« on: 28/10/2017 21:17:13 »
If a body is falling freely towards a black hole will time dilation cancel the tidal forces so that the equivalence principle remains in tact?I don't see how you get that.
There are two forms of the equivalence principle known as the strong form and weak form. The weak for refers to uniform gravitational fields so you can't apply that to curved spacetimes. The strong form says that any physical law which can be expressed in tensor notation in SR must have the same form in a locally inertial frame of a curved spacetime.
The later is consistent with the notion that if you limit your observations of an experiment in a small enough region of spacetime in a locally inertial frame of reference your observations can be described by SR. I noticed that Evan referred to a small region of space. Its really with a small region of spacetime. Its easy to imagine an experiment which is confined to a small region of space but which manifests the spacetime curvature. For example: place a ball at rest any place within the international space station and record its position as a function of time. At first the ball seems to remain at rest but will undergo a complete cycle back and forth within the time it takes for the station to make one orbit.
Regarding black holes: there's nothing special that goes on near or even at the event horizon as observed by an inertial observer. In fact you can imagine a black hole which has enough mass to make the spacetime as flat (but never zero) as you'd like at the horizon. In fact the book Exploring Black Holes by Taylor and Wheeler often refer to them in that text.