Doing it with Mirrors: Classical analogues for Black Hole radiation

Abstract

We construct analogues for the quantum phenomena of black hole radiation in the context of {\it classical field theory}. Hawking radiation from a (radially) collapsing star is mathematically equivalent to radiation from a mirror moving along a specific trajectory in Minkowski spacetime. We construct a classical analogue for this quantum phenomenon and use it to construct a classical analogue for black hole radiation. The radiation spectrum in quantum field theory has the power spectrum as its classical analogue. Monochromatic light is continually reflected off a moving mirror or the silvered surface of a collapsing star.The reflected light is fourier analysed by the observer and the power spectrum is constructed. For a mirror moving along the standard black hole trajectory,it is seen that the power spectrum has a ``thermal'' nature. Mirror-observer configurations like an inertial mirror observed in an accelerated observer's frame and an accelerated mirror observed in a Rindler frame are investigated and conditions for obtaining a ``thermal'' power spectrum are derived.The corresponding results in the black hole case are then elucidated.It is seen that a ``thermal'' spectrum can arise either due to the collapse of the star or due to the motion of the observer in the Schwarzchild spacetime. The ``temperature'' of the Planckian spectrum seen is therefore dependent on whether the star or the observer is in motion.In the latter case it is possible to obtain a ``temperature'' which is entirely independent of the mass of the star.