# 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.

What matters is that the body is within the Schwarzschild radius, not the density differential.

Your thought experiment can not affect the black hole.

No way to destroy the black hole from outside. The only possibility is the Hawking radiation which can cause a cosmological black hole to evaporate in the very long term.

• But this is not the scenario - we're not in empty space. As an example, if the universe had uniform density, then even if it was high enough to constitute a black hole in empty space, it wouldn't - because no point would be 'special' and the gravitational force everywhere would be zero. – Alon Navon Aug 20 '18 at 18:17
• Furthermore, PBS explicitly state that what we need is a density differential, and that is the reason why the whole universe isn't a big black hole, as obviously it started out with incredible density. – Alon Navon Aug 20 '18 at 18:20
• I agree that a uniform density would not allow for a black hole to form, but my concern was that it is not possible to destroy a black hole from outside. There is no communication between the interior region and the exterior region of a black hole. As measured from outside, a particle or a light ray would take an infinite time to reach the horizon. – Michele Grosso Aug 21 '18 at 16:13