Quantum Aspects of Black Holes - Lecture 2

Delve into the quantum aspects of black holes in this advanced lecture by Juan Maldacena, part of the Kavli Asian Winter School on Strings, Particles and Cosmology. Explore the full Schwarzschild solution, the ER=EPR conjecture, and the AMPS paradox. Examine simple models of 2D gravity and nearly AdS2 gravity, including perturbative quantum corrections. Investigate gravitational interactions between highly boosted particles in flat space and their time delay effects. Analyze chaos in classical and quantum systems, focusing on out-of-time-order correlators and operator growth. Discover why black holes are considered maximally chaotic and how this insight inspired bounds applicable to many-body quantum systems. Engage with complex topics in theoretical physics, including the S-matrix and long-time behavior in chaotic systems.

Full Schwarzschild solution
What should we make of these?
Full Schwarzschild solution = entangled Sta Juan Maldace.
ER = EPR
Some interesting lessons
AMPS paradox
A side comment
Simple models
A particularly simple 2d theory of gravity
Nearly AdS2 gravity
Infinite number of other configurations with the same
A particularly simple 2d theory of gravity
Dynamics
Perturbative quantum gravity
This includes al perturbative gravity corrections.
End of lecture 1
Dynamics
[Demo]
Is this relevant
Gravitational interactions between highly boosted particles in flat space.
The main effect is a time delay.
There is an interaction between the infalling particles and the outgoing particles.
Chaos in classical systems
If we look at a thermal state,
Quantum mechanical system
Out of time order correlator
Operator growth picture
OTOC as the overlap between two states
OTOC = Scattering amplitude
Black holes are maximally chaotic
Q&A
Thinking about black holes inspiration for a bound that applies to any many body quantum system
Chaos in the S-matrix
Longer times