Both Hawking radiation and the Unruh effect feature coordinate systems with coordinate horizons (the event horizion and the Rindler horizon respectively) and the simalirity between an event horizon and a Rindler horizon are often pointed out when comapring the two effects. Also Stephen Hawking is fond of explaing hawking radaition in terms of virtual particle pairs, one falling in to the event horizon and one escaping.
I have a bais understanding that these two effects are due to the way creation and anihilation operators transform in certain coordinate systems. Though the exact deatils are way beyond me.
My question is are the horizons a necessary feature in order to get simlair effects? Is it impossible to have a simlair effects say round a star for which the space around could be approximately described by the Schwarchild solution, but would not feature an event horizon?
What do you mean by “coordinate horizons”? The horizon itself is a coordinate-independent phenomenon. Now, in the usual coordinate system used for black holes, the coordinates blow up at the horizon, and this is sometimes called a coordinate singularity, since it’s a feature of the coordinate system, not actually anything going on at that location. There are coordinate systems for black holes which do not have this coordinate singularity at the horizon, and there are also coordinate systems for perfectly ordinary situations (not involving horizons or black holes) that have coordinate singularities.
I couldn’t think of a better word, but I would call a coordinate horizon as the kind of coordinate singualrities that occur in Schwarchild coordinates and Rindler coordinates that divide space in to two regions. Hawking radiation occurs in Schwarzchild coordinates (for a Schwarzchild black hole) and the Unruh effect occurs in Rindler coordinates (for Minkowski spacetime).
I wasn’t familiar with the Unruh effect, so I thought “Unruh effect? What does accepting a lobbyist’s money and still voting against his bill have to do with black holes?”
In political space, Unruh radiation is quantized in dollars.
Wait, I think I get what you’re asking now. Hawking/Unruh radiation only show up in some reference frames; are those reference frames identically the ones which have two-dimensional unbounded coordinate singularities?
Leaving aside quibbles about the distinction between coordinate systems and reference frames, I think that the answer is that you can get horizon-like coordinate singularities without radiation, but you can’t get the radiation without the coordinate singularities. I’m not sure, though.
Basically that’s it. Rindler coordinates and Schwarchild coordinates both share the property that they incompletely describe spacetime and the Rindler horizon and the Schwarchild horizon are respectively the boundaries of the region of spacetime that they describe and there’s plenty of analogies that can be drawn between the two. What from my very limited knoweldge about semiclassicla gravity and quantum field theory as a whole I don’t understand is why the effects (I assume from what i have read) are limited to frames with these incomplete descriptions.
By having a spacetime (which would be like the one that describes a star) that is described in part by the Schwarchild vacuum solution and in part by the interior Schwarchild-like solution you surely get a kind of ‘natural’ coordinate system (which reduces to Schwarzchild coordinates in the vacuum) where those at coordinate rest are almost all locally experincing proper acceleration. Why wouldn’t we expect to see the same effects in this situation? What’'s the connection with coordinate horizons?
