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Sometimes, the holographic principle is stated as follows: "Every theory with gravity in D-dimensions (in certain preexistent space-time background) can be described by a (D-1)-field theory WITHOUT gravity on the boundary (of the space-time background, I presume)". My question is: What is the holographic dual of the most general gravity described by general relativity in 4 space-time dimensions? That is, what is the dual of general relativity metric in general (if it exists)? AdS metrics are dual to CFT, but what about dS space-times in Cosmology/cosmological settings and more general Petrov D-type space-times? And furthermore...Does the holographic principle in this form remain valid for ANY metric?

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    $\begingroup$ it is far from being known. $\endgroup$ – AccidentalFourierTransform Mar 2 '17 at 22:05
  • $\begingroup$ There are definitely some attempts at dS/CFT stuff (I know of a paper by de Haro, among others...). $\endgroup$ – Danu Mar 2 '17 at 22:58
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    $\begingroup$ If that was known we'd have a complete mapping from gravity to field theory. And we don't. Also, as far as I know ther holographic principle is still a conjecture, it has not been proven. What's been proven is the AdS/CFT correspondence and a few other special cases like some dS mappings. I don't think there is a complete dS mapping known. If we did have the full GR mapping we would have quantized GR in effect. That's the goal, we are very far indeed from it. $\endgroup$ – Bob Bee Mar 3 '17 at 2:37

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