23 - Thursday

Met with Tim today. Discussed the choice to flip the sign of the null geodesic equation when crossing the horizon, this prevents opposing rays from being focused together and fixes some bizarre issues with the Schwarzschild coordinates when comparing inside vs outside the horizon. I'm going to have a look to see if it's possible to directly map the Gullstrand-Painleve null geodesics to the modified Kruskal coords, as I think these don't require a sign flip.

Also going to look at the case for a growing black hole in a thermal bath. At first I can just reverse the sign of the mass time dependence, but will need to look at finding a more rigorous power law in future.