# preserve information in a black hole

How is information preserved on the surface of a black hole? Is there an compression algorithm for storing the information?

1. What if there is a uniformaly complex object dropped to the black hole? Then there will be no compression of information.

2. How is there enough space on the surface (2D) to encode something which is in 3D. The planck distance is the same in the black hole as in the universe. So how can the black hole encode information about an object in 3D that is both uniformly complex and as dense as the black hole? Or is there a law that says 3D objects cannot be more dense then some level - which is sufficiently sparse so that when collapsed to a black hole all its information can be encoded on the surface of a sphere? Has this limit been found - given that a sphere has the lowest surface to volume of any object: https://en.wikipedia.org/wiki/Surface-area-to-volume_ratio ?

Edit: added '3D' to first sentence of 2. question.

• Have you read en.wikipedia.org/wiki/Bekenstein_bound ? – PM 2Ring Jan 13 '19 at 10:30
• I'm voting to close this question as off-topic because while a black hole is an astronomical object, this query is theoretical physics-based – Rory Alsop Jan 13 '19 at 13:54
• Your question seems to have a strong digital influence with discrete things. Current physics see the world as completely analogous on the deepest level we know (and indeterministic). There is no problem with information compression, in an analogous world you can compress any signal by decreasing the length of the coordinates. Also I feel that it can't happen over any limit; but it is just my feeling, as far I know the spacetime seems to be continuous at least until the plank length ($\approx 10^{-41} m$). – peterh - Reinstate Monica Jan 13 '19 at 15:00
• @Rory I thought we'd stop doing that? astronomy.meta.stackexchange.com/questions/450/… – user1569 Jan 13 '19 at 21:15
• @jan - I had a look at that, and this one feels very much in the theoretical space, so that doesn't apply. – Rory Alsop Jan 13 '19 at 22:02

How is information preserved on the surface of a black hole?

We have no evidence that it is. We have some claims of this nature, associated with the holographic principle. But I'd say the physics concerned is hypothetical and speculative. It isn't in the same league as general relativity, which is one of the best tested theories we've got. See Clifford M Will's paper on the confrontation between general relativity and experiment for details of that.

Is there an compression algorithm for storing the information?

Not that I know of.

What if there is a uniformly complex object dropped to the black hole? Then there will be no compression of information.

Instead there will be a gamma ray burst. Friedwardt Winterberg wrote about this. See the 2013 AMPS paper an apologia for firewalls. Tucked away in the conclusion is footnote 31, containing a reference 87 to Winterbergâ€™s 2001 paper gamma ray bursters and Lorentzian relativity. I'm confident that Winterberg is essentially correct.

How is there enough space on the surface (2D) to encode something which is in. The planck distance is the same in the black hole as in the universe. So how can the black hole encode information about an object in 3D that is both uniformly complex and as dense as the black hole?

I don't think it can.

Or is there a law that says 3D objects cannot be more dense then some level - which is sufficiently sparse so that when collapsed to a black hole all its information can be encoded on the surface of a sphere? Has this limit been found - given that a sphere has the lowest surface to volume of any object: https://en.wikipedia.org/wiki/Surface-area-to-volume_ratio?

As far as I know there is no law or limit. And as far as I know there is no evidence to support the holographic principle. I for one do not take it seriously. But please advise if you receive any useful answers about this subject on any other website.

• This lecture by Prof Susskind explains question 2. youtube.com/watch?v=yMRYZMv0jRE Quantum mechanically the information that can be stored on the horizon is finite, and as Prof Susskind says its limited by the planc distance. This was discovered byjacob bekenstein in 1972. – Endre Moen Jul 2 '20 at 19:20