On the Particle Definition in the presence of Black Holes

Details On the Particle Definition in the presence of Black Holes On the Particle Definition in the presence of Black Holes

2000-03-07

arxiv.org/abs/gr-qc/0003020v3

Phys.Rev. D63 (2001) 024014

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

44 pages, LaTeX, no figures, accepted for publication in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.63.024014

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 Hamiltonian splits up into two independent parts accounting for the interior and the exterior domain, respectively. It turns out that a reasonable particle definition may be accomplished for the outside region only. The Hamiltonian of the field inside the black hole is unbounded from above and below and hence possesses no ground state. The corresponding equation of motion displays a linear global instability. Possible consequences of this instability are discussed and its relations to the sonic analogues of black holes are addressed. PACS-numbers: 04.70.Dy, 04.62.+v, 10.10.Ef, 03.65.Db.

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