# Trace reverse perturbation

1. Nov 22, 2012

### nikhilb1997

From the tensor, $\bar{h}^{ij}=h^{ij}-1/2\eta^{ij}h$
Where, h=$h^i_i$,
Prove that $\bar{h}=-h$,
Where, $\bar{h}=\bar{h}^i_i$

Last edited: Nov 23, 2012
2. Nov 22, 2012

### TSny

Hello, and welcome to PF!

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Your Latex formating will work if you use $instead of . 3. Nov 23, 2012 ### andrien just contract both sides with ηij. 4. Nov 23, 2012 ### nikhilb1997 I tried it but I guess I made a mistake since I got h(bar) on the left side and on the right side I got h-1/2h. Please help. 5. Nov 23, 2012 ### andrien No,you get on the right side h-(1/2)(4)h=h-2h=-h,can you verify it? 6. Nov 23, 2012 ### nikhilb1997 I had to find the absolute value of the$n_{ij}## matrix. Is this is where I went wrong. Thank you very much

Last edited: Nov 23, 2012
7. Nov 23, 2012

### andrien

Not necessarily,after contraction you get
ηijηij00η0011η11
22η2233η33,
all others are zero,right.now this is =(1*1)+(-1*-1)+(-1*-1)+(-1*-1)=4,it does not depend on your signature.you can take as well as(-,+,+,+).

8. Nov 23, 2012

### nikhilb1997

Thanks a lot andrien.