Black Holes in the Universe: Generalized Lemaitre-Tolman-Bondi Solutions

We present new exact solutions {which presumably describe} black holes in the background of a spatially flat, pressureless dark matter (DM)-, or dark matter plus dark energy (DM+DE)-, or quintom-dominated universe. These solutions generalize Lemaitre-Tolman-Bondi metrics. For a DM- or (DM+DE)-dominated universe, the area of the black hole apparent horizon (AH) decreases with the expansion of the universe while that of the cosmic AH increases. However, for a quintom-dominated universe, the black hole AH first shrinks and then expands, while the cosmic AH first expands and then shrinks. A (DM+DE)-dominated universe containing a black hole will evolve to the Schwarzschild-de Sitter solution with both AHs approaching constant size. In a quintom-dominated universe, the black hole and cosmic AHs will coincide at a certain time, after which the singularity becomes naked, violating Cosmic Censorship.