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.