Bekenstein bound and Cauchy's integral formula

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SUMMARY

The Bekenstein bound asserts that the information content of a region in space correlates with its surface area rather than its volume. In contrast, Cauchy's integral formula establishes that the values of a holomorphic function within a closed curve are determined solely by its values on the curve itself. The discussion highlights the conceptual similarities between these two principles and seeks references that connect the Bekenstein bound to holomorphic functions, particularly through the Cardy formula, which relates to black hole entropy calculations.

PREREQUISITES
  • Understanding of Bekenstein bound and its implications in theoretical physics.
  • Familiarity with Cauchy's integral formula and its application in complex analysis.
  • Knowledge of holomorphic functions and their properties.
  • Basic concepts of black hole thermodynamics and entropy.
NEXT STEPS
  • Research the Cardy formula and its application in black hole entropy calculations.
  • Explore the relationship between information theory and quantum gravity.
  • Investigate papers that discuss the intersection of Bekenstein bound and complex analysis.
  • Study advanced topics in theoretical physics that involve holomorphic functions.
USEFUL FOR

The discussion is beneficial for theoretical physicists, mathematicians specializing in complex analysis, and researchers exploring the connections between information theory and black hole physics.

haael
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Bekenstein bound states that the amount of information in some region of the space is proportional to the surface of the region, not the volume.

Cauchy's integral formula states that for any holomorphic function on a complex plane inside some region defined by a closed curve the values of that function inside that region are completely defined by the values of that function on the curve.

These statements sound strikingly similar. I immediately did a quick googling, but didn't found anything satisfactory. Does anyone know about some paper that tried to explain Bekenstein bound in terms of holomorphic functions?
 
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Not directly, I think, but the Cardy formula used in calculation of the entropy of some black holes uses the properties of holomorphic functions eg. http://relativity.livingreviews.org/Articles/lrr-2012-11/ section 3.1.
 
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