Particle definition in the presence of black holes - art. no. 024014

A canonical particle definition via the diagonalization of the Hamiltonian for a quantum field theory in specific curved space-times is presented. Wit hin the provided approach radial ingoing or outgoing Minkowski particles do not exist. An application of this formalism to the Rindler metric recovers the well-known Unruh effect. For the situation of a black hale the Hamilto nian splits up into two independent parts accounting for the interior and t he exterior domain, respectively. It turns out that a reasonable particle d efinition may be accomplished for the outside region only. The Hamiltonian of the field inside the black hole is unbounded from above and below and he nce possesses no ground state. The corresponding equation of motion display s a linear global instability. Possible consequences of this instability ar e discussed and its relations to the sonic analogues of black holes are add ressed.