On the Particle Definition in the presence of Black Holes

TL;DR

This paper proposes a canonical particle definition in curved space-times, analyzing black holes and Rindler space, revealing limitations inside black holes and discussing implications of instabilities and analogues.

Contribution

It introduces a Hamiltonian diagonalization approach for defining particles in curved space-times, highlighting the differences between interior and exterior black hole regions.

Findings

Particle definition is feasible outside black holes but not inside.

The Hamiltonian inside a black hole is unbounded and unstable.

The formalism recovers the Unruh effect in Rindler space.

Abstract

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.