The event horizon of a black hole has a finite surface area, i.e. it is a more or less well defined area of space-time. Black hole thermodynamics now tell us that we can associate entropy with that surface area, and by definition entropy is in turn related to the number of micro-states of a system. So, the event horizon is not a material object but rather a region of space-time, and we can associate a well-defined entropy with such a region, which, in turn, allows us to compute a number associated to micro-states, and that number will be. Would this not automatically imply that the space-time region of the event horizon must be fundamentallyfinitesince it has a finite number of micro-states ? In the absence of anything but space-time ( the event horizon is not a tangible surface as such ) the entropy cannot be associated with anything but micro-states of space-time itself, so it ought to be impossible for such a space-time to be a continuum because the entropy would then be infinite.discreet

Furthermore, since the entropy depends only on the area of the horizon and not on any other property of the black hole, we should in principle be able to chooseclosed surface / connected region of space-time, regardless of whether that is an event horizon or not, and associate entropy to it, and that entropy should correspond to a finite number of micro-states. That would mean that space-time in general ought to be discreet on a microscopic level, and not a continuum.any

What do you think ?