[ET Trac] #2549: inlcude FLRWSolver in ET

[Chi Tian]

#2549: inlcude FLRWSolver in ET

 Reporter: Roland Haas
   Status: new
Milestone: ET_2022_05
  Version: development version
     Type: enhancement
 Priority: major
Component: 

Comment (by Chi Tian):

Hi all, I have reviewed the documents and majority of the the codes. At least at physics level, everything looks fine to me. Only some tiny issues regarding the way FLRWSolver dealing with the extrinsic curvature:

1. It seems there is a typo in Eq. \(10\) in the document, where minus sign is missing \(at least for the case where the author mentions “Setting f =1/3 and n=2 in the above yields ∂tα=∂ta for EdS“\).
2. The name of the variable `kvalue` in several `flrw_*.f90` files seems a little confusing. From its name, it seems this variable represents the extrinsic curvature K. However, its true value seems to be `3 * kvalue` if my understanding was correct.
3. By following the gauge condition `\dot{\alpha} = f * K`, effectively it is setting the coordinate time to something closed to the conformal time `\eta`, and the value of `\alpha` will grow roughly following the growth of the scale factor `a`. Could this possibly introduce numerical instabilities to `GRhydro` when starting from a very high redshift, and universe keeps expanding for quit long? Since I would guess most of astrophysical GR simulations may choose gauge conditions that make `\alpha` close to 1. 

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Ticket URL: https://bitbucket.org/einsteintoolkit/tickets/issues/2549/inlcude-flrwsolver-in-et
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