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Approaching a Black Hole

How these connect

Schwarzschild radius and what it relates to. Every line is an evidence-backed relation, and the arrangement is fixed — this address draws this picture, today and next year.

derived_from — For a non-rotating black hole the horizon sits exactly at the Schwarzschild radius, which is where the solution's coordinate description of a static observer breaks down.derived_from — The photon sphere lies at one and a half Schwarzschild radii and the shadow it casts has a diameter of about 5.2 Schwarzschild radii, so both scale linearly with mass.created_by — The radius appears in the exact vacuum solution Schwarzschild derived in 1916, within weeks of the field equations being published.constrained_by — Because the horizon radius grows linearly with mass while tidal acceleration falls as the cube of distance, the tide at the horizon falls as the inverse square of mass - so crossing a supermassive horizon is locally gentle.derived_from — The redshift factor between a static clock and a distant one is the square root of one minus the ratio of Schwarzschild radius to radius, and it vanishes at the horizon.The photon sphere and the shadowThe photon sphere and the…Schwarzschild radiusSchwarzschild radiusThe event horizonThe event horizonKarl SchwarzschildKarl SchwarzschildTime dilation near a horizonTime dilation near a hori…Tidal stretching near a black holeTidal stretching near a b…
6 drawn · 4 reachable and not drawn · positions derived from object ids, never from a simulation
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Every relation drawn, in words5
  1. The event horizon · derived_from · Schwarzschild radius

    For a non-rotating black hole the horizon sits exactly at the Schwarzschild radius, which is where the solution's coordinate description of a static observer breaks down.

  2. The photon sphere and the shadow · derived_from · Schwarzschild radius

    The photon sphere lies at one and a half Schwarzschild radii and the shadow it casts has a diameter of about 5.2 Schwarzschild radii, so both scale linearly with mass.

  3. Schwarzschild radius · created_by · Karl Schwarzschild

    The radius appears in the exact vacuum solution Schwarzschild derived in 1916, within weeks of the field equations being published.

  4. Tidal stretching near a black hole · constrained_by · Schwarzschild radius

    Because the horizon radius grows linearly with mass while tidal acceleration falls as the cube of distance, the tide at the horizon falls as the inverse square of mass - so crossing a supermassive horizon is locally gentle.

  5. Time dilation near a horizon · derived_from · Schwarzschild radius

    The redshift factor between a static clock and a distant one is the square root of one minus the ratio of Schwarzschild radius to radius, and it vanishes at the horizon.