Rescale Metric

[Nathan Moynihan]

Is it possible to rescale the metric by some particular factor, in such a way as I could then read off the associated objects dependant on the metric? (Riemann tensor, Christoffel symbol etc etc).

Thanks,

Nathan

[Alex Vañó Viñuales]

Something like the following? 

DefMetric[-1,metric2[-i,-j],cd2,ConformalTo->{metric1[-i,-j],factor[]}] , 

defined with respect to an existing metric metric1[-i,-j] and a previously defined conformal factor factor[]. 

You can then use the ConformalRules[metric1,metric2] to obtain the relation of the two. However, I do not know very well how that carries over to the associated objects. 

Cheers,

Alex

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[Nathan Moynihan]

Thanks, i'll give that a try :)

[Cyril Pitrou]

Hi,

In xPand I have defined a function Conformal which carries to general expressions

what Alex mentioned.

Once you have defined a metric g[.,.] and a scale factor a[] and a new metric which is conformally related to

(say ga2[.,.]) then you can do

Conformal[g,ga2][expr]

to transform a general expression.

In the expample notebooks of xPand, one is dedicated to the use of this Conformal[][] function.

Cheers,

Cyril