• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  The surface area to volume ratio of a sphere and the Bekenstein bound

+ 4 like - 0 dislike

I am trying to relate the surface-area-to-volume-ratio of a sphere to the Bekenstein bound. Since the surface-area-to-volume-ratio decreases with increasing volume, one would surmise that, per unit of volume, a small space is richer in information than a large one. How can this be and how can this bound work for black holes of various sizes?

Thank you very much Mr. Rennie. I appreciate and have investigated your answer. It turns out that I am familiar with the AdS/CFT correspondence and have sufficient understanding of the math (just barely) to be intrigued with the conjecture and, of course, the holographic theory. If the correspondence only works for a certain diameter black hole, the conjecture seems, to me, weak because of the changing surface-area-to-volume-ratio of a sphere. For myself, it would appear to be, likely, a mathematical curiosity or fluke. However, if, through some aspect that I do not understand, the correspondence holds for varying diameters, in fact, all diameters of black holes, then it seems quite astonishing, indeed. After searching for some time, I have once seen the amount described as trivial and possibly in another instance, that it may have something to do with informational redundancy. I’m afraid I cannot site these references as they were far too brief to be of any help.

This post imported from StackExchange Physics at 2014-03-07 13:38 (UCT), posted by SE-user Jim McKenzie
asked Oct 3, 2013 in Theoretical Physics by Jim McKenzie (20 points) [ no revision ]
You ask "How can this be?". If I had a really good answer to that I would be writing off to Stockholm for my Nobel prize. As far as I know (which is not much) the AdS/CFT conjecture (en.wikipedia.org/wiki/AdS/CFT_correspondence) is the best currently known approach to the issue.

This post imported from StackExchange Physics at 2014-03-07 13:38 (UCT), posted by SE-user John Rennie
blogs.discovermagazine.com/outthere/2013/08/20/… I think this answers my question. Apparently I understand the concept and can follow the math but I fail to believe it. As a black hole gets bigger and bigger, it is less and less dense, until eventually it isn't particularly dense at all. Faith in mathematics would seem to be my issue. Thank you for your help. Jim McKenzie.

This post imported from StackExchange Physics at 2014-03-07 13:38 (UCT), posted by SE-user Jim McKenzie

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights