The horizon appears to be key to the production of Hawking radiation. However, the presence of a massive object does not appear to be necessary at all. An accelerating observer will also detect Hawking-like radiation known as Unruh radiation; the accelerating observer will also detect a horizon known as the Rindler horizon. Acoustic horizons can also develop in smooth fluid flows, either within the fluid for flows whose velocity exceeds the sound speed or on the surface for flows that exceed the speed of surface waves. Both of these situations are expected to exhibit horizon radiation as well. I suggest that you consult various papers by W. Unruh both on the acceleration radiation and so called dumb holes (acoustic horizons).

The horizon appears to be key to the production of Hawking radiation. However, the presence of a massive object does not appear to be necessary at all. An accelerating observer will also detect Hawking-like radiation known as Unruh radiation; the accelerating observer will also detect a horizon known as the Rindler horizon. Acoustic horizons can also develop in smooth fluid flows, either within the fluid for flows whose velocity exceeds the sound speed or on the surface for flows that exceed the speed of surface waves. Both of these situations are expected to exhibit horizon radiation as well. I suggest that you consult various papers by W. Unruh both on the acceleration radiation and so called dumb holes (acoustic horizons).

Thank you for the answer Jeremy, as well as pointing me to Unruh papers. I will consult them. As I understand, the Hawking radiation which is a thermal radiation requires necessarily a horizon in the sense that there should states in the system which are not accessible by the observer. The entanglement to these states replaces stochasticity in ordinary thermodynamics. This horizon, however, should not be necessarily a Schwarzschild horizon. But will the stationary observer at infinity see any type horizon if the object didn't collapse beyond its Schwarzschild radius?

Hi Corneliu!

IMO Jeremy's answer is pretty good (upvoted!). 

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In the case of acoustic metrics, Hawking radiation through a horizon is the result of indirect radiation effects, and yes, those effects will still operate even if there's no horizon involved ... but perhaps we humans require there to be a horizon in order for us to find these effects interesting!

There's probably a tendency to define Hawking radiation as an effect that allows us to detect radiation from a region that would otherwise be considered off-limits (a horizon-bounded region) and to consider Unruh radiation as being radiation that we wouldn't otherwise be able to detect.

However, the basic mechanisms should still be in play in the absence of a horizon, and should modify the statistical signature of the signals being seen (timing, energies), even if the signals themselves only contain information that would still have been able to reach the detector even without these effects in play.

So if you have a star at the bottom a a gravity-well that doesn't contain a horizon, you might expect the mechanisms behind Hawking radiation to make that star radiate a tiny, tiny amount faster, and you might expect there to be a tiny, tiny weighting towards the blue end of the spectrum. Similarly, in the case of Bekenstein radiation (radiation thrown off by a rotating black hole), there's no obvious reason why the effect shouldn't also happen for a normal rotating star without a horizon.