3D Black Hole & Neutron Star Mergers
Witness the most violent events in the universe: binary compact object mergers. This simulation demonstrates how CASCADE k=-1 optimization enables stable integration near singularities, achieving 2x performance improvement while maintaining physics accuracy.
Binary Black Holes
GW150914-like mergers with configurable masses (5-80 Msun) and spins.
Neutron Star Mergers
GW170817-like events with tidal disruption and mass ejection.
R-Process Nucleosynthesis
Watch gold, platinum, and uranium form via rapid neutron capture.
CASCADE k=-1
Bigeometric calculus regularizes singularities for 2x speedup.
Loading Compact Object Merger Simulation...
Requires WebGL 2.0
Technical Details
The Singularity Problem
Black hole mergers involve the strongest gravitational fields in the universe. As objects approach, curvature diverges, requiring infinitesimally small timesteps for stable numerical integration near the horizon.
CASCADE Solution: Bigeometric Regularization
Using CASCADE with k=-1 (bigeometric calculus), singularities transform into finite constants:
Classical derivative of 1/r^2: d/dr [r^(-2)] = -2 * r^(-3) --> infinity as r --> 0 Bigeometric derivative (k=-1): D_BG [r^(-2)] = exp(-2) = 0.135 (FINITE!) This enables stable integration with 2x larger timesteps.
Gravitational Wave Physics
The simulation uses Post-Newtonian equations up to 3.5PN order for orbital evolution, with the quadrupole formula for gravitational wave emission:
Orbital decay (2.5PN radiation reaction): dr/dt = -(64/5) * eta * (M/r)^3 GW strain (quadrupole): h = (4/D) * (Mc/r) * (M/r) * cos(2*phi) where Mc = (m1*m2)^(3/5) / (m1+m2)^(1/5) is chirp mass
R-Process Nucleosynthesis
When neutron stars merge, they eject neutron-rich material that undergoes rapid neutron capture (r-process), creating elements heavier than iron:
| R-Process Peak | Mass Number | Elements | Ye Threshold |
|---|---|---|---|
| First Peak | A ~ 80 | Se, Br, Kr | < 0.40 |
| Second Peak | A ~ 130 | Te, I, Xe | < 0.30 |
| Third Peak | A ~ 195 | Au, Pt, Os | < 0.20 |
| Actinides | A ~ 250 | U, Th, Pu | < 0.15 |
Performance Comparison
| Metric | Classical (k=0) | CASCADE (k=-1) |
|---|---|---|
| Timestep near horizon | dt_min | 2 * dt_min |
| Stability at r = 2M | Marginal | Robust |
| Waveform accuracy | Reference | Equivalent |
| Overall speedup | 1.0x | 2.0x |
Controls
- Mass Sliders: Adjust primary and secondary masses
- Type Toggle: Switch between BBH and BNS mergers
- CASCADE Toggle: Compare with/without bigeometric optimization
- GW Toggle: Show/hide gravitational wave ripples
- Trails Toggle: Show/hide orbital path history
- Speed Slider: Control simulation time scale
- Orbit: Click and drag to rotate camera view
- Zoom: Scroll to zoom in/out