Bekenstein bound and Cauchy's integral formula

In summary, the Bekenstein bound and Cauchy's integral formula both deal with the relationship between a region and its boundaries, stating that the information contained within the region is determined by what happens on the surface or boundary rather than in the volume. While there are some connections between these concepts, there is no direct explanation of the Bekenstein bound in terms of holomorphic functions, although the Cardy formula used in calculating black hole entropy does utilize the properties of holomorphic functions.
  • #1
haael
539
35
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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  • #2
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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1. What is the Bekenstein bound and how does it relate to physics?

The Bekenstein bound is a theoretical limit on the amount of information that can be contained within a finite region of space. It relates to physics through its connection to the laws of thermodynamics and black hole entropy. The bound states that the maximum amount of information that can be contained in a finite region is proportional to the area of its boundary.

2. How was the Bekenstein bound discovered?

The Bekenstein bound was first proposed by physicist Jacob Bekenstein in 1972 as a way to reconcile the laws of thermodynamics with the properties of black holes. He theorized that black holes have a finite amount of entropy, and thus a limit on the amount of information they can contain.

3. What is Cauchy's integral formula and how is it used in mathematics?

Cauchy's integral formula is a fundamental theorem in complex analysis that relates the values of a function at points within a region to its values on the boundary of that region. It is used to evaluate complex integrals and to solve boundary value problems in differential equations.

4. Who is Cauchy and what other contributions did he make to mathematics?

Augustin-Louis Cauchy was a French mathematician who lived in the early 19th century. Along with his work in complex analysis and calculus, he made significant contributions to the fields of algebra, number theory, and mathematical physics. He also developed the Cauchy distribution in probability theory and the Cauchy-Schwarz inequality in linear algebra.

5. How are the Bekenstein bound and Cauchy's integral formula connected?

The Bekenstein bound is related to Cauchy's integral formula through the concept of holography. This principle states that the information contained within a region can be encoded on its boundary. In physics, this is seen in the holographic principle of black hole entropy, where the information of the black hole is encoded on its event horizon. Similarly, Cauchy's integral formula relates the values of a function within a region to its values on the boundary, connecting the two concepts through the idea of boundary information encoding.

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