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Logarithmic Corrections to Kerr Thermodynamics.

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Quantum corrections to black hole entropy reveal 3/2logT_{Hawking} behavior in near-extremal Kerr black holes. This study addresses infrared divergences and predicts a lifting of ground state degeneracy for extremal Kerr black holes.

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Area of Science:

  • Theoretical Physics
  • Black Hole Thermodynamics
  • Quantum Gravity

Background:

  • Loop corrections from massless particles yield 3/2logT_{Hawking} entropy corrections in charged black holes.
  • Near-extremal charged black holes exhibit dominant thermodynamic behavior from these corrections.

Purpose of the Study:

  • Adapt analysis of loop-induced entropy corrections to near-extremal Kerr black holes.
  • Investigate and resolve infrared divergences in the Euclidean near-horizon extreme Kerr (NHEK) partition function.
  • Characterize quantum-corrected entropy and ground state degeneracy of extremal Kerr black holes.

Main Methods:

  • Analysis of normalizable zero modes in the NHEK metric, analogous to AdS2xS2.
  • Employing path integral over zero modes, leading to infrared divergence.
  • Regulating divergence by including finite temperature corrections in the NHEK scaling limit, creating a "not-NHEK" geometry.

Main Results:

  • The "not-NHEK" geometry resolves infrared divergences by lifting zero-mode eigenvalues.
  • Quantum-corrected near-extremal entropy displays the characteristic 3/2logT_{Hawking} behavior.
  • Prediction of a lifted ground state degeneracy for the extremal Kerr black hole.

Conclusions:

  • The study successfully adapts entropy correction analysis to Kerr black holes.
  • The findings align with the Schwarzian model and provide insights into quantum black hole thermodynamics.
  • The research predicts observable effects on the ground state degeneracy of extremal Kerr black holes.