How does a black hole know how big it should be?

[phinds]

Naty, I wonder if it is correct to call the EH a "surface" since it is in no way physical and really is just a spherical coordinate r.

 

[Naty1]

I wonder if it is correct to call the EH a "surface" since it is in no way physical ...

It is a causal boundary and to me that's quite physical...but what we call it varies a lot.
In terms of the Holographic principle, 'surface' seems especially common.

 

[PeterDonis]

Naty, I wonder if it is correct to call the EH a "surface" since it is in no way physical and really is just a spherical coordinate r.

The term "surface" is pretty general; it can apply to just about any submanifold of a spacetime. The EH is the set of all points in the spacetime with r = 2m, but with no other coordinate constraints. A more precise term for it would be a "null 3-surface", meaning a submanifold with three linearly independent tangent vectors, one of which is null. (The other two are spacelike.)

As far as whether the EH is "physical", it's no less so than any other submanifold. Since it's an outgoing null surface, outgoing light rays emitted exactly at the EH stay at the EH, so there can certainly be physical things that "mark out" the EH.

 

[Nugatory]

Naty, I wonder if it is correct to call the EH a "surface" since it is in no way physical and really is just a spherical coordinate r.

It's an unambiguously specified set of points in spacetime. No matter what coordinates you're using, if you present me with the coordinates of a point, I'll be able to answer the question "is that point on the EH?" and the answer will be same no matter which coordinate system you choose. That strikes me as a pretty good operational definition of something that is "physical".

 

[Naty1]

I wonder if it is correct to call the EH a "surface" since it is in no way physical and really is just a spherical coordinate r.

I was just reading the other posts and remembered ALL the horizons we discuss in the forums have 'physical' attributes...like the Rindler horizon associated with Bells Spaceship paradox and Unruh effect...and Hawking radiation of black holes.

In fact perhaps the craziest horizon of all would be that during cosmological inflation...when the original particles [primordial perturbations] from the Big Bang were widely dispersed and sparse but were repopulated by the inflationary expansion...which only happens if a horizon is present...in other words geometrical curvature horizons induce the appearance of particles!. Somehow, it appears, that an accelerating space-time or even accelerating observers, which are accompanied by horizons, induces localized mass energy...particles. Geometric circumstances create particles!Check out this discussion with links,papers, and concepts:

https://www.physicsforums.com/showthread.php?t=590798bapowell has an explanation with some math and says in post #17:

It's a nice exercise though to work through the evolution of a scalar field fluctuation during inflation, from its birth in the vacuum out to super horizon scales if you haven't done it. What you find once you've done this is that you end up with a spectrum of perturbations across a range of length scales.

'perturbations' ARE particles! Without such horizons we would be in an empty universe.