Before the Big Bang?

"George Dishman" schrieb
My
point was that if you allow for the increase of kinetic
energy in the solar sail case then energy is conserved
but there appear to be situations globally where there is
no equivalent way to do that in GR.

There is the Landau pseudotensor. You can use it
to define a conserved notion of energy in any given
system of coordinates. The only problem is that
the resulting energy distributions depend on the
choice of coordinates.

This leads to problems if you want to define it
for nontrivial manifolds. But our universe seems
to be flat, one chart seems sufficient.

No, it isn't choice if GR is accurate then energy may
not be conserved globally even though it is locally.

There is no "local but not global" energy conservation
in GR. The equation nabla_m T_mn = 0 which is
sometimes named local conservation law is the
generalization of a local conservation law but
does not have the form of a local conservation law
partial_m T_mn = 0.

I say "may not" because I think it depends on overall
topology or possibly just curvature. For example we
might make the problem go away by _assuming_ that the
universe is asymptotically flat. I'm not sure what a
full set of 'necessary and sufficient' conditions would
be though.

One consistent way, but with modification of GR:

1. Postulate that there exists a single preferred global chart.
2a. Use the Landau tensor in this chart.
2b. Postulate that this global chart is harmonic. Use the
harmonic equation as the local conservation law.
3. Add the harmonic equation as a new equation.
4. If you want a Lagrangian for this, add a term
which enforces harmonic gauge: n_ab g^ab sqrt(-g)
with Minkowski metric n_ab does the job.
5. Observe interesting properties of the additional
term: It stops the BH collaps and the BB singularity.

And, for people without prejudice against the e word:

6. Add a preferred frame and use the ADM decomposition
to give an ether interpretation in terms of density, velocity
and stress tensor of some ether, so that the harmonic condition
translates into continuity and Euler equations.

More see gr-qc/0205035

Ilja

"Ilja Schmelzer" wrote in message
...

"George Dishman" schrieb
My
point was that if you allow for the increase of kinetic
energy in the solar sail case then energy is conserved
but there appear to be situations globally where there is
no equivalent way to do that in GR.

There is the Landau pseudotensor. You can use it
to define a conserved notion of energy in any given
system of coordinates. The only problem is that
the resulting energy distributions depend on the
choice of coordinates.

Isn't that always true, e.g. kinetic energy.

This leads to problems if you want to define it
for nontrivial manifolds. But our universe seems
to be flat, one chart seems sufficient.

That was what I was alluding to when I said that
with some assumptions the problem may be able to
be resolved. In fact I mention that just a few
lines below.

No, it isn't choice if GR is accurate then energy may
not be conserved globally even though it is locally.

There is no "local but not global" energy conservation
in GR. The equation nabla_m T_mn = 0 which is
sometimes named local conservation law is the
generalization of a local conservation law but
does not have the form of a local conservation law
partial_m T_mn = 0.

OK, maybe I was inaccurate in summarising the first
few paragraphs of the FAQ:

http://math.ucr.edu/home/baez/physic...energy_gr.html


I say "may not" because I think it depends on overall
topology or possibly just curvature. For example we
might make the problem go away by _assuming_ that the
universe is asymptotically flat. I'm not sure what a
full set of 'necessary and sufficient' conditions would
be though.

One consistent way, but with modification of GR:

1. Postulate that there exists a single preferred global chart.
2a. Use the Landau tensor in this chart.
2b. Postulate that this global chart is harmonic. Use the
harmonic equation as the local conservation law.
3. Add the harmonic equation as a new equation.
4. If you want a Lagrangian for this, add a term
which enforces harmonic gauge: n_ab g^ab sqrt(-g)
with Minkowski metric n_ab does the job.
5. Observe interesting properties of the additional
term: It stops the BH collaps and the BB singularity.

Is such a solution testable? Wouldn't it produce
very bright supermassive BHs if impacting mass
doesn't cross the event horizon?

And, for people without prejudice against the e word:

I have no prejudice against it, but I would want to
see specific evidence for its existence otherwise
Occam's Razor applies.

George

"George Dishman" schrieb
"Ilja Schmelzer" wrote
One consistent way, but with modification of GR:

1. Postulate that there exists a single preferred global chart.
2a. Use the Landau tensor in this chart.
2b. Postulate that this global chart is harmonic. Use the
harmonic equation as the local conservation law.
3. Add the harmonic equation as a new equation.
4. If you want a Lagrangian for this, add a term
which enforces harmonic gauge: n_ab g^ab sqrt(-g)
with Minkowski metric n_ab does the job.
5. Observe interesting properties of the additional
term: It stops the BH collaps and the BB singularity.

Is such a solution testable? Wouldn't it produce
very bright supermassive BHs if impacting mass
doesn't cross the event horizon?

No, the surface would be highly redshifted, so
that nothing is visible.

And, for people without prejudice against the e word:

I have no prejudice against it, but I would want to
see specific evidence for its existence otherwise
Occam's Razor applies.

There are lots of them, but the best is imho my
ether model for the standard model. I have posted
it some time ago in
Message-ID:

Ilja