What Happens When a Star Falls In

Before a star falls in, it has to be in the right cluster. The cluster comparator sorts every Milky Way globular by mass, half-light radius, distance, age, or IMBH candidate mass. Sort by IMBH candidate mass and ω Cen immediately floats to the top — it is the only cluster with an IMBH lower limit (Häberle 2024: ≥ 8,200 M⊙) rather than just an upper limit. This is the predicate for everything that follows: the only reason this particular encounter is interesting is because the cluster hosts a candidate IMBH, not a diffuse stellar core.

A star in the outer cluster is gravitationally scattered onto a plunging orbit by two-body relaxation — the same process that concentrates massive stellar remnants near the centre (see Demo L, Step 3). The orbital-dynamics tool shows the crowded stellar environment near the IMBH in Häberle mode, including the seven high-velocity stars whose orbits constrain the IMBH mass. The inbound star traces a hyperbolic or highly eccentric trajectory before it reaches the tidal disruption radius at Step 3. The closer the pericenter, the higher the peak fallback luminosity.

A star is tidally disrupted when the BH's tidal force across its diameter exceeds its self-gravity. The tidal disruption radius is r_t = R_* (M_BH/M_*)^1/3. For the star to be disrupted outside the event horizon (a visible TDE), we need r_t > r_s = 2GM_BH/c². For a 1 M⊙ star approaching an 8,200 M⊙ BH the mass ratio contributes (8,200)^1/3 = 20.2, giving r_t ≈ 1.4×10¹⁰ m ≫ r_s ≈ 2.4×10⁷ m, a factor of 580 — the star is shredded far outside the horizon and roughly half its mass fallbacks into the accretion disc. For a white dwarf, the calculation is different — try the compact scenario above.

The disrupted debris circularises into an accretion disc. Where the disc's inner edge settles depends on the BH's spin: for a Schwarzschild (non-spinning) BH the innermost stable circular orbit (ISCO) is at r_ISCO = 6 r_g = 3 r_s; for a near-maximal Kerr BH (a ≈ 0.99) the prograde ISCO plunges to r_ISCO ≈ 1.45 r_g = 0.73 r_s. Note that r_g = GM/c² is half r_s; the two are routinely confused in quoted ISCO values. The ergosphere — the region where spacetime itself rotates faster than light — only exists for spinning BHs; it is where the Blandford–Znajek process (see Demo B) extracts rotational energy. The Kerr geometry tool shows both boundaries and lets you trace the equatorial and polar cross-sections at any spin and mass.

As the disrupted debris spirals inward, it passes through regions of intense gravitational time dilation. A clock on the Schwarzschild ISCO runs 1.41× slower than one far from the BH, using dτ/dt = √(1 − 3/r + 2a/r^3/2)/(1 + a/r^3/2) for a circular orbit; at the Kerr prograde ISCO with a = 0.998 the factor reaches 10.8×. For the accretion disc, this means: the peak-luminosity flare that observers at Earth see stretched in time is the sum of emission from across a range of orbital radii, each time-dilated by a different factor. The time-dilation tool lets you place two fiducial radii — say, the ISCO and 6 r_g — and read off the ratio of proper time rates simultaneously.

The half of the stellar mass that crosses the event horizon carries with it every bit of information encoded in its quantum state — the positions and momenta of ≈ 10⁵⁷ nucleons. By the Bekenstein bound, the maximum information that can be encoded in a mass M within radius R is I ≤ 2πRMc/(ℏ ln 2). That infalling mass adds to the BH's entropy by exactly this amount (the Hawking–Bekenstein formula S = kA/4l_p²). The information is not destroyed per the Page curve / unitarity argument — but it takes ≈ 1.2×10⁷⁹ yr to emerge in Hawking radiation. The Bekenstein tool lets you verify the entropy bookkeeping at each scenario's mass and spin.