Dynamic Realization of the Unruh Effect for a Geodesic Observer

Abstract

We study a dynamic version of the Unruh effect in a two dimensional collapse model forming a black hole. In this two-dimensional collapse model a scalar field coupled to the dilaton gravity, moving leftwards, collapses to form a black hole. There are two sets of asymptotic ($t\to\infty$) observers, around $x\to\infty$ and $x\to-\infty$. The observers at the right null infinity witness a thermal flux of radiation associated with time dependent geometry leading to a black hole formation and its subsequent Hawking evaporation, in an expected manner. We show that even the observers at left null infinity witness a thermal radiation, without experiencing any change of spacetime geometry all along their trajectories. They remain geodesic observers in a flat region of spacetime. Thus these observers measure a late time thermal radiation, with exactly the same temperature as measured by the observers at right null infinity, despite moving geodesically in flat spacetime throughout their trajectories. However such radiation, as usual in the case of Unruh effect, has zero flux, unlike the Hawking radiation seen by the observers at right null infinity. We highlight the conceptual similarity of this phenomenon with the standard Unruh effect in flat spacetime.