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Holographic Complexity and Thermodynamic Volume.

Abdulrahim Al Balushi1, Robie A Hennigar2, Hari K Kunduri2

  • 1Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.

Physical Review Letters
|March 30, 2021
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Summary
This summary is machine-generated.

We found that thermodynamic volume, not entropy, governs the holographic complexity of rotating black holes. This thermodynamic volume provides a lower bound for the complexity of formation in large black holes.

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Area of Science:

  • Theoretical physics
  • Quantum gravity
  • Black hole thermodynamics

Background:

  • Holographic complexity conjectures propose relationships between black hole properties and quantum information.
  • Previous studies often linked black hole complexity to entropy.

Purpose of the Study:

  • To investigate the holographic complexity conjectures for rotating black holes.
  • To explore the relationship between the complexity of formation and thermodynamic volume.
  • To propose that thermodynamic volume, rather than entropy, controls black hole complexity.

Main Methods:

  • Analysis of holographic complexity conjectures (complexity equals action and complexity equals volume).
  • Examination of rotating black hole solutions.
  • Mathematical derivation of relationships between complexity, thermodynamic volume, and entropy.

Main Results:

  • A direct relationship between the complexity of formation and the thermodynamic volume of rotating black holes was uncovered.
  • Thermodynamic volume is proposed as the primary controller of complexity of formation for large black holes.
  • The proposal generalizes previous findings and holds broader scope.

Conclusions:

  • The thermodynamic volume dictates the holographic complexity of formation for large rotating black holes.
  • A conjectured inequality on thermodynamic volume implies complexity of formation is bounded below by entropy.
  • This work refines our understanding of black hole complexity and its connection to geometric properties.