Quantum fields interacting with colliding plane waves: particle creation

Abstract

The quantization of a scalar field on a spacetime representing the head on collision of two gravitational plane waves is studied. In the spacetime considered the waves focus into a non-singular Killing-Cauchy horizon. The interaction region of the waves is locally isometric to a region inside the event horizon of a Schwarzschild black hole with the Killing-Cauchy horizon corresponding to the event horizon. Two unambiguous and physically meaningful quantum vacuum states may be defined: the “in” vacuum associated to the positive-frequency mode solutions in the flat region before the collision of the waves and the “out” vacuum related to the positive-frequency modes defined through the two null vector fields on the Killing-Cauchy horizon. It is found that the “in” vacuum contains a number of “out” particles which is proportional to the inverse of the frequency. In the long-wavelength limit the spectrum is consistent with a thermal spectrum at a temperature which is inversely proportional to the focusing time of the gravitational plane waves.