June 13, 2021

Conformal diagrams

During the 2021 pandemic some students asked me to extend my course of gravitational-wave physics and cover conformal diagrams. Because some of them could not attend all of the lectures, which were quite a few and very detailed, I made a summary for them.

I am very thankful to my friends Leor Barack, Kostas Tzanavaris and Nikos Chatzarakis.

If you are in China, you will not have access to youtube. In that case, you can access the videos on bilibili.

01 – Space-time diagrams and flat spaces (42 min)

02 – Schwarzschild spacetime, vacuum solution in spherical symmetry (57 min)

Infalling Schwarzschild spacetimes ahead.

03 – Schwarzschild spacetime, curvature “in spite” of vacuum (16min)

04 – Schwarzschild spacetime, continuation (1h 13min)

05 – Noether’s theorem and Killing vector fields (28 min)

06 – The Kerr solution, Penrose conjecture and Dafermos and Luk’s 2017 results (1h)

07 – The Kerr solution and the C^0 extension, second part (26min)

08 – The gravitational collapse and the apparent horizon (43min)