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Physics

Curved spacetime

Compute massive and null geodesics in Schwarzschild spacetime. A Flamm embedding, orbital trail, static-clock redshift and conserved-energy residual connect geometry with measurable quantities.

Curved spacetime — Actual application image
Actual application image

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Geometrized units G = M = c = 1. The surface embeds a spatial slice; its slope is not a Newtonian force. Massive or light trajectories follow Schwarzschild geodesics.

Equations used in the module
Equations
r″ = −κ/r² + L²/r³ − 3L²/r⁴; φ′ = L/r²
E² = r′² + (1−2/r)(κ + L²/r²)
t′ = E/(1−2/r); κ = 1 (massive), 0 (light)
zFlamm = 2√[2(r−2)]; dτstatic/dt = √(1−2/r)

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