Jerusalem Lectures on Black Holes and Quantum Information

TL;DR

These lectures survey the quantum information perspective on black holes, outlining Hawking radiation, the information paradox, and the development of firewall ideas. They integrate traditional black hole thermodynamics with holographic duality (AdS/CFT), explaining how entanglement, scrambling, and the RT/HRT proposals recast the problem in a unitary, holographic framework. The notes discuss key concepts such as the Page curve, the thermofield double state, and the interior-exterior dictionary, and present several interior proposals (including computational complexity and postselection) while also highlighting unresolved tensions and the need for a deeper theory of quantum gravity. Overall, the work frames black hole information as a testbed for quantum gravity, leveraging quantum information tools to probe the consistency and structure of spacetime at the horizon.”

Abstract

In these lectures I give an introduction to the quantum physics of black holes, including recent developments based on quantum information theory such as the firewall paradox and its various cousins. I also give an introduction to holography and the AdS/CFT correspondence, focusing on those aspects which are relevant for the black hole information problem.

Figures (27)

• Figure 1: The $XT$ plane of the Kruskal extension. Lines of constant $U$ and $V$, or in other words radial null geodesics, are straight lines with slope $\pm \pi/4$. Lines of constant $r$ are hyperboloids centered at the origin, with the blue regions having $r>1$ and the red/green regions having $r<1$. The horizons are the dashed lines. The original exterior region is the right light blue wedge, the new exterior is the left blue wedge, the future interior is in green, and the past interior is in red. It is manifest that no radial null geodesic can escape the future interior into one of the blue regions, and it is also clear that no null geodesic connects the right and left blue wedges.
• Figure 2: On the left, the full Minkowski space is the pink wedge in the $RT$ plane. Radial light rays move on lines of slope $\pm \pi/4$. Some slices of constant $t$ are shown in blue and a slice of constant $r$ is shown in red. On the right we formalize this into a genuine Penrose diagram.
• Figure 3: The Penrose diagram of de Sitter space. The $\mathbb{S}^2$ shrinks to zero size on both the left and the right boundaries, while it grows to infinite size at $i^{\pm}$. Note that here $i^\pm$ are each spacelike surfaces instead of just points; it is this property that leads to the presence of horizons.
• Figure 4: The Penrose diagram for the Schwarzschild geometry. The $\mathbb{S}^2$ shrinks to zero size only at the singularities at the top and bottom horizontal lines. There are two copies of the asymptotic boundaries of Minkowski space, one on either side. For convenience the horizons are marked with dashed lines.
• Figure 5: Classical black hole formation. On the left we have a black hole forming from the collapse of a cloud of massive particles, shown in orange. On the right we have a black hole forming from the collapse of a spherical shell of photons. In both cases the top boundary is the singularity, the left boundary is the origin of polar coordinates, and the other boundaries are the usual asymptotic ones for Minkowski space. In the right-hand figure, the geometry above the orange line is exactly a piece from the upper right corner of the Schwarzschild geometry, while below it we have a piece of Minkowski space. As usual the horizon is a dashed line.