piles up enough mass in a concentrated region of space one ends up with a black hole. Some readers may ponder why do we need to consider a concentrated region of space. The reason is that if we allow the clock to be more massive by making it bigger, it also deteriorates its performance. For instance, in the case of two mirrors and a photon, if one makes the mirror big, there will be uncertainty in its position due to elastic effects like sound waves traveling across it, which will negate the effect of the additional mass (see the discussion in [@ngotro] in response to [@baez]).

A black hole can be thought of as a clock (as we will see it turns out to be the most accurate clock one can have). It has normal modes of vibration that have frequencies that are of the order of the light travel time across the Schwarzschild radius of the black hole. (It is amusing to note that for a solar sized black hole the frequency is in the kilohertz range, roughly similar to that of an ordinary bell). The more mass in the black hole, the lower the frequency, and therefore the 