Pedagogy, or even physics, may benefit from "toy cosmos"s.
Mine start with a three sphere (s3). Then i try some (naive) Physics :
**hyp.1** : if it shrinks, i see the photon i put inside gaining enormous amounts of energy. (blue shifted at each round trips) Decrease of spacetime with creation of (boson) energy becomes part of the playground.
**hyp.2** : since "Schwarzschild radius" (for on b.h. of M~0~) inside our (big unfriendly) universe has been found to be :
r~(s)0~ = 2GM~0~ / c²
So, in flat space, say i put 1000 (mini) black holes, each one of mass :
M~1~ = M~0~ / 1000
Their total (Schwarzschild) volume (for 1000 x M~1~ black holes) is about :
( 1000 x 3/4pi x r~1~³ )
Then, they all fit comfy inside (v~0~) :
( 1 x 3/4pi x r~0~³ )
which is the (Schwarzschild) volume of their collective masse. (volume ratio is 1000³)
So, what i say is that one can bend spacetime using many well spaced black holes that collectively have one larger (rs~0~) Schwarzschild radius. And now, flat space is bent to s3 with room to play inside. Cosmic radius to cosmic energy relations can be tried here. Would black holes, in this, lose their energy to other objects ?
(should this be posted in AskLemmy ?)