EAS Doctoral Dissertation Defense by Manas Vishal
Extreme-mass-ratio inspirals occur when a small compact object, such as a neutron star or a stellar-mass black hole, gradually falls into a much larger black hole. These systems produce faint gravitational waves that carry detailed information about the spacetime geometry very close to the massive hole. To compare theoretical predictions with future observations from the space-borne detector LISA we need a simulation approach that can resolve both the object's localized effect and the waves as they propagate to infinity in a unified framework.
In this work I present a time-domain method based on high-order discontinuous Galerkin discretization that incorporates the point-source exactly and achieves superconvergent accuracy without artificial smoothing. A hyperboloidal compactification is used to bring the far-field region onto a finite grid, which makes it possible to extract clean waveforms directly at null infinity. This approach has been tested on perturbations of Schwarzschild and Kerr black holes, showing excellent agreement with known results, including flux and self-force calculations for circular orbits. The implementation also employs mixed-precision strategies to reduce memory and computation costs, and preliminary GPU benchmarks indicate that the core routines perform efficiently on modern accelerators. This framework offers a combination of accuracy and scalability that will help pave the way for generating extreme-mass-ratio inspiral waveforms suitable for real-time analysis and parameter estimation in upcoming gravitational-wave astronomy.
Advisor: Dr Scott Field, Department of Mathematics
Committee members:
Dr. Gaurav Khanna, Department of Physics, URI
Dr. Sigal Gottlieb, Department of Mathematics
Dr. Sarah Caudill, Department of Physics
TXT 105
: Virtual
Dr. Scott Field
sfield@umassd.edu
https://umassd.zoom.us/j/92743420577?pwd=ihOdwW6zRCHUQqSCwg1xz369i6B2XB.1