Isolated Horizons: Definition & Use

[hellfire]

I am confused with the fact that nearly all recent work about black holes in canonical quantum gravity is based on the definition of http://relativity.livingreviews.org/open?pubNo=lrr-2004-10&page=articlesu1.html . These seam to be a generalization of event horizons, and, it seams that their definition does not need of asymptotic flatness. But, if asymptotic flatness is not needed, then there is not always a notion of mass and even no Hawking temperature and no thermodynamics. So can someone explain a bit the definition of isolated horizons and why it is so useful?

 

[hellfire]

May be this could have more success in the subforum "Beyond the Standard Model"?

 

[Stingray]

Isolated horizons have their own notion of mass which only requires knowing quantities on the horizon itself. Also, all of the classical laws of black hole mechanics have been shown to hold true with isolated horizons (or dynamical ones where appropriate).

One reason for doing all of this is that event horizons are very difficult to use in general. Their definition requires knowing the entire history of the universe. There are also examples of spacetimes where portions inside an event horizon are actually completely flat. Isolated (and more generally dynamical) horizons are a completely local definition. They can only exist in a strong-field region, and identifying them doesn't require knowing the future.

The original laws of black hole "thermodynamics" often had somewhat difficult interpretations owing to the nonlocal definitions of event horizons. This situation goes away when looking at the formulation of these laws in the isolated/dynamical horizon framework.

There are actually precise flux laws that one can write down describing the evolution of the hole's mass and angular momentum based on the flux of (what are essentially) gravitational waves and matter across its horizon. The fact that all of this was possible in exact GR was a complete surprise to almost everyone. And that includes the people who developed this formalism.

 

[hellfire]

Thank you very much Stingray, your insights are always very much appreciated. I would like to understand the definition and get an intuition for this.

For example, definition 1 in the link I gave above is for a non-expanding horizon, which is used as basis for the definitions of weakly isolated and isolated horizons. How does this definition differ from the definitions of trapped and marginally trapped surfaces? As far as I can remember, these are based also on the sign of the expansion $\theta$.

The intuitive picture of event horizons as limiting surfaces of no-return volumes, is still valid for isolated horizons, or is there any difference?

 

[Stingray]

For example, definition 1 in the link I gave above is for a non-expanding horizon, which is used as basis for the definitions of weakly isolated and isolated horizons. How does this definition differ from the definitions of trapped and marginally trapped surfaces? As far as I can remember, these are based also on the sign of the expansion $\theta$.

Trapped surfaces are usually defined to be 2-dimensional and closed. But a NEH is a 3d hypersurface. Besides the vanishing expansion, it is also required to be null and to have a reasonable topology. The matter fields also have to obey an energy condition.

The intuitive picture of event horizons as limiting surfaces of no-return volumes, is still valid for isolated horizons, or is there any difference?

That's still valid. I'm pretty sure that all isolated horizons can be proven to lie within an event horizon. The reverse is not true, however.

 

[Demystifier]

What is the relation/difference between isolated and apparent horizons? (Both are defined locally. I understand the concept of the apparent horizon, but not that of isolated one.)