# Black Hole Quantum Complexity

1. Aug 17, 2015

### Justice Hunter

Leonard Susskind talks about Black hole Quantum Complexity in one of his online lectures. I was wondering what you guys on the forums think about this, and what you guys think it means.

Here's a link to the video

He points out that the complexity increases linearly with time, and at the point of maximum complexity it cuts off and the singularity stops growing (in complexity). I'm interested in what the implications could be for this abrupt stop in complexity, and what is actually physically happening.

2. Aug 18, 2015

### phinds

Asking people to watch an hour video to answer your question is not a great idea. Say where in the lecture the pertinent stuff is.

3. Aug 19, 2015

### Physics Monkey

Classically the wormhole grows forever, but if the wormhole growth is dual to the growth of complexity in the quantum state then because complexity cannot be too large the classical picture of eternal wormhole growth must also break down.

If the entropy of the black hole is S and we model the system as S qubits then the maximum complexity is of order $e^S$.

Hence one expects the wormhole to grow for a time exponential in the entropy after which time something should happen. What happens remains mysterious on the gravitational side. It seems that the bulk geometry should in a sense dissolve and become very non-classical, perhaps via some instanton effect?