israel showed that accordingly to GR non rotating
black holes must be very simple, they were perfectly
spherical" etc
"At first many people argued that since BH had to be
perfectly sperical a BH could only form from a perfect
spherical object. Any real star - (not perfect sperical) -
could therefore only collapse to form a naked singularity."
"There was however a different interpretation...
According to this view, any non rotating star would end up
as a perfectly spherical Black Hole ....
and it soon came to be adopted generally"

No more mention about singularity inside a BH.

Except at the beginning of Chapter 7.
"Before 1970, my research on GR had concentrated
mainly on the question of whether or not there had been
a Big Bang singularity"

No answer. No definition. Strange very strange.

Does a singularity has a size ?

See also my previous reply to Abe in this thread.

Nicolaas Vroom
http://users.pandora,be/nicvroom/

In article om,
says...
On Mon, 15 Mar 2004 00:31:30 +0000, Abe wrote:

Incidentally, what do mean by "what kind of singularity"? Surely
there's only one kind, given that it's a zero-dimensional object?

In a rotating (Kerr type) BH, singularity takes a ring form.

AH, so it seems my concept of "singularity" is too simplistic here.
Does this mean that singularities can have a "volume" (for want of a
better word)? In other words, a single point of space-time can be
extended into several dimensions?