Black Hole Formation and Growth: Simulations in General Relativity
arXiv preprint arXiv:0711.1537, S. L. Shapiro (2007)
A clear bell rings in the paper: large computer simulations in full general relativity can now trace how black holes form, how they grow, and how they can power bright bursts.
Key Concepts – the Lanterns the Authors Carry
- Black Hole (an object so dense light cannot escape)
- Hypermassive Neutron Star (HMNS) (a heavy, fast-spinning dead star)
- Magnetohydrodynamics (MHD) (how magnetic fields move hot gas)
- Equation of State (EOS) (how dense matter behaves)
Guiding Questions
- How do different stellar deaths and mergers make black holes?
- How do those holes then gain mass?
- Can these processes explain short and long gamma-ray bursts and the existence of early supermassive black holes?
The study gathers and summarizes many recent simulations to show the routes.
Tools – Maps of Spacetime Solved on a Computer
- The 3+1 split and BSSN scheme recast Einstein’s equations so the computer can follow them stably (p. 2–3).
- Simulations include
- Neutron star pairs meeting,
- Strongly magnetized, differentially rotating HMNSs,
- Collapsing massive stars,
- Tiny early black hole seeds growing by gas falling in (p. 4–11).
Results – Patterns That Emerge
1. Neutron-Star Mergers
| Total Mass Condition | Outcome |
|---|---|
| Above ~2.5–2.7 M☉ | Prompt collapse to a black hole |
| Below ~2.5–2.7 M☉ | HMNS survives for ~100 ms → delayed collapse → short burst of gravitational waves |
2. Magnetized HMNS “Clockworks”
- Process: Magnetic winding & instabilities move angular momentum outward
- Timescale: Collapse after ≈66 rotation periods
- Final State:
- Black hole ≈0.9 M☉
- Hot, accreting torus ≈0.1 M☉
- Field lines focused along spin axis
- Energy Output: Torus lives ~10 ms, emits ~10⁵⁰ ergs in neutrinos before being swallowed
“All these properties make this system a promising central engine for a short-hard GRB.”
3. Collapsing Very Massive Stars
- Outcome:
- Black hole mass: M_h ≈ 0.95 M☉, spin: J_h/M_h² ≈ 0.7
- Thick, hot torus feeds turbulent, episodic accretion
- Magnetic fields collimate along axis
Described as a “viable candidate for the central engine of a long-soft GRB.”
4. Growing Small Seeds into Supermassive Beacons
- Key: Efficiency ε_M of turning mass into light matters
- Turbulent MHD disk: ε_M ≈ 0.19 → growth feasible
- Standard thin disk: ε_M ≈ 0.32 or higher → growth harder or impossible
Caveats – Careful and Quiet About Limits
Results depend on
- The assumed EOS,
- The initial magnetic strength,
- Simplifications such as axisymmetry and frozen spacetime.
The authors call for more detailed relativistic MHD work—including radiation effects—to sharpen the map.
Metaphorical Closing
Think of these simulations as a set of lanterns along a dark path.
Each lamp—merger, magnetized collapse, accreting disk—shows a different route to a black hole and a different way to light the sky.
Together, they stitch local, relativistic physics into the larger story of how black holes grow and power bursts across the universe.