Executive Summary : | The research proposal aims to explore the distribution of dark matter, dynamics of black hole binaries, and gravitational waves in the astrophysical environment, their evolution over cosmic time scales, and the formation of galaxies. It considers binary black hole systems, particularly extreme mass ratio inspirals, where a stellar-mass object inspirals a supermassive black hole in the presence of an astrophysical environment. The proposal will investigate gravitational wave signals through black hole perturbation methods and test results from the numerical relativity domain. The team will use Teukolsky formalism, a scalar equation technique, and Green's function method to solve perturbation equations. The study will estimate gravitational wave fluxes, amplitudes, and mismatches in gravitational waveforms, including the effect of dark matter environment. The proposal also explores the gravitational memory effect, a permanent change in the orientation of gravitational wave detectors even after the passage of gravitational waves. This will be the first step in investigating the signatures of the astrophysical environment in gravitational memory. The proposal captures the ideas of the research community and opens up various directions in gravitational wave astronomy and astrophysics. |