Suggestion for proof to establish the correctness of Hawking's 2005 Information Paradox resolution

Introduction: Hawking in 2005 argued that the so-called "information parodox" whereby black hole radiation cause a loss of quantum coherence (and hence, causality to the eternal dismay no doubt of Laplace), can be resolved by summing over only trivial Euclidean metrics to contribute to scattering calculations in anti-deSitter space. That is, to make predictions for the universe we observe, we can disregard the contributing metrics that have black holes and only use the ones without black holes - no black holes, no information parodox. The issue at stake is whether we can safely disregard the non-trivial (black hole containing) Euclidean metrics in our calculations. We can only do this if quantum corellation functions asymptotically decay on these non-trivial spacetimes, in which case we would have no choice but to use the trivial spacetimes in our calculations, thereby side-stepping the information paradox issue entirely (and resucuing causality - and our friend Laplace - in the process). The below high-level sketch of a proof aims to do just that by demonstrating in broad-outline how this could be done, though certain subtelties no doubt remain for further explication.


Axiom:

Correllation functions on non-trivial Euclidean metrics decay as the limit goes towards future infinity.

Proof:

I. Observers will disagree on vacuum state value depending upon their acceleration by rules of General Relativity.

II. By I., two systems, initially with same vacuum state, may over time in anti-DeSitter spacetime have entirely different vacuum states, depending upon their acceleration, so correllation functions between them will decay as the limit reaches future infinity.

III. Timelike geodesics in the neighborhood of a singularity forever approach it, but do not reach it (a la Zeno's paradox) by rules of General Relativity, therefore, a timelike geodesic escaping to future infinity and going towards a future singularity are in a sense equivalent.

IV. By II. and III. two time-like systems becoming arbitrarily nearer to a singurily will measure more and more diverging vacuum values between them, that is, their correlation functions will decay.

V. By IV., once we have Wick-rotated into a singular (non-trivial) Euclidean 4-sphere, and the geodesics in IV. become spacelike, this correllation function decay will remain in arbitrarily close regions to the circular singularity embedded in the 4-sphere.

:: Therefore, correllation functions on non-trivial Euclidean metrics decay as the limit goes towards future infinity.


Consequences:

If it can be (as above) established that correllation functions decay on non-trivial Euclidean metrics, then as Hawking (2005) said, we should only use trivial Euclidean metrics in scattering calculations in anti-deSitter spacetime (ADS), and if this is done, the so-called "information paradox" goes away, since we are now only dealing with trivial spacetimes (e.g. without black holes). Thus establishing the above, establishes that the "information paradox" may be resolved as Hawking 2005 argued.

If as above outlined above, the relativistic effects on vaccuum states due to different reference frames, are such that they asymptotically impact correlation functions, this ought to have predictable (measurable) effects, that is the effects of various accelerating reference frames upon locally measured vacuum values in those reference frames, and the interaction between these systems, seem to be an avenue for further exploration.

Further explication needed as to above:

The above rests on point II., the effect on correllation functions resulting from the differing vacuum states measured in different accelerating reference frames. It seems a logical inference that asymptotically this effect will cause these functions to decay, but precise research would need to establish this. Once established, the rest falls into place, and the information parodox is resolved.