Observing a Schwarzschild black hole with finite precision

¹ ERGA, UMR 8112, 4 Place Jussieu, 75231 Paris Cedex 05, France
² CNRS, UMPA, École normale supérieure de Lyon, 69364 Lyon Cedex 07, France

Received: 6 May 2004
Accepted: 23 November 2004

Abstract

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 de Sitter space-time. However, the “magnitude” of the trace-free Ricci tensor does not vanish for this space-time, whereas it does for de Sitter space-time. Possible cosmological implications, concerning the evaluation of the mean density of the Universe and the cosmological constant, are also discussed.