Ether Flow Visualizer

Theorem 3.2 identifies the Painlevé–Gullstrand metric with the acoustic metric of a radially inflowing ether. Gravity is not curved space — it is flat space with a velocity field. The horizon is where the inflow speed reaches c. Spatial slices are Euclidean; all gravitational effects are encoded in the temporal metric components.

Black hole mass: 10 M_&odot;

Display range: 10 r_s

Key Radii for 10 M_&odot;

Horizon r_s = 2GM/c²: 29.5 km; v_ff = c
Photon sphere 1.5 r_s: 44.3 km; Unstable circular photon orbits
ISCO 3 r_s: 88.6 km; Innermost stable circular orbit
v_ff at ISCO: 57.7% c; √(1/3) × c

Verification

v_ff(r_s) = c exactly (horizon condition)(got 2.998e+8, err 0.00%)

v_ff(10²⁰ m)/c < 10⁻⁷ (approaches zero at infinity)(got 1.719e-8, err 0.00%)

g_TT(r_s) = 0 (horizon: c²-v² = 0)(got 0.000e+0, err 0.00%)

g_TT(∞) → -c² (flat spacetime)(got -8.988e+16, err 0.00%)

r_s(10 M☉) = 29,541 m(got 2.954e+4, err 0.00%)

v_ff(4 r_s) = c/2 (half light speed)(got 5.000e-1, err 0.00%)

The Ether Picture of Gravity

Flat space + flow: The PG metric (Eq 3.21) has Euclidean spatial sections (dr² + r²dΩ²). There is no spatial curvature. All gravitational effects — time dilation, light bending, orbital precession — are encoded in the ether’s velocity field v(r) = √(2GM/r).

The horizon: At r = r_s, the inflow velocity equals c. Inside the horizon, the ether flows faster than light — no signal can propagate outward, defining the trapped region. This is the acoustic analogue of the event horizon.

Free fall: An object at rest in the ether frame is carried inward by the flow. Its trajectory is a geodesic of the PG metric — free fall is the natural state of motion in a flowing medium.

Read §3.1: Acoustic Metrics Hawking Temperature PPN Parameters

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Key Radii for 10 M&odot;

Verification

The Ether Picture of Gravity

Key Radii for 10 M_&odot;