# Bekenstein bound and Cauchy's integral formula

1. Jun 3, 2014

### haael

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?

2. Jun 3, 2014

### atyy

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/ [Broken] section 3.1.

Last edited by a moderator: May 6, 2017