# Event horizon link to entropy

1. Oct 24, 2015

### Alicowie

I am by no means an expert in physics being largely self taught (day job is a medical student) but have an avid interest in trying to understand the fundemental nature of our universe. In doing so I'm currently reading the book "Trespassing on Einstein's Lawn" by Amanda Gefter and came across something interesting. The following is really a list of questions and postulations. I would appreciate help in understanding what might be correct or wrong and why if anybody is able to :)

Firstly, as the title mentions comes the link between the event horizon being proportianal to entropy due to a relationship between the laws of thermodynamics and black holes, in particular with the total entropy being linked to the event horizon rather than total volume of the black hole. Given E=mc2 it doesn't seem too strange that upon reaching the event horizon matter may break down into pure energy rather than remaining as matter (is this correct), especially given mass cannot travel at the speed of light. I also read that both space and time break down at the point of the event horizon (which again makes sense) but then the book begins to talk about an observer within the black hole (past the horizon) viewing out. Surely if both space and time have broken down at the event horizon it would make more sense of there was no inside of the black hole, since the term inside would have no meaning. Instead surely any particle which managed to reach the event horizon would instead be converted to energy which would then be frozen in place at the event horizon creating what from the outside might loom like a shell around something, but in reality from the frozen view point of the event horizon itself it would be impossible to conceive an "inside" but rather that would be it. This might be why rather than the entropy being linked to the volume of a black hole it is linked to the surface area - there is no volume.

As I said, being self taught it is highly possible I have missed something very elementary or made logical leaps which should not have been made so I would appreciate guidance to help correct my understanding where needed :)

2. Oct 24, 2015

### Simon Bridge

volume, for a black hole, doesn't really mean anything. However, you realize that the radius and volume of a sphere are linked right?

No. There is nothing special, as far as the infalling body is concerned, about crossing the event horizon.

its a mathematical breakdown, not a physical one. You use a different set of equations to describe space-time from the pov of an observer within the swarzchilde radius.

Its like how, on a map of the Earth, the surface breaks down at the poles. People can still stand on the poles even though their position is smeared over the edge of the map. They can get around fine just by using a different map.

Relativity is all about the observer. What a black hole looks like depends on where you are in relation to it. The black ball the size of the swartzchild radius is a non-rotating black hole viewed from a long way away.

The book you are reading is entertaining, but not a good reslurce for learning physics.

Last edited: Oct 24, 2015
3. Oct 24, 2015

### Staff: Mentor

You should not try to learn actual science by reading pop science books. Even the good ones aren't the same as a real textbook. Simon Bridge has correctly pointed out several ways in which the book you are reading has apparently misled you.

If you are really interested in learning about the physics you are referring to, I would strongly recommend getting an actual textbook. Sean Carroll's online lecture notes on GR are a pretty good start in the general area you seem interested in. Black hole entropy is a more advanced concept, though, and you might need to look at recent peer-reviewed papers to get a better idea of the current state of play in that area. Ultimately quantum mechanics is going to be involved, and we don't currently have a good theory of quantum gravity, so this is an area in which we don't completely understand how things work.