Dear Guest: I'm not about to start fighting multiple fronts, but the answer to your question is that I said of every frame today. Following a path to the singularity is not encapsulated by that definition. Plus, screw kittens. No, I'm not "simply" contradicting anything, I'm boldly contradicting it using GR's own account of things, as you say. How can the following all be true: 1) An event horizon is formed by circumstances residing in its causal past 2) Those circumstances include a singularity in GR 3) The singularity resides in the causal future for all frames outside of it ?
Such a shame, but not unpredictable. Erm, no. Whenever a collapsing star's radius falls below its Schwarzschild radius, an event horizon is formed (by default, since the exterior solution will coincide the Schwarzschild solution in that region by Birkhoff). Please Register or Log in to view the hidden image!
They're not all true: This is already a dodgy statement. It could be true, depending on exactly what you mean by that. This is false. To the extent that point 1) is true, it does not include the singularity itself. This is a more minor comment, but strictly speaking, only part of the singularity is necessarily in an observer's future light cone. Some of it can also be in the causal present. This is true both inside and outside the event horizon. (In fact for any observer strictly inside the event horizon, part of the singularity is always in their causal present.)
That's a "dodgy dodge". Why don't you modify the language so you concur with it? Are you suggesting that an event horizon spontaneously appears? The EH grows from the center, where pressure to overcome neutron degeneracy is maximum, outward. Do you disagree? The EH radius begins at zero. The singularity is required for this to grow. Also, please define "causal present".
Why don't you do that? You are the one trying to advance a specific claim here that your attempt at an argument appears to depend on. You don't just hand down assertions and demand others supply definitions that make them true for you. That's a bad way to go about analysing just about anything. Like I said just a couple of posts ago, the event horizon is not a physical object. It is simply a light cone. It's really not complicated. You have some matter, like a star, that is undergoing gravitational collapse in a way modelled by GR. The gravitational collapse results in a gravitational singularity. That is the sequence of events in spacetime. Once you've worked out that there's a singularity in spacetime, you can then ask: what is the region of spacetime within which an observer would be unable to avoid that singularity in their future? The boundary of that region defines the event horizon. If you're saying that the singularity must be in the causal past of the event horizon, then that is simply false. The region of spacetime that is spacelike separated from an event, with two events being defined as spacelike separated if they can be connected by a spacelike curve. While I'm not sure this is true in general, at least for the sort of black hole solutions we're talking about here the causal present associated with an event, by the definition above, coincides with everything that is not in or on the past and future light cones associated with that event. In other words, at least for these types of black hole solution, the whole of spacetime is either in the causal past, present, or future associated with any event, or is lightlike separated from that event.
