Black holes in the Universe: Generalized Lemaître-Tolman-Bondi solutions

We present new exact solutions which presumably describe black holes in the background of a spatially flat, pressureless dark-matter-- or dark matter plus dark energy (DM+DE) - or quintom-dominated Universe. These solutions generalize Lema\^tre-Tolman-Bondi metrics. For a dark-matter-- 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.