Hawking radiation without transPlanckian frequencies
Abstract
In a recent work, Unruh showed that Hawking radiation is unaffected by a truncation of free field theory at the Planck scale. His analysis was performed numerically and based on a hydrodynamical analogy. In the present work, by analytical methods, the mathematical and physical origin of Unruh's result is revealed. An alternative truncation scheme which may be more appropriate for black hole physics is proposed and analyzed. In both schemes the thermal Hawking radiation remains unaffected even though transPlanckian energies no longer appear. The universality of this result is explained by working in momentum space. In that representation, in the presence of a horizon, the d'Alembertian equation becomes a singular firstorder equation. In addition, the boundary conditions corresponding to the vacuum before the black hole formed are that the in modes contain positive momenta only. Both properties remain valid when the spectrum is truncated and they suffice to obtain Hawking radiation.
 Publication:

Physical Review D
 Pub Date:
 October 1995
 DOI:
 10.1103/PhysRevD.52.4559
 arXiv:
 arXiv:hepth/9506121
 Bibcode:
 1995PhRvD..52.4559B
 Keywords:

 04.70.Dy;
 03.70.+k;
 Quantum aspects of black holes evaporation thermodynamics;
 Theory of quantized fields;
 High Energy Physics  Theory
 EPrint:
 27 pages, latex, includs 5 postscript figures, encoded using uufiles