In order to perform model-dependent tests of general relativity with gravitational wave observations, we must have access to numerical relativity binary black hole waveforms in theories beyond general relativity (GR). In this study, we focus on order-reduced Einstein dilaton Gauss-Bonnet gravity (EDGB), a higher curvature beyond-GR theory with motivations in string theory. The stability of single, rotating black holes in EDGB is unknown, but is a necessary condition for being able to simulate binary black hole systems (especially the early-inspiral and late ringdown stages) in EDGB. We thus investigate the stability of rotating black holes in order-reduced EDGB. We evolve the leading-order EDGB scalar field and EDGB spacetime metric deformation on a rotating black hole background, for a variety of spins. We find that the EDGB metric deformation exhibits linear growth, but that this level of growth exponentially converges to zero with numerical resolution. Thus, we conclude that rotating black holes in EDGB are numerically stable to leading-order, thus satisfying our necessary condition for performing binary black hole simulations in EDGB.
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