Observing a Schwarzschild black hole with finite precision

We investigate how the space-time of a vacuum Schwarzschild black hole would appear if observed with a finite precision in the measurements of the spatial Kerr-Schild coordinates. For this we use the general procedure for evaluating mean gravitational fields recently presented in (Debbasch 2004b). It is found that the black hole would then appear as surrounded by an apparent matter characterized by a negative energy density and two different pressures, a negative and a positive one. The total combined effect of the apparent matter leads to a space-time of negative scalar curvature, like de Sitter space-time. However, the ‘magnitude’ of the trace-free Ricci tensor does not vanish for this space-time, where as it does for de Sitter spacetime. Possible cosmological implications, concerning the evaluation of the mean density of the Universe and the cosmological constant, are also discussed.