Drag the mass from 3 M☉ to 10¹⁰ M☉ and watch the Schwarzschild radius, mean density, and tidal acceleration transform. The ω Cen IMBH candidate window is shown as a shaded band.
Two published measurements produce irreconcilable bounds. The shaded band on the slider marks both published limits — not a consensus.
r_s = 2GM/c² where G = 6.674×10⁻¹¹ m³/(kg·s²), c = 2.998×10⁸ m/s, M_☉ = 1.989×10³⁰ kg. Numerically: r_s ≈ 2953 × (M/M☉) metres.
Uniform sphere at the Schwarzschild radius: ρ = M / (4π/3 · r_s³). Scales as M⁻². For a 10 M☉ black hole, density exceeds the nuclear density of ~2×10¹⁷ kg/m³; for SMBHs it can be below that of water.
At radius r from the centre, tidal stretching across height h: a_tidal = 2GMh/r³. Here r = r_s and h = 1.8 m (standing human). Note: at the event horizon itself r = r_s, so the formula gives an order-of-magnitude estimate, not a physically meaningful crossing value.
Häberle et al. 2024, Nature 631:285 — stellar kinematic lower bound. Bañares-Hernández et al. 2025, A&A 693:A104 — pulsar timing upper bound.