Grothendieck's point of view and complexity in the black hole paradox

Abstract

These are some speculations on how Grothendieck's point of view and the idea of complexity dynamics can come together in the problem of explaining the black hole information paradox. They are neither complete, nor final, but can seem like a new direction of research. If read as such they could prove useful to some researchers. The basic idea is that entanglement alone cannot fully account for the information extraction in black hole contexts. Complexity has been proposed as an alternative but remains a vague concept. I employ Grothendieck's point of view to expand the idea of entanglement entropy to a categorical context in which the objects (states) and their maps are considered together and the map space has additional topological and geometric structure that intermingles with the object set of the category via Sieves, Sheafs, and Toposes.

accepted for publication in this form in physica scripta

References in corpus (15)

• Black holes as mirrors: quantum information in random subsystems
• Quantum Computational Complexity -- From Quantum Information to Black Holes and Back
• How to Build the Thermofield Double State
• Flux Compactifications of M-Theory on Twisted Tori
• Efficient decoding for the Hayden-Preskill protocol
• Communication through quantum fields near a black hole
• Black Holes, Entanglement and Random Matrices
• Flux compactifications, twisted tori and doubled geometry
• Going beyond ER=EPR in the SYK model
• Bulk Reconstruction Beyond the Entanglement Wedge
• Quantization, Holography and the Universal Coefficient Theorem
• Quantization, Holography and the Universal Coefficient Theorem
• Remarks on Black Hole Complexity Puzzle
• Global aspects of the renormalization group and the Hierarchy problem
• The hidden quantum origin of gauge connections