black holes and singularities

"Joseph Lazio" bravely wrote to "All" (15 Mar 04 08:49:41)
--- on the heady topic of " black holes and singularities"

JL From: Joseph Lazio

"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.

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

JL 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?

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

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

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

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

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

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

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

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

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

I think you are right in holding such an opinion. My only exception is
that to look at the behaviour of matter alone neglects all the other
questions. We must keep in mind that matter and spacetime have an
intrinsic relationship which is deeply philosophical in nature.
Such questions as these quickly become bogged down in axioms which are
very difficult to prove let alone understand. For example what gives a
sub atomic particle its characteristics is the first that comes to
mind. Apparently string theories will be able to take us further into
the very nature of the universe but so far we haven't seen much trace
of experimental proof. I hope some of these pan out...

Asimov
******

.... Where's the KABOOM, there was supposed to be an earth shattering KABOO

"Abe" wrote in message
t...
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?

I don't know about "volume", unless they can be "fuzzed-out"
at planck scales. The singularity of a spinning black hole
could be ring shaped as mentioned, but the ring would be
comprised of a one dimensional line forming a circle.

It makes one wonder what happens to the purported "curled-up"
space dimensions in such situations.

"A" == Abe writes:

A In article om,
A 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.

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

I would define a singularity as a region in which a straightforward
application of physical laws lead to non-physical results.

* In the case of a non-rotating, collapsed star, the singularity is a
point.

* As others have pointed out, if the collapsed star has some angular
momentum, the region is a ring.

* In the case of the Big Bang, the singularity is all of space. If
one simply extrapolates backward in time, the density becomes
infinite everywhere.

--
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 wrote:

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?

Here's probably more than you wanted to know:

It's actually quite hard to define a ``singularity'' in general
relativity, and a lot of work has gone into coming up with a
useful definition. The basic problem is that while most theories
assume a fixed spacetime, in general relativity the physical
evolution determines the spacetime as well (and worse, in the
case of singularities, doesn't determine it uniquely). That
means that if you show me a spacetime in which the curvature
goes to infinity at point P, I can say, ``Oh, that's not really
singular -- point P just isn't part of the spacetime.'' That
sounds like cheating, and in a sense it is, but the same sort
of thing can be less blatant and much harder to spot -- you can
choose whatever coordinates you want, and coordinates can often
disguise whether your spacetime has had a potential singularity
that's been ``cut out.'' To make things worse, components of
the curvature tensor depend on coordinates, and you can have
something that looks like a singularity but is really just a
poor choice of coordinates. And on the other hand, you can have
a singularity in which the curvature stays small arbitrarily
close to the singular point (for instance, the tip of a cone).

The general working definition is that a singularity is an
``edge'' of spacetime -- that is, a point or a set of points
that can be reached by an observer in a finite proper time,
either in free fall or with bounded acceleration (think of a
rocket with a finite amount of fuel), at which the observer's
world line simple ends. You should also add the condition that
the spacetime be inextendible, that is, there is no way to just
add extra points to make the world line continue.

With this definition of a singularity as an ``edge,'' it should
be clear that a singularity can have a very complicated
structure. It can be zero, one, two, or three-dimensional,
or even fractal. It can be spacelike, timelike, or null.
The curvature may go to infinity as you approach a singularity,
but it doesn't have to; or some components may become infinite
while others don't. Lots of possibilities...

Steve Carlip

... 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.

More than that! Invoke, if you like, some UNKNOWN
force that will create enough pressure to stop the
collapse. Well, pressure itself creates gravity, in
this case gravity stronger than the pressure itself.

Ben

In article ,
says...

snip

Thanks for all your responses, folks. Some interesting ideas to chew on
there.

a