Re: Symmetry

Barry <Sirdry@xxxxxxxxxxx> wrote:
carlip-nospam@xxxxxxxxxxxxxxxxxxx wrote:

Barry wrote:

I would appreciate it if you could find my errors in the following
observations. They seem to cause much dissent:

(i) There is nothing in GR, per se, that predicts that "singularities
will not be observed" or that forbids closed timelike curves. Cosmic
censorship has to be invoked in both cases.

This is a misunderstanding of cosmic censorship. The cosmic censorship
conjecture is not something outside of GR that needs to be independently
"invoked."

it is a hypothesis that *within GR*, given certain positivity
conditions for energy, generic initial data never evolves to produce
naked singularities. We don't know whether this hypothesis is correct;
it can be proven in certain special circumstances, and there are no
known counterexamples. If it is correct, it is "in GR, per se."

In short, the response to your claim that "There is nothing in GR, per se,
that predicts that `singularities will not be observed'" is that it is
highly premature -- we don't know whether this is correct or not.

Then can we say that, the mathematics of GR allows for them,

That depends on what kind of "allowing" you mean. We certainly can find
exact solutions of the field equations with naked singularities -- for
example, the Schwarzschild metric with negative mass. But we can't
*make* such singularities in the real world, since we don't (as far as
we know) have access to anything with negative mass to make them with.
Similarly, we can find solutions in which an exactly spherically symmetric
shell with a particular equation of state collapses to form a singularity
that is at least briefly naked. But there's evidence that a tiny deviation
from exact spherical symmetry will destroy this result, and, again, we do
not have access to exactly spherically symmetric configurations of matter.

We do *not* know whether "the mathematics of GR" allows naked singularities
to form from physically reasonable configurations of matter.

(In the same way, "the mathematics of Newtonian gravity" allows bizarre
situations if you allow negative mass -- a negative mass attached
to a positive mass will spontaneously accelerate at a constant rate --
and also permits situations with positive mass in which an object attains
infinite speed in a finite time. Does this indicate something wrong with
Newtonian gravity? Or does it just mean that the initial conditions are
unattainable?

but they
are considered physically unrealistic and, in 1969, the Cosmic
Censorship Conjecture was grafted onto GR for the sole purpose of
forbidding them?

No. Once again: the cosmic censorship conjecture is NOT something
"grafted onto GR" -- it is a hypothesis that GR *already* *in itself*
has certain properties. And no, it was not proposed because people
thought that naked singularities were physically unrealistic; it was
proposed because it seemed to be true in a large number of examples
that suggested a deeper pattern.

I suppose your answer for Closed Timelike Curves would be similar.

In classical GR, Hawking has proven that, as a feature of classical GR
(NOT something "grafted on" from the outside), if energies are positive,
closed timelike curves cannot form in a finite region that initially
does not contain them. There are arguments that in quantum field theory
the assumption of positive energy may not be justified, and continuing
deates on the implications, but classically the issue is settled.

Steve Carlip
.