Observing a Schwarzschild black hole with finite precision
Résumé
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 (2004, Eur. Phys. J. B, 37, 257). 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, unlike deSitter space-time. However, the ``magnitude'' of the trace-free Ricci tensor does not vanish for this space-time, whereas it does for deSitter space-time. Possible cosmological implications, concerning the evaluation of the mean density of the Universe and the cosmological constant, are also discussed.