Re: invariance of negative signature of the metric?

On Mar 11, 8:49 pm, "Ken S. Tucker" <dynam...@xxxxxxxxxxxx> wrote:
On Mar 11, 12:16 pm, Eric Gisse <jowr...@xxxxxxxxx> wrote:



On Mar 11, 11:32 am, "Ken S. Tucker" <dynam...@xxxxxxxxxxxx> wrote:

On Mar 11, 8:29 am, iuval <cle...@xxxxxxxxxxxxxx> wrote:

On Mar 10, 1:36 pm, carlip-nos...@xxxxxxxxxxxxxxxxxxx wrote:

iuval <cle...@xxxxxxxxxxxxxx> wrote:
Is there a theorem saying that if the metric starts out with a
negative signature on a spacelike surface (one or three eigenvalues
negative) that the field equations will preserve this negative
signature for all future and past?

There's some debate about this -- the answer depends on the
details of how you define the field equations. A signature change
necessarily means that the metric becomes degenerate on some
surface, and the Einstein field equations are usually derived
with the assumption of a nondegenerate metric. But the type of
degeneracy required is fairly mild, and there are extensions of
the field equations to cover such situations. The problem is that
the extension is not unique, and different choices give different
answers to your question.

Seehttp://arxiv.org/abs/gr-qc/0012047foradiscussionandsome
references.

Steve Carlip

Thank you!
-Iuval Clejan

Can you find a reason to exclude

&x / &x' = sqrt(-1)

as a legit transformation coefficient?

...because Riemann manifolds aren't complex valued?

h^2 = x^2 + y^2

x=5, y=sqrt(-9),

and in that CS k, x,y are orthogonal and
h = 4,

or in a nonorthogonal CS k',

x'=5,y'=3,h'=4.

and now swap x' and h' to get CS K,

X=4,Y=3,H=5 .

What was the question again?
Oh, yeah, signature in CS k is (+,-)
signature in k' is (+,+), and I don't
give a poop about the sig in CS K,
because I'm happy with either k or k'.

I look in vain for the words or computations related to computing the
number and sign of the metric's eigenvalues. Once again you show you
do not understand what a metric signature is.


Cut out a 3,4,5 triangle, place it on
graph paper, and learn how to transform
complex orthogonal CS's to nonorthogonal
CS's.

Once again Dr, Tucker uses advanced

You are not a doctor.

technology to *experimentally* prove
the General Theory of Relativity's
Principle of Covariance.

Actually when I learned transforming

Spot the lie.

from the GR vanilla orthogonal signature
(+---) , to the nonorthogonal signature
(++++), in Eq.(9) herein,http://physics.trak4.com/modern-spacetime.pdf
there was a fair amount of geometric tedium.

Orthogonality has fuckall to do with the signature. You do not know
what you are talking about.


The above example allows &y'/&y = sqrt(-1).
Regards
Ken S. Tucker

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