Binary Merger Calculator

Compact binaries spiral together, emitting gravitational waves. In LFM, these waves are oscillations in the χ field propagating at speed c.

🌊 GW150914: First Direct Detection

On September 14, 2015, LIGO detected gravitational waves from two black holes merging 1.3 billion light-years away.

  • • Masses: 36 + 29 M☉ → 62 M☉ final
  • • Energy radiated: 3 M☉c² as gravitational waves!
  • • Peak luminosity: 3.6×10⁴⁹ W (brighter than all stars in observable universe)
  • • Signal duration: 0.2 seconds (chirp from 35→250 Hz)

Nobel Prize 2017

Rainer Weiss, Barry Barish, and Kip Thorne received the Nobel Prize in Physics for "decisive contributions to the LIGO detector and the observation of gravitational waves."

LFM Mechanism

In the LFM framework, gravitational waves are propagating χ field oscillations. Orbiting masses create time-varying χ gradients that ripple outward through the lattice. The wave equation for χ (GOV-02) naturally supports wave solutions traveling at c.

∂²χ/∂t² = c²∇²χ − κ(Σₐ|Ψₐ|² − E₀²) → χ waves with v = c

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Gravitational Wave Properties

GW Frequency
2.14 Hz
Time to Merger
5.47 min
Chirp Mass
28.10 M☉
Mass Ratio
q = 0.806
Chirp mass M_c = (m₁m₂)^(3/5) / (m₁+m₂)^(1/5) — determines waveform amplitude
Orbital Period935.19 ms
Orbital Velocity12.9% c
GW Luminosity1.82e+43 W
Strain (at 1 Mpc)h ≈ 5.13e-20
χ/χ₀ at separation0.983192
ISCO (Innermost Stable Orbit)
Radius: 576 km
Frequency: 67.63 Hz
r_ISCO = 6GM/c² — plunge and merger begin inside this radius

The Gravitational Wave "Chirp"

🌀

Inspiral

Objects orbit, losing energy to GW. Orbit shrinks slowly. Frequency increases over millions of years.

⚡

Merger

Final seconds: rapid frequency increase ("chirp"). Peak luminosity exceeds all stars in universe combined!

🔔

Ringdown

Final BH settles to Kerr geometry. Damped oscillations as χ field relaxes.

Inspiral → Merger → Ringdown

Detector Sensitivities

LIGO/Virgo
10 Hz – 5 kHz
Stellar mass mergers
LISA (2035+)
0.1 mHz – 1 Hz
SMBH mergers, EMRIs
Pulsar Timing
1 nHz – 100 nHz
SMBH background

Gravitational waves predicted by Einstein (1916), first detected by LIGO (2015).
LFM describes GW as χ field oscillations propagating through the lattice.