Do we know the mass of a black hole? Mass of some cosmological black
  hole models
  Using a cosmological black hole model proposed recently, we have calculated
the quasi-local mass of a collapsing structure within a cosmological setting
due to different definitions put forward in the last decades to see how similar
or different they are. It has been shown that the mass within the horizon
follows the familiar Brown-York behavior. It increases, however, outside the
horizon again after a short decrease, in contrast to the Schwarzschild case.
Further away, near the void, outside the collapsed region, and where the
density reaches the background minimum, all the mass definitions roughly
coincide. They differ, however, substantially far from it. Generically, we are
faced with three different Brown-York mass maxima: near the horizon, around the
void between the overdensity region and the background, and another at
cosmological distances corresponding to the cosmological horizon. While the
latter two maxima are always present, the horizon mass maxima is absent before
the onset of the central singularity.
