The connection variation with XTrash

[Halil Kuyrukcu]

I have tried taking variation of the following invariant (Krecthmann) with respect to the connection by using XTrash.

Lag= RiemannCD[-a, -b, -c, -d] * RiemannCD[a, b, c, d]

RiemannCD[-a, -b, -c, -d] :=  metric[-d, -e]*  (ChristoffelCD[e, -b, -f] * ChristoffelCD[ f, -a, -c]
- ChristoffelCD[e, -a, -f]*ChristoffelCD[f, -b, -c] -PD[-a]*[ChristoffelCD[e, -b, -c]] + PD[-b]*[ChristoffelCD[e, -a, -c]])  (AS USUAL)

 VarD[ ChristoffelCD[a, -b, -c], CD][Lag] // CollectTensors

The result is

- ChristoffelCD[c, d, e]  RiemannCD[-a, -d, b, -e] -
 ChristoffelCD[b, d, e]   RiemannCD[-a, -d, c, -e] -
 ChristoffelCD[d, -a, e]   RiemannCD[b, -d, c, -e] -
 ChristoffelCD[d, -a, e]   RiemannCD[b, -e, c, -d]
+ CD[-d][RiemannCD[-a, b, c, d]]
+ CD[-d][RiemannCD[-a, c, b, d]]


BUT MUST BE only  for example CD[-d][RiemannCD[d, -a, -b, -c]]

what is wrong?

[magma]

I think you mean xTras
xTrash is still under develoment :-)

[Halil Kuyrukcu]

6 Haziran 2015 Cumartesi 19:40:51 UTC+3 tarihinde Halil Kuyrukcu yazdı:

-----------------------------------------------------------------------------------------------------------------


Sorry yes xTras :))