Abstract: The oscillations that occur in the curved spacetime around compact objects (neutron stars, white dwarf stars, and black holes) are a result of strong background gravitational, electromagnetic, or scalar dark matter fields in these environments. When calculations are attempted in a curved spacetime, a new length scale called the Schwarzschild radius is introduced, which significantly alters the particle oscillation probabilities when compared to standard flat spacetime computations. This thesis focuses on computing the bosonic scalar dark matter, electromagnetic and gravitational wave mixing in curved spacetime using effective field theory techniques. The calculations included in this paper use the axion and axion-like cold dark matter particles. Kerr geometry is necessary for producing curvature correction effects as functions of particle distance from the quasispherical event horizon of compact objects. The mixing that occurs is model-independent and applies to any potential dark matter particle having zero spin. Using effective field theory techniques, I write the equations of motion around these strong gravitational environments to explain how the bosonic mixing occurs. The mixing often induces a cohered state between bosonic dark matter, photons, and gravitons. In strong gravitational environments, the dominant terms in the mixing are those of the energy-momentum tensor, rather than of model-dependent couplings. Thus, axion-like particles with no standard model couplings can mix significantly with the photon via gravitational waves in strong gravity environments. The description of curved spacetime mixing of generic spin-zero scalar dark matter waves with gravity and electromagnetic waves could potentially lead to new signatures that may facilitate new astrophysical measurements, and perhaps a reassessment of sensitivities to axions.

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