The gravitational waterfall
dc1 particles free-fall radially inward toward a central mass. Their velocity at radius r equals the free-fall velocity, producing the Painlevé-Gullstrand form of the Schwarzschild metric exactly.
Mc²
orbital system
dc1 particles fall inward from all directions
At radius r, each dc1
has fallen from infinity
v_ebb = √(2GM/r)
free-fall velocity
Modons in this flow
see an acoustic metric
ds² = −(c²−v²)dt² − 2v·dr dt + dr²
Painlevé-Gullstrand metric
exactly
Schwarzschild metric
All classical GR tests pass
The dc1 ebbing current IS the "gravitational waterfall"
Spacetime curvature is the gradient of the flow