I'm studying properties of Kerr spacetimes and a lot of fuss is made about area of BH. It is defined to be integral of area element on event horizon $r=r_+$, $t=const.$ where $r_+$ is radial coordinate of outer event horizon. In what way this can be interpreted as actual area of anything? What kind of measuring process would yield as a result this area?
What bothers me is the result we get depends on foliation of spacetime we choose, doesn't it?