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The right-hand side is a non-zero constant, implying that the wall is collapsing with constant velocity in the τ co-ordinate. This shows that the collapse into a black hole occurs in a finite time interval for the infalling observer. Further, Hawking has argued [9] that the infalling observer does not detect significant Hawking radiation since the emission is dominantly at low frequencies compared to 1/RS , while the infalling observer can only have local detectors of size less than RS . Thus the infalling observer would appear to see event horizon formation in a finite time, with no significant radiation emanating from the black hole These paradoxical views of the asymptotic and infalling observers need to be reconciled, and the conventional way to reconcile them is summarized in the spacetime diagram of an evaporating black hole shown in Fig. 8. The diagram is drawn so that the asymptotic observer sees evaporation in a finite time and the infalling observer falls into the black hole in a finite time also.

So you'd usually hear that an asymptotic observer will never see an event horizon form, while an infalling observer would. This paper presents a view of the infalling observer that's a little closer to that of the asymptotic observer:

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The conventionally drawn spacetime of an evaporating black hole has features that are not consistent with our findings. Since the asymptotic observer sees Hawking-like radiation from the collapsing wall

Instead it may happen that the true event horizon never forms in a gravitational collapse. We saw that an outside observer never sees formation of a horizon in finite time, not even in the full quantum treatment. What about an infalling observer? As in Hawking’s case, the infalling observer does not see radiation, but this is due to size limitations of his detectors. The mode occupation numbers we have calculated will also be the mode occupation numbers that the infalling observer will calculate, even if they be associated with frequency modes that he cannot personally detect. The infalling observer never crosses an event horizon, not because it takes an infinite time, but because there is no event horizon to cross. As the infalling observer gets closer to the collapsing wall, the wall shrinks due to radiation back-reaction, evaporating before an event horizon can form. The evaporation appears mysterious to the infalling observer since his detectors don’t register any emission from the collapsing wall. Yet he reconciles the absence of radiation with the evaporation as being due to a limitation of the frequency range of his detectors. Both he and the asymptotic server would then agree that the spacetime diagram for an evaporating black hole is as shown in Fig. 9. In this picture a global event horizon and singularity never form. A trapped surface (from within which light cannot escape) may exist temporarily, but after all of the mass is radiated, the trapped surface disappears and light gets released to infinity.

The spacetime picture that we are advocating is similar to that described in Refs. [13, 14] and, more recently, Refs. [15, 16, 17].

*prior*to event horizon formation, the mass of the collapsing wall must be decreasing, and at the point denoted by F in Fig. 8 the entire energy of the wall has been radiated to I + . However, in the spacetime of Fig. 8, it is at precisely this instant that the asymptotic observer sees infalling objects disappear into the event horizon, even though there is nothing left of the collapsing wall to form the singularity. A spacetime region such as the triangular region behind the event horizon only seems reasonable if not all of the collapsing shell energy has been lost to I + up to the point F, and there is some energy-momentum source left behind to crunch up in the singularity. Also, if the spacetime near the event horizon is described by the Schwarzschild metric, there is infinite gravitational redshfit of signals escaping to infinity, while the diagram shows that signals escape to infinity in a finite time. Finally, as is well known, the diagram in Fig. 8 also gives rise to the information loss paradox. While these features of the diagram in Fig. 8 are not inconceivable, they are sufficiently strange as to cast doubt on the validity of the picture.Instead it may happen that the true event horizon never forms in a gravitational collapse. We saw that an outside observer never sees formation of a horizon in finite time, not even in the full quantum treatment. What about an infalling observer? As in Hawking’s case, the infalling observer does not see radiation, but this is due to size limitations of his detectors. The mode occupation numbers we have calculated will also be the mode occupation numbers that the infalling observer will calculate, even if they be associated with frequency modes that he cannot personally detect. The infalling observer never crosses an event horizon, not because it takes an infinite time, but because there is no event horizon to cross. As the infalling observer gets closer to the collapsing wall, the wall shrinks due to radiation back-reaction, evaporating before an event horizon can form. The evaporation appears mysterious to the infalling observer since his detectors don’t register any emission from the collapsing wall. Yet he reconciles the absence of radiation with the evaporation as being due to a limitation of the frequency range of his detectors. Both he and the asymptotic server would then agree that the spacetime diagram for an evaporating black hole is as shown in Fig. 9. In this picture a global event horizon and singularity never form. A trapped surface (from within which light cannot escape) may exist temporarily, but after all of the mass is radiated, the trapped surface disappears and light gets released to infinity.

The spacetime picture that we are advocating is similar to that described in Refs. [13, 14] and, more recently, Refs. [15, 16, 17].

**Edited by Startraveler, 21 July 2007 - 06:58 PM.**