PAllen said:
“Consider a baseball at rest, and another rapidly moving one aimed to miss it by 6 inches. Consider that the gamma factor of the approaching baseball is 10^54. What happens? Assume perfect vacuum and isolation.”
“They don’t miss. Gravity alone turns this into a collision, and the product is a black hole.
First, the scale: a 145 g baseball at γ = 10⁵⁴ carries kinetic energy γmc² ≈ 1.3×10⁷⁰ J — the mass-equivalent of ~1.5×10⁵³ kg, roughly the rest energy of all ordinary matter in the observable universe.
A fast object never becomes a black hole by itself (in its own frame it’s just a baseball). What matters for a two-body encounter is the invariant center-of-mass energy: E_cm ≈ √(2γ)·mc² ≈ 1.8×10⁴³ J, equivalent to ~2×10²⁶ kg — about 34 Earth masses. The Schwarzschild radius of that energy is 2GE_cm/c⁴ ≈ 30 cm. Trapped-surface analyses of ultrarelativistic encounters (Penrose; Eardley–Giddings) guarantee horizon formation for impact parameters up to ~0.8 of that, ≈ 24 cm, and numerical relativity pushes the capture threshold somewhat farther out. Your 6-inch (15 cm) miss is well inside. (Even reading “6 inches” as the gap between surfaces, b ≈ 23 cm — still inside.)
What it looks like: the moving ball’s gravitational field is Lorentz-flattened into a pancake-thin shockwave riding along with it. Nothing precedes it — over the width of the universe the ball trails a photon by ~10⁻⁹⁰ s — so the resting ball gets zero warning. As the shock sweeps past, the geometry between them collapses; a trapped surface forms in under a nanosecond. The baseballs never touch. Matter is irrelevant here — spacetime itself closes around them.
Aftermath: a black hole of roughly 25–34 Earth masses (a sizable fraction of E_cm escapes as one of the most violent gravitational-wave bursts physically possible), born spinning at about half-extremal since b ≠ 0, and still carrying essentially all the original momentum — it departs along nearly the original trajectory at γ ≈ √(γ/2) ≈ 7×10²⁶, its emissions beamed into a ~10⁻²⁷-radian cone. Left in perfect isolation, it evaporates via Hawking radiation after ~10⁵⁵ years.
The kicker: the 6 inches barely mattered. The transverse kick on a bystander mass is Δp ≈ 4GEm/(bc³), which stays relativistic out to b ≈ 4GE/c⁴ ≈ 4×10²⁶ m — about the radius of the observable universe. Aimed to miss by a galaxy, it still shreds the target. Six inches never had a chance.”
javisot said:
It has taken a lot of effort, money, energy and...human intelligence.
And water!!
