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Having just watched the latest in a long line of space movies; Interstellar tries to combat the problem of studying the center of a black hole and understanding what's going on inside. My question is, seeing as most things will either

A) Get ripped apart by a black hole, or

B) Be incinerated (although we dont know that anymore with the firewall and all that).

Would it be possible to study the interior of black holes using quantum entanglement? Send in half of pairs of entangled particles and monitor the changes to the particles they entangled to back here.

Apogee
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This is not possible. Please look at the following links:

  1. https://physics.stackexchange.com/a/170798/75518
  2. https://physics.stackexchange.com/a/154051/75518
  3. https://physics.stackexchange.com/a/170884/75518
  4. http://en.wikipedia.org/wiki/No-communication_theorem

The first describes in a good way what entanglement is (statistical correlation). The second gives a more formal insight into this. The third shows with a concrete example of spin entanglement that no information can be transfered with entanglement only. Finally the fourth is a good summary of all this.

There is also to note, that, according to the no hair theorem, no additional information of a black hole, that isn't accessible on the outside anyway (e.g. mass), can be obtained.

Furthermore, any massive particle restricted by speed $v < c$ would take an infinite time for an outside observer to reach the event horizon of a black hole. In short: Nothing massive falls into it for you anyway. See also https://physics.stackexchange.com/a/171596/75518 or this for more information on that topic.

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