In anticipation of an online conference celebrating the fiftieth anniversary of the publication of “The Four Laws of black hole mechanics” in December (to be announced), this mini-course is the second in a series of three, aiming to prepare students and young researchers for the main event.
We present the zeroth, first and second laws of black hole mechanics and the necessary mathematical tools for their understanding. Along the way, the student will be introduced to several concepts in general relativity and Lorentzian geometry, such as ADM mass and angular momentum, congruences of causal curves, Jacobi fields, Killing fields and bifurcate horizons, conjugate points, achronal boundaries, and energy conditions. We then briefly show how these laws turned into laws of black hole thermodynamics and their current status. The final lecture is dedicated to the physical aspects of black hole evaporation and contemporary lines of investigation.
Pre-Requisite: A standard introductory course in general relativity.