sign convention about 7.8. Induced metrics

[zhr moulaei]

Hello

I have some problem about sign convention in my calculation , i derived opposite sign in some parts .

In[29]:= CD[-a][n[b]]

Out[29]= CD[-a][

n[b]]

In[30]:= % // GradNormalToExtrinsicK

Out[30]= ExtrinsicKmetrich[-a, b] + Accelerationn[b]   n[-a]

in other parts yet i have opposite sign so i do not know how i  can fix this problem ? may i ask you answer to my question ?

Thank you very much  

[Thomas Bäckdahl]

Hi!

You have set $Extrinsicksign = -1; and $Accelerationsign = -1;, but the correct names are $ExtrinsicKSign = -1; and $AccelerationSign = -1;.

I hope this helps. Otherwise give us a minimal example pinpointing where the problem appears.

Regards
Thomas

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[zhr moulaei]

Thank you very much for your comment , my problem solved for your note. but i have other problem in the last part as : for deriving  induced Ricci Scalar i can not derive the correct result . may you help me?

In[129]:= inducedRicciScalar[] = % /. LapseRule // Expand

Out[129]= 

ExtrinsicKmetrich[-a, -b]   ExtrinsicKmetrich[a, b] + 

 ExtrinsicKmetrich[a, -a]   ExtrinsicKmetrich[

  b, -b] + RicciScalarcd[] - RicciScalarCD[] + 

 metrich[a, b]   metrich[c, d]   RiemannCD[-a, -c, -b, -d] - (2 (

cd[-a][

cd[a][

lapse[]]]))/lapse[] - 2  metrich[b, c]   n[a]  (

CD[-a][

ExtrinsicKmetrich[-b, -c]])