16 - Thursday

Meeting with Tim and Josh today. #

We went over some of the plots Josh made in mathematica, it turns out that instead of using Nic's dynamic Kruskal coordinates (which introduces paradoxes, things like lengths becoming non-physical) he created sets of plots where the coordinates are static and use the final or inital mass, and then map the Schwarzschild trajectories during the evaporation across. I'll need to decode how exactly he does this, as the mapping will be time dependent.

The other aspect of these coordinates is that it is constructed to make trajectories through the origin continuous. In the standard Kruskal coordinates, the trajectories through the origin are reflected and move upwards into region II. Currently we are interested in looking at trajectories that cross the origin and move between regions I and III, however it would also be interesting to take a look at if we traced the rays that are normally reflected into region II backwards and made them continuous.

Some other interesting situations to look at:

• There are a number of different choices for time when choosing the evaporation power law, Schwarzschild is probably a safe bet. At the very least it's fine to make an assumption here and correct it in future if it causes issues.
• In the current state of the universe, all black holes have a temperature far far less than the background 3K. As such, these black holes are actually growing rather than evaporating, even if they aren't swallowing any matter. It's an interesting case of thermodynamics where the systems aren't moving to equilibrium, the black hole absorbs energy, but becomes colder as a result. Looking at trajectories in this case could prove insightful.
• We can also look at trajectories for massive particles (\(\mathrm{d}s^2<0\)). Which can result in some unique trajectories in these extreme metrics.