On 5 Mar 2020, at 15:42, Erik Schnetter 
<[email protected]<mailto:[email protected]>> wrote:

Beyhan

The QuasiLocalMeasures thorn can examine not only horizons, but also
other 2-surfaces. You can set up a surface that is large and which
encloses both the remnant and surrounding matter, but which is still
inside the emitted gravitational wave train. QuasiLocalMeasures can
then calculate the angular momentum contained inside that sphere.

I'm not familiar with the method as applied to neutron stars, but for a black 
hole system, I would probably try to do this by computing the "ADM angular 
momentum" of the spacetime, as well as the "Bondi angular momentum loss", their 
difference being the "remaining" angular momentum in the system.  I think this 
is fairly rigorous when done with masses, but I put the quotes around the 
angular momenta as I don't think these quantities are on as firm a footing.

In practice, one *should* be able to compute the "ADM angular momentum" on the 
initial data slice by evaluating the formula on a set of finite-radius spheres 
using QuasiLocalMeasures, similar to what Erik mentioned, and then 
extrapolating to spatial infinity.  I don't know if there are reasons why this 
won't work for neutron star initial data.  The "Bondi angular momentum loss" 
could be calculated by measuring the angular momentum flux in the emitted 
gravitational waves.  This is technically very challenging to get accurate.  
You need quite a lot of resolution, and wave extraction far enough out that you 
can cleanly extrapolate it to future null infinity.  There are also severe 
complications due to junk radiation.

So this approach is quite hard to implement.

--
Ian Hinder
Research Software Engineer
University of Manchester, UK

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