The gravastar model, which postulates a strongly correlated thin shell of anisotropic matter surrounding a region of anti-de Sitter space, has been proposed as an alternative to black holes. We discuss constraints that present-day observations of well-known black hole candidates place on this model. We focus upon two black hole candidates known to have extraordinarily low luminosities: the supermassive black hole in the Galactic Center, Sagittarius A*, and the stellar-mass black hole, XTE J1118+480. We find that the length scale for modifications of the type discussed in Chapline et al. (2003) must be sub-Planckian.
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