SEMINAR: Physics Seminar

We show that a quantum scalar particle in the gravitational field of a massive body of radius R which slightly exceeds the Schwarzschild radius rs, possesses a dense spectrum of narrow resonances. In the limit R goes to rs their lifetimes tend to infinity, and one can interpret the capture of the free particle into these states as absorption. In this limit the spacing between the resonances tends to zero, which allows one to calculate the energy-averaged (optical) capture cross section. Surprisingly, for R goes to rs this cross section reproduces Unruh's black hole absorption cross section. Thus, a non-singular static metric may have black hole properties without the actual formation of a black hole.

The bound-state energy levels of a scalar particle in the static gravitational field of a massive body of radius R which slightly exceeds the Schwarzschild radius rs, are found. Bound states with zero energy (where the binding energy is equal to the rest mass of the scalar particle) only exist when a singularity occurs in the metric. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. As pair production is a necessary condition for Hawking radiation to occur, this suggests that these objects do not Hawking radiate.

For the Florides metric the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the centre. The energy spectrum is shown to become quasi-continuous as the metric becomes singular. All levels with finite principal quantum number n collapse to zero energy.

1. Dense spectrum of resonances and particle capture in a near-black-hole metric, V. V. Flambaum, G. H. Gossel, and G. F. Gribakin, arXiv:1012.2134 Submitted to Phys. Rev. Lett.

2. Energy levels of a scalar particle in a static gravitational field approaching the black hole field, G. H. Gossel, J. C. Berengut and V. V. Flambaum , Gen. Rel. Grav. 43, 2673 (2011)