Gravitational waves are detected, analyzed and matched filtered based on an approximation of General Relativity called the Post Newtonian theory. This approximation method is based on the assumption that there is a weak gravity field both inside and around the body. However, scientists cannot justify why Post-Newtonian theory (meant for weak fields) works so well with strong fields of black hole mergers when it really should have failed [C. Will 2011]. Yunes and Pretorius gave another approach called parameterized post-Einsteinian (ppE) theory that uses negligible assumptions and promises to identify any deviation on the parameters through post-processing tests. This thesis project proposes to develop a method for the parametric detection and testing of gravitational waves by computation of ppE for the inspiral phase using ChirpLab. A set of templates will be generated with ppE parameters that can be used for the testing. / Master of Science / Electromagnetic waves were discovered in the 19th century and have changed our lives with various applications. Similarly, this new set of waves, gravitational waves, will potentially alter our perspective of the universe. Gravitational waves can help us understand space, time and energy from a new and deeper perspective. Gravitational waves and black holes are among the trending topics in physics at the moment, especially with the recent release of the first image of a black hole in history. The existence of black holes was predicted a century ago by Einstein in the well defined theory, “Theory of General Relativity”. Current approaches model the chaotic phenomenon of a black hole pair merger by the use of approximation methods. However, scientists Yunes and Pretorius [69] argue that the approximations employed skew the estimation of the physical features of the black hole system. Hence, there is a need to approach this problem with methods that don’t make specific assumptions about the system itself. This thesis project proposes to develop a computational method for the parametric2 detection and testing of gravitational waves.

Gravitation is the dominant influence in most astrophysical interactions. Weak-field interactions have been extensively studied, but the strong-field regime remains largely unexplored. Gravitational waves (GWs) are an excellent means of accessing strong-field regions. We investigate what we can learn about both astrophysics and gravitation from strong-field tests and, in particular, GWs; we focus upon extreme-mass-ratio (EMR) systems where a small body orbits a much more massive one. EMR bursts, a particular class of GW signals, could be used to determine the properties of massive black holes (MBHs). They could be detectable with a space-borne interferometer from many nearby galaxies, as well as the Galactic centre. Bursts could provide insightful constraints on the MBHs' parameters. These could elucidate the formation history of the MBHs and, by association, their host galaxies. The Galactic centre is the most promising source. Its event rate is determined by the stellar distribution surrounding the MBH; the rate is not high, but we still expect to gain useful astronomical information from bursts. Strong-field tests may reveal deviations from general relativity (GR). We calculate modifications that could be observed assuming metric f(R)-gravity as an effective alternative theory. Gravitational radiation is modified, as are planetary precession rates. Both give a means of testing GR. However, existing laboratory measurements already place tighter constraints on f(R)-gravity, unless there exists a screening effect, such as the chameleon mechanism, which suppresses modifications on small scales. To make precision measurements of astrophysical systems or place exacting bounds on deviations from GR, we must have accurate GW templates. Transient resonances are currently not included in the prescription for generating EMR inspiral waveforms. Their effects can be estimated from asymptotic expansions of the evolving orbital parameters. The quantitative impact on parameter estimation has yet to be calculated, but it appears that it shall be necessary to incorporate resonances when creating inspiral waveforms.