[Users] w_lorentz factor in TOVSolver external.inc

[Bruno C. Mundim]

Hi Roland:

Roland Haas wrote:
> Bruno Coutinho Mundim wrote:
>> Hi Roland,
>>
>> your patch seems correct to me if w_lorentz_2 actually represents the
>> square of the lorentz factor. If it does, then we would have to modify
>> in other parts of the file where it is being consistently defined as
>> w^2=1-v^2.
> Thanks. I had not noticed those.
> 

After looking at the equations carefully yesterday, I would strongly
suggest that you apply your patch to all definitions of w_lorentz_2 in
external.inc. The equations there do follow the Valencia formulation as,
for example, it appears in eqs. 26 and 27 of Font et al's paper
(gr-qc/9811015).


>> However, I suspect that this definition of w is more in the
>> lines of equation 2.17 of Shibata et al's PRD68, 084020 (2003). I am
>> checking the equations again to see if this is true or not and will
>> get back to you later. 
> Thank you.
> 
>> Hopefully we can clear up any inconsistency
>> there.
> I was using the LRR article on GRHD, under Equ. (31):
> 
> http://relativity.livingreviews.org/Articles/lrr-2008-7/articlesu1.html#x6-30002.1 
> 
> 
> the PRD paper uses the four velocity u^j whereas LRR uses the three 
> velocity.
> 
> Frank: Are TOV_Velocity_[xyz] components of u^i, u_j, or v^i (in the 
> Valencia terminology)?
> 

TOV_Velocity_[xyz] are actually components of v^i. I think we should 
make this more explicit in the code. Maybe change these names to
TOV_Velocity_[xyz]_up. The same goes for the momenta sources.

Also I think we should indicate that the functions Set_Rho_ADM and 
Set_Momentum_Source are not setting the ADM sources but a rescaled
version of them. Particularly I would rather let the thorns calling
these functions to decide about rescaling them or not.

Cheers... Bruno.


> Yours,
> Roland
>