Origin of Hawking radiation

In the first part of the paper, the possible influence that quantum corrections could have on the existence and position of an event horizon in a spherically symmetric collapse is studied. A counterexample is constructed proving that the small value of 〈$T_{\mu \nu }$〉 near the gravitational radius does not guarantee the formation of an event horizon. In an exactly solvable model of black-hole evaporation, the spacetime structure is manipulated in the Planck neighborhood of the singularity so that the event horizon is shifted arbitrarily to the future or removed completely. This change in the position of the event horizon has no observable consequences until the retarded time of the end of the black-hole evaporation is reached. However, even in the absence of the event horizon, the Hawking radiation survives. In the second part of the paper, its origin is studied. The old idea is adopted that it is coming from a neighborhood of the so-called ergosphere. The concept of the ergosphere is generalized to nonstationary, spherically symmetric spacetimes using the notion of Hawking quasilocal mass. The boundary of such an ergosphere is shown to coincide with the locus of apparent horizons. It seems, therefore, that the Hawking effect is associated with the apparent rather than the event horizon. An extrapolation of some properties of 〈$T_{\mu \nu }$〉 from a neighborhood of the Schwarzschild horizon to that of an apparent horizon forming in a collapse leads to the result that too much energy is radiated away already before the apparent horizon forms, similarly as in the Boulware scenario of gravitational collapse.