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Complexity Growth Rate in Lovelock Gravity.

Pablo A Cano1,2, Robie A Hennigar3, Hugo Marrochio1,3

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We calculated the late-time growth of complexity for charged black holes in Lovelock gravity. The growth rate depends on internal energies and reproduces known results with corrections, showing complexity can plateau for low-mass black holes.

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Area of Science:

  • Theoretical Physics
  • Quantum Gravity
  • Black Hole Physics

Background:

  • The complexity=action framework offers insights into black hole physics.
  • Understanding the late-time growth of complexity is crucial for quantum gravity.
  • Lovelock gravity provides a framework for higher-order gravitational theories.

Purpose of the Study:

  • To compute the late-time growth of complexity for charged black holes in Lovelock gravity.
  • To analyze the contributions of different components within the Wheeler-DeWitt patch.
  • To investigate corrections to the standard 2M/π result.

Main Methods:

  • Application of the complexity=action framework.
  • Calculation of late-time contributions from the joints of the Wheeler-DeWitt patch.
  • Analysis of charged black holes in Lovelock gravity.

Main Results:

  • The late-time growth rate is determined by the difference in internal energies of the inner and outer horizons.
  • For large masses, the result approaches 2M/π with corrections from Lovelock couplings.
  • A minimum mass was identified below which black hole complexity remains constant.

Conclusions:

  • The complexity=action framework successfully describes black hole complexity in Lovelock gravity.
  • Corrections to the growth rate depend on the specific gravitational theory.
  • The existence of a minimum mass suggests novel behaviors in black hole thermodynamics.