We present a visualization and analysis of a supercomputer simulation displaying the apparent horizons' curvature and radiation emitted from a binary black hole system modeling the LIGO observed signal GW150914. The simulation follows the system from seven orbits prior to merger down to the resultant final Kerr black hole. Apparent horizons are calculated during the simulation with mean curvature data displayed on them. Radiation data was visualized via the real part of the $\Psi_4$ component of the Weyl scalars, which were determined using a numerical quasi-Kinnersley method. We also present a comparative study of the differences in using the quasi-Kinnersley and PsiKadelia tetrads to construct $\Psi_4$ and the benefits, particularly in the strong field region of a binary black hole system, of using a tetrad in a transverse ($\Psi_1=\Psi_3=0$) frame. The second part of our studies focus on the relationship between the mean curvature displayed on the apparent horizons and the trajectories of the black holes. We notice that prior to merger, for each black hole, the directionality of the mean curvature tracks that of the trajectory with either a positive or negative phase shift between the two curves. Finally, we provide a brief analysis suggesting that the phase shift and the frame dragging effects are likely related.

Library of Congress Subject Headings

Black holes (Astronomy)--Computer simulation; Double stars--Computer simulation; Gravitational waves--Mathematical models

Publication Date


Document Type


Student Type


Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

School of Mathematical Sciences (COS)


Carlos Lousto

Advisor/Committee Member

Yosef Zlochower

Advisor/Committee Member

Elizabeth Cherry


RIT – Main Campus

Plan Codes