Simulation · Relativity

Gravitational Time Dilation Simulation

Reading time: 6 minConfidence: HighLast verified: July 2026

This simulation lets you choose a massive astronomical object and a distance from it, showing how strongly time dilates at that distance using the exact Schwarzschild formula, alongside a visual representation of the surrounding spacetime curvature.

Interactive simulation

Object Distance (multiples of Schwarzschild radius)10.0 r_s

Schwarzschild radius: —

Time dilation factor: —

1 second here = — far away

The physics behind this simulation

The exact Schwarzschild time dilation formula relates a clock's tick rate at radius r to its rate infinitely far from the mass:

t_∞ = t_r√(1−r_s/r)

As r approaches r_s (the Schwarzschild radius), the term under the square root approaches zero, meaning t_∞ approaches zero too — from the perspective of a distant observer, a clock falling toward the event horizon appears to tick slower and slower, effectively freezing at the horizon itself, though the falling observer's own clock (and experience) continues normally through their own reference frame.

Common mistakeThe formula is undefined for r < r_s — inside the event horizon, r and t effectively swap their usual roles in the Schwarzschild metric, and the concept of a "static" clock at fixed r no longer applies. This simulation only shows the region outside the event horizon (r > r_s), where the static, external description remains valid.

Sources

Schwarzschild, K. (1916). Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften, 189–196.

Last verified: July 2026 · Source: Schwarzschild (1916) · Confidence: high

Interactive simulation

The physics behind this simulation

Sources

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