Complexity, chaos and black hole microstates

Research output: ThesisPhD Thesis

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The black hole information paradox, the question whether information is pre-served in the presence of black holes, is one of the main puzzles of theoretical physics today. Resolving it means to solve a quantum mechanical problem in a strong gravitational field which is vital to the understanding of quantum gravity. In addition, it is known that black holes carry a large amount of information, but it is not understood how this information is carried by the black hole. In other words, what are the microstates that make up the black hole? It is widely believed that the answers to these questions can be found within the framework of the holographic principle, relating a gravitational theory to a theory without gravity in one dimension less. Recently, new entries to the holographic dictionary relating the quantum computational complexity of a region in the boundary theory to various quantities in the gravity theory have been proposed. While quantum computational complexity can be defined in a rather elegant way, its computation is very hard for systems involving more than a few degrees of freedom. We have therefore developed an upper bound that we have been able to determine numerically for a range of quantum mechanical systems. Furthermore, we have demonstrated that this bound can distinguish reliably between chaotic and integrable behavior in these systems. The second question raised in the first paragraph has been answered for specific black holes in the context of string theory, where explicit microstates have been identified more than twenty years ago. The so-constructed microstates are called fuzzballs. Later, it was shown that some of these microstates correspond to smooth classical geometries without any horizon, so-called microstate geometries. On the other hand, more recent developments using holography have connected probes of quantum chaos in the boundary theory, in particular the out-of-time-order correlator (OTOC), to scattering problems in the gravity theory. In black holes, the scattering happens close to the horizon. Wehave computed the OTOC in the black hole corresponding to a well-studied microstate geometry, the (1, 0, n) superstrata, and we have studied how the OTOC is modified in the horizonless microstate geometry.
Original languageEnglish
Awarding Institution
  • Vrije Universiteit Brussel
  • Craps, Ben, Supervisor
Award date29 Jun 2023
Publication statusPublished - 2023


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