I am a bit unclear about the teleological property of event horizon. For example, in Poisson's Relativists' Toolkit text page 175, it is said that the entire future history of the spacetime must be known before its position can be determined.

  • This is not a problem for static or stationary spacetimes. But for any radiating spacetimes (like Vaidya spacetimes or simply black hole evaporation), this means that one can never know the location of event horizon "unless one knows the future". Is this bad for physics?
  • If event horizon is dynamical, would not that mean that in some sense, null geodesics inside the horizon that is very close to the horizon may actually get out of horizon (e.g. when the horizon recedes due to e.g. Hawking evaporation?

All these are very qualitative but I believe there is something conceptual I missed out.


The defintion of the black hole event horizion is "the boundary of future null infinity".

In lay language, this means:

  1. Evolve all light rays all of the way to the future
  2. Find the light rays that escape to infinity
  3. The marginal light rays, that are going toward the future, but just baaaaarely aren't making it to infinity are the black hole event horizon (For a schwarzschild spacetime, consider the null geodesic $x^{\mu}(s) = (0,2Ms,0,0)$, i.e., the radially outward light ray that sits exactly on the horizon, unable to escape, but not falling in, either)

In this language, the problem is immediate -- we can't know where the event horizon is unless we ultimately know all of the evolution of spacetime. In cases where the evolution is trivial, this isn't a problem. But say that we're starting with what is initially a binary black hole system, and numerically evolving it -- we never know the distant future, and thus can't construct the black hole.

Furthermore, there are additional problems with event horizons -- since they are global properties of the spacetime, you can construct perverse solutions, where event horizons form in empty space with no matter nearby, thanks to future behaviour of matter, and you can construct event-horizonless black holes with Hawking radiation, provided the singularity is timelike, and the hole evaporates quickly enough.


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