Modeling the Frequency of Gravitational Waves Emitted by a Binary Black Hole S<span style="box-sizing:border-box; margin:0px; padding:0px">ystem Using Computational and Theoretical Analysis

Gravitational waves disturb spacetime as they pass through by stretching one tunnel and squeezing the other. Due to destructive interference, the laser beams recombine perfectly at the detector, canceling each other. But if spacetime is disturbed due to a passing gravitational wave, the beams won’t cancel out altogether, revealing the presence of the wave. An interesting parallel exists between how LIGO detects gravitational waves and how the Bat-Signal works, using the alignment analogy to explain LIGO’s detection mechanism. There is a strong relationship between the mass of the black holes and the frequency of the emitted gravitational waves. Black holes' orbital motion causes them to lose energy by emitting gravitational waves. The energy loss shrinks the orbit, increasing the frequency of emitted waves as the black holes spiral inward. The time delay between when a wave hits each detector can help determine the wave's direction.

The presented study mimics the evolution of a binary system by calculating the orbital decay due to energy loss and modeling the frequency of emitted gravitational waves. We rely on several key formulas from gravitational wave physics and Newtonian mechanics to model the frequency evolution. The rate at which energy is lost from the system, primarily due to gravitational wave emission, is given by the Peters-Mathews formula, which shows how the energy of the system decreases over time, causing the black holes to spiral inward. Numerical and computational methods are used to solve for how the orbital separation and gravitational wave frequency evolve over time.

This study simulates the orbital motion of a binary black hole system and how it radiates gravitational waves, which is fascinating, especially since presented research studies using simplified formulas (not full general relativity) and still match observed LIGO data.