Higher harmonics in gravitational wave signals from binary black hole mergers
Summary
In the year 2019 two separate gravitational wave observations were done at the Virgo and LIGO detectors which were in both cases caused by two coalescing black holes of significantly different masses. These observations were GW190412 [Aea20a] and GW190814 [Aea20b]. In previous studies evidence was found for the prensence of higher harmonics in these black hole mergers [Aea20a]. This is also predicted by Einstein’s General Relativity.
By working out the first few orders of the gravitational waves, using the linearized Einstein equations and using data analysis on the observations, we can test general relativity in a new way to check if Einstein’s predicitons were indeed correct. In this thesis we will work out the calculations and algorithms needed to do this test.
Additionally, we examinate the relation between higher harmonics in gravitational waves and spin-weighted spherical harmonics. We will find that the wavefunction can be written in terms of tensor spherical harmonics. Next, we prove that we can express the tensor harmonics in terms of spin-2 weighted spherical harmonics. This allows us in the end to find an equation for the waveform in terms of spin-2 weighted spherical harmonics.