Feature Stories 2021: Physics Undergraduate Research Presentation by Kyle MacKenzie

Abstract: If disturbed, black holes “settle” with a very characteristic gravitational wave (GW) signal, called quasi‐normal ringing (QNR). This is typically observed at the late stages of GW emission from a binary black hole merger. Computing these frequencies from theory is,therefore, a very important problem in gravitational wave physics. We will explore an application of the “shooting” method,asused in atomic physics, to computationally find the frequencies that satisfy the conditions of the QNR. Computation of the QNR for the simplest black hole may be reduced down to solving a wave equation with a simple potential andradiative boundary conditions. For the potential, we areusing the Poschl‐Tellerscalar field as a proxy to prove the viability of the shooting method in black hole physics. We were able to reduce the original partial differential wave equation into an ordinary differential, eigenvalue equation by substituting out the equation’s time dependence. By implementing a Runge‐Kutta‐4 numerical method, the eigenvalue “modes” were found to a high order of accuracy and precision. Higher nodes for the Poschl‐Teller potential require much smaller step sizes and samples; thus, we implemented a parallelization through OpenMP to greatly increase the efficiency of the program when run on multi‐core computers. This result exemplifies the viability, of the shooting method, in solving for QNR frequencies and, in the future, can be applied to a true black hole potential.

Advisor: Dr. Gaurav Khanna

Full presentation: 2020-MacKenzie_K