/courses/serc-school/ Recent content in SERC School on Black Holes and Information on Suvrat Raju Hugo -- gohugo.io en © 2026 /courses/serc-school/notes-lecture-1/ Mon, 01 Jan 0001 00:00:00 +0000 /courses/serc-school/notes-lecture-1/ Lecture 1 covered the Schwarzschild Black Hole solution, which we derived assuming only spherical symmetry. We proved Birkhoff’s theorem. We also reviewed the gravitational redshift and the Kruskal extension, which shows that the horizon is locally a smooth region. Download PDF of Lecture Notes /courses/serc-school/lecture-2/ Mon, 01 Jan 0001 00:00:00 +0000 /courses/serc-school/lecture-2/ In Lecture 2, we reviewed the Oppenheimer-Snyder solution that shows how black holes can be formed via the collapse of dust. We also considered other kinds of black hole solutions, including the Reissner-Nordstrom black hole, and charged Kerr black holes. Download PDF of Lecture Notes /courses/serc-school/lecture-3/ Mon, 01 Jan 0001 00:00:00 +0000 /courses/serc-school/lecture-3/ In Lecture 3, we considered the causal structure of the R-N black hole. At first sight, this leads to an exotic Penrose diagram. But after we looked at this diagram more closely and considered the instability of the inner horizon, the conclusion was that, qualitatively, for realistic collapse leading to a charged black hole or a charged rotating black hole, the causal structure of the spacetime is much like the causal structure of the Oppenheimer-Snyder solution. /courses/serc-school/lecture-4/ Mon, 01 Jan 0001 00:00:00 +0000 /courses/serc-school/lecture-4/ In lecture 4, we complete our discussion of the Penrose process and frame the laws of Black Hole Thermodynamics. The rest of the lecture is an overview of what happens when we add quantum mechanics. We will review the old information paradox, which is a simple question of reversibility, and can be resolved rather easily. Then, we sketch more modern versions of the information paradox which are more subtle and may require us to accept that degrees of freedom in quantum gravity are (1) not exactly local and (2) state-dependent. /courses/serc-school/lecture-5/ Mon, 01 Jan 0001 00:00:00 +0000 /courses/serc-school/lecture-5/ In Lecture 5, we discussed the basics of QFT in curved space. Since, in a general spacetime, there is no canonical choice of a time coordinate, the notion of “particles” becomes observer-dependent. We discussed how the physics of two different observers, using a different basis of mode functions, was related by Bogoliubov transformations. We then started to apply this formalism to understand how flat space appears for accelerated observers by quantizing a free-field in Rindler coordinates. /courses/serc-school/lecture-6/ Mon, 01 Jan 0001 00:00:00 +0000 /courses/serc-school/lecture-6/ In lecture 6, we completed our discussion of the Unruh effect. The central result that for a set of observers in region I, using Rindler modes, even the Minkowski vacuum appears to be a thermal density matrix. We then applied this intuition to black holes. There we found that locally, the change of coordinates from Schwarzschild coordinates to Kruskal coordinates was very similar to the transformation between Rindler and Minkowski coordinates. /courses/serc-school/lecture-7/ Mon, 01 Jan 0001 00:00:00 +0000 /courses/serc-school/lecture-7/ In this lecture, we proceeded to derive the formula for Hawking radiation in two different ways. First, we examined Hawking’s original geometrical optics approach. This is useful because it gives us insight into where the radiation at future infinity originates from. Then, we started a more precise derivation using the properties of correlation functions in any smooth geometry. The geometry of the collapsing shell tells us that field correlators in position space have to have some universal properties. /courses/serc-school/lecture-8/ Mon, 01 Jan 0001 00:00:00 +0000 /courses/serc-school/lecture-8/ In lecture 8, we considered the “old information paradox”. This is the paradox, that appears to arise because Hawking radiation is thermal, and so this suggests that if we start with a pure state, that collapses to form a black hole, the process of Hawking radiation will convert it into a mixed state. Such evolution, from a pure to a mixed state would, of course, violate unitarity. But this is not really a paradox, because in large statistical systems, generic pure states look almost exactly like thermal states. /courses/serc-school/lecture-9/ Mon, 01 Jan 0001 00:00:00 +0000 /courses/serc-school/lecture-9/ In the last lecture, we considered the modern information paradox. This starts with Page’s observation that although unitarity tells us that the final radiation will be pure, we can get a stronger result by adding the assumption that the black hole is a “generic state”. In this situation, we expect that the von Neumann entropy of the outgoing radiation will start to decrease after, what is called the “Page time” (after roughly “half” the black hole has evaporated) and continue to decline monotonically to zero (at which point the outgoing radiation is pure).