# Black holes and relative density

In "Black Holes from the Dawn of Time" by PBS Digital Studios (https://www.youtube.com/watch?v=rcv_tYcRgw4&list=PLsPUh22kYmNBl4h0i4mI5zDflExXJMo_x&index=3) it is stated, very logically, that in order for a black hole to exist it isn't enough to have an enormous mass in a small volume of space (i.e high absolute density), but that you need a high density differential (i.e high relative density). If for example the universe had uniform density, no matter how high it was, the net gravity everywhere would be $0$ (supposedly that is why the universe isn't full of primordial black holes).

But if all that matters is the density differential, we can reduce the differential from outside the hole. Say, by enveloping the black hole with an incredibly dense particle cloud. Actually, if there is a 'critical' density differential, then it seems to me that just by sending a bit of material in a very fast trajectory around the edge of the event horizon (without falling in), you could reduce the density differential to subcritical, and 'destroy' the black hole.

Is this theoretically possible? Could a black hole be 'plugged' this way?

The Schwarzschild metric describes the geometry of spacetime in the empty space surrounding a static and spherically symmetric mass. When the Schwarzschild radius $r_s = 2M$ (natural units $c = G = 1$, being $M$ the gravitating body mass) is higher than the mass boundary, the metric outlines a black hole.