Holographic computational complexity innon-relativistic field theories

The aim of the project is to study the holographic complexity of black holes and black branes. We discuss basic concept of complexity. We see how quantum computational complexity is related to black hole physics. In the process we look at the difference between classical and quantum complexity. We solve for the holographic complexity of pure AdS and pure Lifshitz spacetime. We then study the AdS black hole in detail. We first try to find the nature of the maximal volume slice at a finite time, and then see the small black hole limit of it using the perturbation method. We perform similar late time analysis on the Lifshitz black hole as well. Lastly we try to understand the notion of complexity from first principle calculations. We retrace the procedure of calculating the complexity of a system and try to compare with the holographic quantity. However, although the two approaches are similar in a lot of aspects, they don't match perfectly. ii