Are quantization rules for horizon areas universal?

Doubts have been expressed on the universality of holographic/string-inspired quantization rules for the horizon areas of stationary black holes, or the products of their radii, already in 4-dimensional general relativity. Realistic black holes are not stationary but time-dependent. We produce three examples of 4-dimensional general-relativistic spacetimes containing dynamical black holes for at least part of the time, and we show that the quantization rules (even counting virtual horizons) cannot hold, except possibly at isolated instants of time, and do not seem to be universal.

Figure 1

The proper radii of the AHs of a dust-dominated McVittie metric vs time. The negative radius represents the virtual horizon. At a critical time a cosmological AH (dashed curve) appears together with a black hole AH (solid curve), the former expanding and the latter shrinking.

Figure 2

The radii of the AHs of the generalized (accreting) McVittie spacetime vs time. There are always either two virtual AHs (with negative radii) or two real AHs with $R\ge 0$ (a cosmological AH, thick solid curve, and a black hole AH, dashed curve, both appearing at a critical time).

Figure 3

The proper radii vs time of the real AHs of an electrically charged McVittie spacetime with a spatially flat, dust-dominated, FLRW background.