Authors: C.A. Laforet
The (proper) transit time of a light signal emitted by an observer at rest at r_0 in a Schwarzschild gravitational field, reflected by body at some distance r>r_0 and received by the observer is shown to decrease as the observer is moved closer to the event horizon. This suggests that observers at rest close to the event horizon will see an increasingly length contracted Universe. We then seek to discover whether the free falling observer will also see the Universe similarly contracted as he/she falls toward the horizon. Using the definition of the Kruskal-Szekeres coordinates (T, X) in terms of Schwarzschild coordinates (r, t) and expanding the expression for dT/dX, it is shown that the worldlines of both timelike and spacelike observers must have slopes approaching 1 on the Kruskal-Szekeres coordinate chart implying that the free falling observer should indeed see an increasingly length contracted Universe as he/she falls toward the horizon.
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[v1] 2015-11-19 07:41:35
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