What the subject says. Working through Gravitation(MTW), waited until I
was in mid chap 14 before going back and having another look at this bit,
but am still stumped here. (ie, page 326, problem 13.12b)

Tried some index jiggerpokery but am still stumped. Any help would be
appreciated, thanks.

Psy-Kosh

On Jan 24, 1:39 pm, Psy-Kosh wrote:
What the subject says. Working through Gravitation(MTW), waited until I
was in mid chap 14 before going back and having another look at this bit,
but am still stumped here. (ie, page 326, problem 13.12b)

Tried some index jiggerpokery but am still stumped. Any help would be
appreciated, thanks.

Psy-Kosh

The Einstein tensor has zero covariant divergence. Ricci doesn't.
IIRC, the Einstein tensor is derivable from a contraction on the
Bianchi identities of the Riemann Curvature. You should be able to
find it in just about any good GR textbook. Doesn't MTW derive this in
an understandable way?

On Jan 24, 11:11 am, "Igor" wrote:

The Einstein tensor has zero covariant divergence. Ricci doesn't.

What does that mean?

IIRC, the Einstein tensor is derivable from a contraction on the
Bianchi identities of the Riemann Curvature. [...]

Bullsh*t! The Einstein tensor can only be derived from the
Einstein-Hilbert Lagrangian.

The Einstein tensor has zero covariant divergence. Ricci doesn't.
IIRC, the Einstein tensor is derivable from a contraction on the
Bianchi identities of the Riemann Curvature. You should be able to
find it in just about any good GR textbook. Doesn't MTW derive this in
an understandable way?


If it derives it, it does so elsewhere in the book that I haven't seen yet.

So far what I've seen is it defines the EINSTEIN in terms of a contraction
of the double dual of the curvature tensor, then states the equation
relating the RICCI tensor to the EINSTEIN tensor and the curvature scalar,
and leaves the derivation as an exercise. Specifically, exercise 13.12

Do you happen to know if a solution guide for MTW exists, for that matter?
(wait... a comprehensive solutions guide to MTW + MTW itself would
probably crush the scale... heck, crush the table they're set on. o_O)

Oh, Bianchi identities, while briefly mentioned already, don't really get
dealt with until later in the book. (Actually, chap 15, I think.)

Thanks anyways.

Psy-Kosh

On Jan 24, 3:56 pm, "Koobee Wublee" wrote:
On Jan 24, 11:11 am, "Igor" wrote:

The Einstein tensor has zero covariant divergence. Ricci doesn't.

What does that mean?

If you don't know, look it up.

IIRC, the Einstein tensor is derivable from a contraction on the
Bianchi identities of the Riemann Curvature. [...]

Bullsh*t! The Einstein tensor can only be derived from the
Einstein-Hilbert Lagrangian.

This is coming from the same guy that doesn't know how to transform a
domain.

Formal education is often a good cure for ignorance. Stupidity, on the
other hand, is incurable.

On Jan 24, 6:21 pm, Psy-Kosh wrote:
The Einstein tensor has zero covariant divergence. Ricci doesn't.
IIRC, the Einstein tensor is derivable from a contraction on the
Bianchi identities of the Riemann Curvature. You should be able to
find it in just about any good GR textbook. Doesn't MTW derive this in
an understandable way?If it derives it, it does so elsewhere in the book that I haven't seen yet.

So far what I've seen is it defines the EINSTEIN in terms of a contraction
of the double dual of the curvature tensor, then states the equation
relating the RICCI tensor to the EINSTEIN tensor and the curvature scalar,
and leaves the derivation as an exercise. Specifically, exercise 13.12

Do you happen to know if a solution guide for MTW exists, for that matter?
(wait... a comprehensive solutions guide to MTW + MTW itself would
probably crush the scale... heck, crush the table they're set on. o_O)

I really don't know about that one. If there is, I've never seen it.

Oh, Bianchi identities, while briefly mentioned already, don't really get
dealt with until later in the book. (Actually, chap 15, I think.)


Here's a good link that shows how the Einstein tensor is derivable from
the Bianchi identities:

http://www.mth.uct.ac.za/omei/gr/chap6/node14.html

On Jan 24, 11:56 am, "Koobee Wublee" wrote:
On Jan 24, 11:11 am, "Igor" wrote:

The Einstein tensor has zero covariant divergence. Ricci doesn't.

What does that mean?

The true disciple of Riemannian geometry doesn't know what a covariant
derivative is.

You can't pay for this kind of comedy, folks.


IIRC, the Einstein tensor is derivable from a contraction on the
Bianchi identities of the Riemann Curvature. [...]
Bullsh*t! The Einstein tensor can only be derived from the Einstein-Hilbert Lagrangian.

Only?

Section 14.2 of MTW would be illuminating. Hell, I think all of it
would be.

On Jan 25, 9:36 am, "Igor" wrote:

Here's a good link that shows how the Einstein tensor is derivable from
the Bianchi identities:

http://www.mth.uct.ac.za/omei/gr/chap6/node14.html

You got to be kidding me with that convoluted derivation of the field
equations.

On Jan 24, 10:39 am, Psy-Kosh wrote:
What the subject says. Working through Gravitation(MTW), waited until I
was in mid chap 14 before going back and having another look at this bit,
but am still stumped here. (ie, page 326, problem 13.12b)

Tried some index jiggerpokery but am still stumped. Any help would be
appreciated, thanks.

Ugh. It looks like a bit of index gymnastics. The problem is not to
derive Einstein's field equation but to verify the usual relationship
between G^a_b and R^a_b given the definitions of both as contractions
of certain tensors (*Riemann* in the first case and the plain Riemann
in the second, where "*" is the Hodge star).

I think I'll pass... :-)

--
Jan Bielawski

On Jan 25, 1:16 pm, "Koobee Wublee" wrote:
On Jan 25, 9:36 am, "Igor" wrote:

Here's a good link that shows how the Einstein tensor is derivable from
the Bianchi identities:

http://www.mth.uct.ac.za/omei/gr/chap6/node14.htmlYou got to be kidding me with that convoluted derivation of the field
equations.