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Holographic complexity in black holes shows universal growth and saturation, similar to chaotic quantum systems. This behavior stems from specific pole structures and quantum chaos principles in spectral statistics.

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Area of Science:

  • Theoretical Physics
  • Quantum Gravity
  • Black Hole Physics

Background:

  • Holographic complexity is the bulk dual of quantum complexity, revealing black hole interior geometry.
  • The complexity = anything proposal connects quantum complexity to geometric properties.

Purpose of the Study:

  • Introduce a spectral representation for holographic complexity generating functions.
  • Analyze the universal behavior of holographic complexity measures.

Main Methods:

  • Utilize generating functions and their spectral representation.
  • Apply the residue theorem to analyze pole structures.
  • Connect to random matrix theory and spectral statistics.

Main Results:

  • Generating functions exhibit a universal slope-ramp-plateau structure.
  • Demonstrate that specific pole structures are necessary and sufficient for linear growth.
  • Show that spectral level repulsion causes late-time saturation.

Conclusions:

  • Holographic complexity exhibits universal dynamics analogous to chaotic quantum systems.
  • The study provides a theoretical framework linking quantum chaos to black hole complexity.
  • Confirms the origins of universal growth and saturation in holographic complexity.