Peters, Jeremy2020-08-262020-08-262020-08-26http://hdl.handle.net/10222/79721We study the algebraic structure of the Weyl tensor by tracing the level--0 set of the complex scalar polynomial invariant, D, through a numerical simulation of a quasi-circular binary black hole merger. We approximate the level-0 sets of D with level--epsilon sets of |D| for small epsilon. We locate the local minima of |D| and find that the positions of these local minima correspond closely to the level-epsilon sets of |D| and we also compare with the level-0 sets of Re(D). The analysis provides strong evidence that the level-epsilon sets track a unique geometric horizon. By studying the behaviour of the zero sets of Re(D), Im(D) and their product, we observe that the level-epsilon set that best approximates this geometric horizon is given by epsilon = 0.001.enGeometric HorizonGeometric Horizon ConjectureMarginally Outer Trapped SurfaceApparent HorizonEvent HorizonBlack Hole HorizonBinary Black Hole MergerPetrov ClassificationBoost Weight ClassificationScalar Polynomial InvariantDifferential Scalar Polynomial InvariantExtended Cartan InvariantWeyl TensorLevel SetsNumerical RelativityDifferential GeometryA Study of the Geometric Horizon Conjecture as Applied to a Binary Black Hole Merger