Steve Lawrence (sal the programmer) wrote:
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.htmlI took a look at that page.

It sounded very familiar.

Some of the text on that page is lifted word for word from Schutz's 1985
book, "A first course in general relativity", page 174. The derivation
given on the web page is the same as Schutz's, very slightly altered.

Who cares about convoluted derivations? shrug Especially, you know
the answer already.

Example: Text from the web page by Peter Dunsby, 1996 (cut and paste from
the browser window):

It is more like voodoo mathemagics. shrug

"The tensor G^uv is constructed only from the Riemann
tensor and the metric, and it is automatically divergence free as an
identity. It is called the Einstein tensor, since its importance for
gravity was first understood by Einstein. We will see in the next chapter
that Einstein's field equations for General Relativity are..."

There is only one valid way to derive the field equations in which the
Einstein tensor reveals itself. This is not it.

Text from the book by Schutz, 1985 (typed in from the book):

"The tensor G^ab is constructed only from the Riemann tensor and the
metric, and is automatically divergence free as an identity. It is called
the Einstein tensor, since its importance for gravity was first
understood by Einstein. (In fact we shall see that the Einstein field
equations for GR are..."

Introducing the Einstein tensor before the field equations is utterly
absurd and useless. shrug Einstein tensor suits no useful purpose
except in the form of the field equations. shrug

I looked at a couple other pages. Dunsby seems to have been "heavily
inspired", shall we say, by Schutz; his derivations follow along line by
line with Schutz and his sentences typically differ slightly from what
Schutz wrote.

Spread the word. The emperor's clothes are beautiful.

Does Dunsby acknowledge his debt to Schutz anywhere on that site?

Does anyone care on something thoroughly convoluted? shrug

On Jan 26, 10:27 pm, "Koobee Wublee" wrote:
Steve Lawrence (sal the programmer) wrote:

[...]

If you are going to take snipes at other people's qualifications, you
had damn well better be prepared to rationalize your own.

I don't even see why you talk about general relativity.

You had never seen the proof of Birkhoff's theorem until it was shown
to you recently though that did not stop you from commenting on it. You
have no idea what a covariant derivative is. You think tensors are
coordinate dependent. You think you can introduce curvature via a
coordinate transformation. You reject explicit calculations that prove
you wrong. You reject trivial assumptions as "convoluted" like setting
R_uv = 0 in vacuum.

You seriously need to shut the **** up.