Astrophysical Benchmarks & Controls
3 M☉ Stellar
4.3M M☉ Sgr A*
10B M☉ Ultramassive
Drag to Tilt Relativistic Accretion Disk & Einstein Ring
M = 4.27 × 10⁶ M☉
Schwarzschild Rs
12.60M km
0.084 AU
Kerr ISCO Radius
1.16 Rs
η = 15.6% Mass→Energy
Time Dilation (dt/dτ)
1.50× Slower
z_grav = 0.500
Shadow Diameter
5.20 Rs
Disk Peak: 1.4×10⁵ K
General Relativity Benchmark Table: Stellar, JWST "Little Red Dots" & Supermassive Black Holes
Bottom Line Up Front: Around any black hole of mass M, the event horizon is bounded by Rs = 2GM/c², unstable photon orbits form a bright lensed ring at Rph = 1.5 Rs (projecting an apparent shadow diameter of 3√3 Rs ≈ 5.196 Rs), and prograde Kerr spin (a*) drags space-time so strongly that matter can orbit down to 0.5 Rs before plunging inside.
| Black Hole System | Mass (M☉) | Schwarzschild Radius (Rs) | Kerr Spin (a*) | Tidal Spaghettification at Horizon |
|---|---|---|---|---|
| Cygnus X-1 (HDE 226868) | 21.2 M☉ | 62.6 km | > 0.92 | Extreme (~3.4×10⁷ g/m lethal before horizon) |
| GW150914 Merger Remnant | 62.0 M☉ | 183.1 km | 0.68 | Severe (~4.0×10⁵ g/m across human body) |
| Sagittarius A* (Milky Way Center) | 4.30 × 10⁶ M☉ | 12.70M km (0.085 AU) | ~0.90 | Mild (0.0012 g/m — cross horizon unharmed) |
| JWST "Little Red Dot" (z=7 AGN) | 7.00 × 10⁷ M☉ | 206.7M km (1.38 AU) | ~0.85 | Negligible (2.8×10⁻⁷ g/m at horizon) |
| M87* (Virgo A Supergiant) | 6.50 × 10⁹ M☉ | 19.20B km (128.3 AU) | ~0.94 | Zero Tidal Shear (3.5×10⁻¹³ g/m) |
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