[Users] Evolution of Schwarzschild Initial Data How?

[Ian Hinder]

On 15 Feb 2010, at 15:21, fahad nasir wrote:

> Hi,
>
> Im not sure is this the correct forum to ask this question. Well  
> coming to the point. I have evolved a simple static Schwarzschild  
> initial data and evolved wiht ADM formalism. The simple parameter  
> file is as under..
>
>
> admbase::evolution_method = "ADM"
> adm::method= "stagleap"
> admbase::initial_lapse = "one"
> admbase::lapse_evolution_method = "1+log"
>
> admbase::metric_type = "static conformal"
> admbase::initial_data = "schwarzschild"
> idanalyticbh::mass = 1.0
>
>
> Im still confused how can you evolved Schwarzschild initial data  
> (which surely a static solution), even in isotropic coordinates.

It depends on the gauge you use.  Whilst the initial data is in  
isotropic coordinates, if you evolve with 1+log lapse the evolved  
solution will no longer be in Schwarzschild isotropic coordinates, as  
the lapse you compute from the isotropic Schwarzschild metric does not  
satisfy the 1+log lapse condition.

> I was also able to extract Weyl scalars which shows signs of some  
> kind of waves. Surely this is not due to lapse because Weyl scalar  
> is gauge invariant quantity. My is question is simple..
>
> Is this because of black hole is initially perturbed initially ?
>
> Or there is some kind of numerical stability  which grows in time ?
>
> Or some kind of non-symmetry of black hole ?

You could check whether it is a numerical effect by computing the  
solution at different resolutions.  If the Weyl scalars converge to  
zero then you are just seeing finite differencing error.  If they  
appear to "blow-up" as you increase the resolution, then you are  
probably seeing an instability, but I would be surprised at this  
(though this is ADM, which will be unstable in general).

If there are "gauge waves" in your solution, which I would expect from  
a 1+log slicing condition, then while the Weyl scalars should be  
constant at a given areal coordinate R, your solution coordinate r  
will be different to the areal coordinate R.  I'm not sure if this is  
the reason for the waves that you see though.

-- 
Ian Hinder
ian.hinder at aei.mpg.de