After my marathon 50 laps yesterday, I crashed in the afternoon. And not just a little afternoon siesta, either – I was out for three hours! Yesterday evening Ekaterin and I had dance practise, which was most enjoyable. We didn’t get around to going firefly hunting though. Maybe another time.
This morning, I continued my week of early mornings, and got to the pool at about ten past eight. I felt that I could have done 50 laps and then some quite happily, but they kicked me out of the pool at 46. I forced myself to stay awake today; it’s going to be an early night to bed tonight. However, I also had a wonderfully productive day, and managed to nut out the problem I’ve been working on for a few weeks. Well, I managed to nut out the details of what other people have already done, but I managed to do it analytically, when they were doing it numerically, so I was rather proud of myself
The pinnacle of my success is in the form of the following plot, which to the uninitiated is known as a Penrose diagram. The squiggly lines at the top and bottom represent the singularity associated with a black hole and white hole, respectively. The black outer lines (the diagonal ones) are known as future and past null infinity (the future ones are up the top). The dashed lines show curves of constant observer time and areal radius (red and blue dashed curves, respectively). The strong red lines are event horizons. None of that is particularly special. What is special are the green curves, which define a foliation of spacetime into spacelike hypersurfaces. These particular green curves have the special name of “maximally sliced trumpet embeddings”, and they’re of some importance in solving the equations of general relativity for black holes on a computer.
Tomorrow I’m planning on getting to the pool a little earlier, and seeing if I can’t crack a mile. I’m excited to move onto the next step in this little mini project, too.
One other thing I’d like to share with you all. While I was riding home yesterday, this lovely thing was sitting just outside my apartment complex. She didn’t seem at all perturbed at the funny human trying to take photos of her.