On the Particle Definition in the presence of Black Holes

A canonical particle definition via the diagonalisation of the Hamiltonian for a quantum field theory in specific curved space-times is presented. Within 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 hole the Hawking temperature exhibits a genuine dependence on the special dynamics of the collapse. The latter result is confirmed with the concept of Hadamard states known from axiomatic quantum field theory. Evaluating the expectation value of the energy-momentum tensor within the presented technique and the rather general dynamics under consideration one obtains no late-time Hawking radiation and thus no black hole evaporation. The investigation of the quantised field beyond the horizon yields a linear instability. PACS-numbers: 04.70.Dy, 04.62.+v, 10.10.Ef, 03.65.Db