Applications of Test Masses in Uniform Circular Motion to Detect Millihertz Gravitational Waves

Abstract

In this doctoral dissertation, starting from the first principles of the general theory of relativity, the geodesic deviation of test masses in uniform circular motion is calculated, due to the passage of gravitational waves (GWs) from astrophysical sources. The results of this theoretical analysis are used to conceive of experimental setups that could utilize this principle to detect GWs. These setups are based on, but are not limited by, the current status of technology. Mainly, circular particle accelerators in the mode of storage rings are considered. The major sources of noise for a storage ring gravitational wave observatory (SRGO) are explored, and basic noise estimates are made based on the specifications of existing facilities such as the Large Hadron Collider (LHC). A major part of the dissertation consists of numerical simulations of toy models of an SRGO. The response signal of the GW detector is explored as a function of various model parameters. Errors on estimating the model parameters are found using Markov Chain Monte Carlo (MCMC) methods applied to artificially generated data with added noise. It is shown that an ideal version of such a detector would be sensitive to millihertz GWs by design, and would be able to single-handedly obtain accurate constraints on the GW source parameters. An attempt has been made to incorporate as much physics as currently possible, which covers the essential aspects of reality without over-complicating the models for a first study of this novel experiment concept. The overall focus has been to establish a strong conceptual foundation, to obtain robust qualitative conclusions, and to make order-of-magnitude estimates. Comparisons with the theory and practices of existing GW detectors have been made throughout. Wherever possible, the results are presented in the conventions followed by the GW community at the time of writing this dissertation.