May 18th 2022
Hi Tom Roberts –
I know very well who you are from sci.physics.relativity.
Perhaps as long as 7 years ago I talked to you there about
this metric:
|a 0 0 0 |
|0 a 0 0 | = the given spacetime metric
|0 0 a 0 |
|0 0 0 -a|
where: a = a(t) = "the scale factor" is a
simple well behaved function of time.
(Well behaved in the sense of the FRW
scale factor).
And I told you that plugging this metric into MAXIMA
I got the following result for the Ricci scalar:
6 a (a..) - 3 (a.)^2
_______________ = R = Ricci scalar curvature
2 a^3
(a..) = 2nd derivative of a w.r.t. tme
(a.) = 1st derivative of a w.r.t. time
And I asked you if you would plug the metric into
Mathematica and tell me if you got the same answer?
And you said that you did, and that "the answer was correct".
Notice that the answer MAXIMA gave, is very similar to
the well known Ricci scalar for the FRW metric !
And I assumed the difference was that I was not using
"conformer time".
That and also the fact that I used "a" for the scale factor
and not "(a^2)" !
At any rate, is there any chance that you could
enter that metric again in Mathematica and confirm
that the above result is actually true?
Some people have argued that the curvature is actually ZERO
It is a matter of considerable and urgent importance to
research (unrelated to gravity) in another academic field
which I will not mention (but related to psychology).
Thanks in advance, absolutely desperate,
Kurvature (George Hammond)