# why nontrivially space-like connected event horizons do not respect unitarity?

I want to understand the assertion that the gluing between distant event horizons is forbidden by unitarity. What is exactly the argument that unitarity will necessarily forbid topological nontrivial spacetimes?

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that gluing has to be explained by a nonlinear quantum mechanics, i.e. no unitary account of the process, standard quntum mechanics SQM is linear.

... The evolution is determined by a unitary operator #, and unitarity implies that information is conserved in the quantum sense...

#....a unitary operator is a bounded linear operator... linearity requirement in the definition of a unitary operator

Hawking assumes the unitarity of the AdS/CFT correspondence but loss of unitarity is not a real problem, gravitation broke the linearity of linear process.

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I believe two different singularities won't (or even can't) respect unitarity as a general rule, because each has their own unitive sum of probabilities. To be entangled with another event horizon would violate their own unitarity.

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Gluing two distant horizons in such a way that one is a future horizon and one is a past horizon, so that matter falling into one is emitted by the other, is easily seen to be paradoxical from mass-energy conservation--- you throw matter into the porthole, and one horizon grows, while the other side of the porthole shrinks. In order to match up under identification of this sort the two horizons must be matched.

Further, you can give paradoxes involving unitarity. Holography borderline violates no-cloning (something which was difficult to sort out, and which is so counterintuitive, it was used recently by a group including Polchinsky to falsely argue that black holes are firewalls), so that information about a state is naively in two places at once. If you have spacelike separated portholes and you throw one end into a large black hole, you can turn the apparent violation of no-cloning into true violation. Send one end of the porthole into the black hole, and throw in some quantum particle, suitably entangled, or whatever. Let it go through the porthole on the interior, and catch it on the outgoing leg. The information about the state is imprinted now both in the horizon fluctuations and in your copy of the particle that you recieve.

The paradoxes seem pretty severe, but if you have an idea how to get around them, please say.

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