Grant: Discovery Grants Program - Individual

1a. The characterization of the inspiral orbits of a compact black hole (BH) into a supermassive BH is an important aspect in constructing correct templates for Gravitational Wave (GW) forms. There is a change of eccentricity, energy, and angular momentum and emission of GW radiation in such orbits. We develop a new concept termed as the ""Abutment"". It is defined by a particular set of near-polar retrograde orbits. The abutment tests the consistency of the evolution equation for the Carter constant and reveals the significance of second order effects due to radiation back-reaction. This study is significant for the Laser Interferometer Space Antenna (LISA). 1b. Matched filtering for pulsar signals is not possible with foreseeable computing resources available to GW astronomers. Tomographic Reconstruction (TR) is a promising alternative approach and will be used to determine the source parameters of a detected GW Pulsar Signal that is buried in the systemic noise of a GW detector such as the Laser Interferometer Gravitational Observatory (LIGO) and LISA. The Radon Transform, the essence of TR, will be applied to theoretical responses of these detectors. LISA is expected to observe a large population of Galactic white dwarf binaries whose collective signal is likely to dominate the instrumental noise at observational frequencies in the milli-hertz range. 2. Some applications of the transcendental Lambert W function in astrophysics, space and mathematical physics will be studied. The Lambert W and Polylogarithm functions are of particular relevance in finding solutions to the magneto hydrodynamic equations with hourglass morphology that occur in star formation. We will seek the most general analytic solutions that can describe hourglass magnetic fields so that they can be used as a tool to compare with astronomical observations, and thereby measure interstellar magnetic field strengths. These functions will also help in understanding the quantum statistics of D dimensional Bose and Fermi gases and Thermoelectric Materials.