| > the event horizon - Schwarzschild radius - is defined by the specific value of gravitational potential (escape speed equals speed of light) The Schwarzschild radius does have the property that, if you plug it into the classical equation for escape velocity, you get the speed of light. That doesn't mean arbitrary classical analogies (like the "thrown stone" example) hold. In particular, consider that you can escape the earth while never achieving escape velocity. Just keep firing your rockets to counteract gravity. But if this were possible with black holes, then they would not be very interesting! > The various local effects like time dilation, light path curving, etc... are defined by the value of gravitation force, not gravitational potential. These are not local effects! Locally, there is no time dilation, and no curvature of light. I see my watch tick at the same rate, no matter where I am, because my watch and my eyes are in the same local reference frame. In order to see effects like time dilation or curvature of light, you must compare events separated in spacetime. For example, we can look at the paths of light emitted by distant stars. And since the light had to get to our eyes, we have to account for the entirety of the path that it took. So the time dilation I observe for an event depends on the entirety of spacetime along the path from the event to me, not just the local curvature for the event. In mathematical language, if you want to move a vector from one point to another on a curved manifold, you can't just specify the start and end point. The path you take affects the resulting vector. > The potential defines the fact that anything originating at or below the horizon would never escape completely the gravitational field, i.e. never reach the infinity. So objects originating outside the event horizon reach infinity in a finite time? Huh? |