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Never heard this used as a technical term. The term "event horizon" has a well-known meaning, but this might be colloquial usage. There are boundaries of other spacetime regions that have interesting properties, e.g. in the case of rotating black holes, etc. but I don't usually hear those referred to as horizons.
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The physicist in the quote is Andrew Hamilton from University of Colorado. They were definitely talking about this "Inner Horizon" as something you would encounter later after having already passed through the event horizon.
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Okay, I just googled "Nova Inner Horizon of a Black Hole Andrew Hamilton from University of Colorado" and here are a couple of links
http://www.nasa.gov/vision/universe/..._roadshow.html
http://www.pbs.org/wgbh/nova/transcr..._blackhol.html