Overview

Space-time geometry fluctuations are expected to be a generic feature of a successful theory of quantum gravity. Despite the lack of such a theory, it is still possible to explore the physical implications of space-time fluctuations. The techniques employed are gauge invariant---being based on the Riemann tensor correlation function. Two scenarios will be discussed within the semiclassical theory of General Relativity. In the first, the space-time is taken to be nearly Minkowskian on average. Fluctuations are induced by the presence of either a linearized quantum graviton field or a thermal bath of gravitons, and are characterized by fluctuations in the trajectory or flight time of null rays traversing the fluctuating space-time from a distant source to an observer. The observable manifestation of these fluctuations are a blurring of the angular position of the source or a broadening of the spectral line of the source. It is shown that these effects are quite small and are likely not observable. In the second scenario under investigation, the space-time is taken to be Schwarzschild on average and the context is that of an evaporating black hole. Fluctuations of the horizon are induced through three models of ingoing quantum fields---a scalar graviton model that is a conformal transformation of the metric where the conformal factor is a scalar field, a linearized graviton model, and a scalar field stress tensor model. Fluctuations to the space-time are characterized by fluctuations in the squared length of a vector used to describe the deviation of outgoing null geodesics near the horizon and what effect these fluctuations could have on Hawking radiation. It is shown that fractional fluctuations of the squared length of the separation vector may be of order one, concordant with results obtained by previous authors in somewhat different contexts. Furthermore, it is found that the Hawking process appears to be very robust against these types of fluctuations.

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