|
|
|
|
|
|
by madrocketsci
2823 days ago
|
|
|
Do you mind if I ask you some questions about this? I always have trouble picturing how, dynamically, a charge inside an event horizon is supposed to be able to propagate an electric field outside the event horizon of a black-hole. (retarded vector potential travels from a charge along light-paths to another point in space-time. There isn't any way for the influence of a point charge to get out?) Perhaps some other related questions too:
Charge and current density is a 4-vector in SR, which transforms along with all the other 4-vectors (momentum-energy 4-vector, etc). In a situation where the effective mass of an object reversibly lowered to the event-horizon (slowly moved relative to the event horizon with small velocity) goes to zero (all the mass energy ends up somewhere else) - wouldn't the effective charge density from a non-infalling external observer's perspective also be going to zero? If we're just drawing a box around a black-hole and declaring that charge is conserved, we would have as much/little reason to declare any other conservation also holds? |
|
|
Fully classically, the field lines point to the sources; they get "stuck" to the horizon as the source crosses. To a naive outside distant observer for whom the horizon subtends a small angle of the sky, so does each source. When thinking about collapsing charged matter forming a new black hole, substitute a spherically symmetric shell and shrink its area, while keeping the charge and mass constant and uniformly distributed on the shell -- the electric field and gravitational field outside the shell then both follow gauss-laws, so even without a horizon, observers outside the shell at a large distance (such that the shell looks virtually pointlike) cannot get the full information about the shell using only local measurements, including whether the shell is inside or outside a horizon.
Semiclassically, one can use virtual photons which aren't as restricted as real matter, especially in that the black hole horizon is not necessarily a trapping surface for them. Typically one sets up the black hole as a background that has already determined the relevant quantum fields, and then introduces a test particle onto that background. If the test particle radiates a photon, the black hole will only react once the photon enters the horizon; unless and until that happens, the background is kept constant. (Hawking introduces negative energy particles in his formalism precisely to keep the background always constant.) Changing the background is tricky, but never involves real particles crossing from the interior of the horizon to the exterior.
> we would have as much/little reason to declare any other conservation also holds
Sure, no-hair as a theorem (rather than as a principle) only tells you that given classical vacuum, Maxwell's electromagnetism (in tensor form), and an eternal black hole metric, spacetime and all its contents are totally determined everywhere by a small handful of parameters. As a principle it suggests that perturbing that setup (e.g. by adding a source outside the horizon) does not lead to wildly inaccurate results.
I'm sorry that I don't understand what it is that you're asking in your second-last paragraph. There is a body of literature on black hole "mining" (it's a common thought-experiment when trying to distinguish between general relativity an alternative theory, especially a quantum one) that maybe touches on what you're curious about.