Particle production and complex path analysis

Abstract

This paper discusses particle production in Schwarzchild-like spacetimes and in an uniform electric field. Both problems are approached using the method of complex path analysis. Particle production in Schwarzchild-like spacetimes with a horizon is obtained here by a new and simple semi-classical method based on the method of complex paths. Hawking radiation is obtained in the (t,r) co-ordinate system of the standard Schwarzchild metric {\it without} requiring the Kruskal extension. The co-ordinate singularity present at the horizon manifests itself as a singularity in the expression for the semi-classical propagator for a scalar field. We give a prescription whereby this singularity is regularised with Hawking's result being recovered. In the case of the electric field, standard quantum field theoretic methods can be used to obtain particle production in a purely time-dependent gauge. In a purely space-dependent gauge, however, the tunnelling interpretation has to be resorted to. We attempt, in this paper, to provide a tunnelling description for both the time and space dependent gauges. The usefulness of such a common description becomes evident when `mixed' gauges, which are functions of both space and time variables, are analysed. We report, in this paper, certain mixed gauges which have the interesting property that mode functions in these gauges are found to be a combination of {\it elementary} functions unlike the standard modes. Finally, we present an attempt to interpret particle production by the electric field as a tunnelling process between the two sectors of the Rindler spacetime.Comment: 26 pages, Latex file, one eps figur

Quantum tunneling beyond semiclassical approximation

“…We next consider an alternate method for calculating the imaginary part of the action, making use of the Hamilton-Jacobi equation [7,34,35], from which we will calculate the Hawking temperature. The analysis goes beyond the semiclassical approximation by including all possible quantum corrections.…”

“…al. [7]. Later, many people [8] used the radial null geodesic method to find out the Hawking temperature for different spacetime metrics.…”

“…The idea is that the energy of the particle changes sign as it crosses the horizon, so that a pair created just inside or outside the horizon can materialise with zero total energy, after one member of the pair has tunneled to the opposite side. In this method [6,7], the particles are allowed to follow classically forbidden trajectories, by starting just behind the horizon onward to infinity. The particles then travel back in time, since the horizon is locally to the future of the external region.…”

Charged fermions tunnelling from Kerr–Newman black holes

“…The earliest work with black hole tunnelling was done by Kraus and Wilczek [1], and was refined by various researchers [2,3,4]. From this approach an alternative way of understanding black hole radiation emerged.…”

“…For scalar field emission it has been shown to be very robust, having been successfully applied to a wide variety of interesting and exotic spacetimes, including the Kerr and Kerr-Newman cases [10,11,14], black rings [12], the 3-dimensional BTZ black hole [7,13], the Vaidya spacetime [18], other dynamical black holes [19], Taub-NUT spacetimes [14], Gödel spacetimes [22], and dynamical horizons [19]. Tunnelling methods have even been applied to horizons that are not black hole horizons including those with cosmological horizons [5], [6], [25],and Rindler Spacetimes [4], [14], [24] for which it has been shown the Unruh temperature [30] is in fact recovered.…”