Modeling Compact Objects with Effective Field Theory - Martinez, Rodriguez Irvin Fabian (Department of Mathematics and Applied Mathematics, 2023)
In this master's thesis we have developed a worldline Effective Field Theory of compact objects, by extending the model of spinning extended objects derived using the coset construction [1], from which one can derive the effective theory from symmetry principles. To massive spinning extended objects, we have added electromagnetic charge and the finite-size structure including dissipation, such that we describe charged spinning compact objects, the most general compact object allowed in a theory of gravity such as General Relativity with classical electrodynamics. To the derived effective action, we have matched the coefficients of the theory from the literature and obtained the leading order post-Newtonian expansion of our effective description of compact objects to show its predictability. We have expanded on the theoretical foundations of the effective theory for spinning extended objects by showing that the developed theory can be equivalent to the currently used theories as a special case. Nonetheless, the effective theory itself is more general and does not require additional degrees of freedom to be introduced, other than the ones derived from symmetries. We bring new results on the interaction and internal structure of charged spinning compact objects. On the numerical side, based on the Effective Field Theory reasoning, we have introduced a framework for evolving a compact object binary. Within this approach, we obtain the leading order waveform emitted by the binary during its late inspiral and compare it to a waveform from standard methodologies. Then, by performing illustrative numerical experiments of systems that the LIGO-Virgo observatories have already detected, we show the role of the stellar structure and their coefficients in the phase evolution of the waveform, as well as the order in which they arise and the sensitivity required for the gravitational wave observatories to measure them. If these coefficients are to be measured, tight constraints on fundamental physics can be placed.