How much energy from gravitatational waves does the sun absorb? I was wondering how much energy from gravitational waves the sun could absorb since it is so big and also has a massive gravitational pull. Is it possible for the sun to trap gravitational waves within its volume and eventually get absorbed by the hydrogen? If not, how would it not be possible? This question was based on the fact that maybe pulsars could absorb gravitational waves and spin because of it. I am wondering whether such a thing would make the sun spin faster or get hotter.
 A: That's an interesting question, but also a hard one.  There isn't a lot of convincing work dealing with this regime — mostly people have been interested in "tenuous" matter like the interstellar/intergalactic medium, to understand whether we'd even see distant gravitational-wave sources.  For example, see this paper, another paper by Hawking, or this paper by Dyson.  Hawking's result is probably most relevant, but it's also hard to compute, and relies on viscosity in the Sun, which I can't find good numbers for.  A full treatment would probably require some sort of plasma dynamics and detailed stellar structure.
Just for a rough idea of what we're talking about, Dyson calculates absorption via elastic motion of the Earth's surface, which is probably a terrible approximation to the Sun's behavior, but comes up with a fraction $10^{-21}$ of the energy being absorbed.  My guess is that the Sun would absorb a fraction somewhere very roughly in that neighborhood — I wouldn't be surprised at $10^{-10}$ or $10^{-30}$.
So it may be helpful to look at how much energy from a typical binary black-hole merger actually passes through the Sun.  Looking at the JSON file supplied with the LIGO/Virgo/KAGRA catalog, it turns out that the first detection, GW150914, was the best case for this (as of this writing).  The total energy given off was $3.1 M_\odot\, c^2$, and was about $440\,\mathrm{Mpc}$ away.  I calculate that just over $10^{18}\,\mathrm{J}$ of gravitational-wave energy passed through the Sun from that event.
Now, remember that the Sun would absorb only a small fraction of that energy.  But for comparison, the Sun emits about $4\times 10^{26}\,\mathrm{J}$ every second.  So even if the Sun absorbed all that gravitational-wave energy (which it wouldn't), it would only gain about one billionth the energy that it emits every few seconds.
Of course, any energy it does absorb would indeed make the Sun that tiny bit hotter.  But the energy would be absorbed symmetrically, so there wouldn't be any change in angular momentum at all.  In fact, because angular momentum would be conserved, and the temperature increased ever so slightly, you might argue that the Sun would increase in size eeeevver so slightly, which means that its rotation rate would have to slow down.  But these effects would surely be immeasurably small compared to random fluctuations in all parts of the Sun.
