A no-hair theorem for non-isolated black holes

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Written by Norman Gurlebeck

The no-hair theorem states that black holes are entirely characterized by their mass, angular momentum and charge alone. For this result to hold, the black hole must be isolated, i.e., there should be no additional sources of the gravitational field in their neighborhood like accretion disks. However, measurements of the angular momentum of the black hole rely heavily on the existence of such an accretion disk. Naturally, the question arises if the additional matter, say, an accretion disk impedes the suggested tests of the no-hair theorem. I will give a possible formulation of the no-hair theorem for such astrophysical black holes surrounded by matter alongside with a proof for static black holes. The proof employs the source integral formalism, which I review shortly. In the end of my talk, I will elude to some appliciations of this no-hair theorem to certain existence and uniqueness questions in mathematical relativity .