[dr_lew]

The inevitability of gravitational collapse into a black hole is a simple consequence of E = mc².

Realizing that pressure, as force/area, represents an energy density, as energy/volume, we see that a certain pressure within a volume, R³, will give rise to a mass, M = pR³/c², which will create a gravitational pressure, GM²/R²

So, as soon as

GM²/R > Mc² or GM/c > R ,

we have reached a point where pressure created within the volume in order to resist collapse, creates enough mass to overwhelm itself by gravitation, and collapse accelerates.

This simple analysis gives the Schwarzschild radius except for a factor of 2.

[decimon]

<...except for a factor of 2.

There's always that little catch.

[dr_lew]

Realizing that pressure, as force/area, represents an energy density, as energy/volume, we see that a certain pressure within a volume, R³, will give rise to a mass, M = pR³/c², which will create a gravitational pressure, GM²/R²

Oops. The last term should be energy/volume or GM²/R/R³ = GM²/R⁴

Then

GM²/R⁴ > p = Mc²/R³ becomes GM/c² > R