Logarithmic correction to the bekenstein-hawking entropy

Area of Science:

• Theoretical physics
• Quantum gravity
• Black hole thermodynamics

Background:

• The Bekenstein-Hawking formula provides a semiclassical entropy for black holes proportional to their horizon area.
• Previous work established an exact entropy formula for four-dimensional non-rotating black holes using quantum geometry and Chern-Simons theory.

Purpose of the Study:

• To reexamine the previously derived exact entropy formula for large black hole horizon areas.
• To identify and analyze corrections to the semiclassical Bekenstein-Hawking entropy.

Main Methods:

• Analysis of the exact entropy formula within the quantum geometry formulation.
• Investigation of boundary states in a three-dimensional Chern-Simons theory.
• Asymptotic expansion of the entropy formula for large horizon areas.

Main Results:

• The Bekenstein-Hawking contribution proportional to the horizon area was confirmed.
• A novel contribution proportional to the logarithm of the horizon area was discovered.
• Subleading corrections in inverse powers of the area were identified.

Conclusions:

• The study refines our understanding of black hole entropy beyond the semiclassical approximation.
• The findings provide new insights into the quantum structure of black hole horizons.
• The results support the quantum geometry formulation of black hole thermodynamics.