Numerical black hole initial data and shadows in dynamical Chern-Simons gravity

Abstract

We present a scheme for generating first-order metric perturbation initial data for an arbitrary background and source. We then apply this scheme to derive metric perturbations in order-reduced dynamical Chern-Simons gravity (dCS). In particular, we solve for metric perturbations on a black hole background that are sourced by a first-order dCS scalar field. This gives us the leading-order metric perturbation to the spacetime in dCS gravity. We then use these solutions to compute black hole shadows in the linearly perturbed spacetime by evolving null geodesics. We present a novel scheme to decompose the shape of the shadow into multipoles parametrized by the spin of the background black hole and the perturbation parameter ${\epsilon }^2$. We find that we can differentiate the presence of a pure Kerr spacetime from a spacetime with a dCS perturbation using the shadow, allowing in part for a null-hypothesis test of general relativity. We then consider these results in the context of the Event Horizon Telescope.

31 pages, 8 figures Updated to match accepted version in Classical and Quantum Gravity

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• Numerical relativity simulation of GW150914 beyond general relativity
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• The Science of the Einstein Telescope
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• Photon ring test of the Kerr hypothesis: Variation in the ring shape
• Numerical relativity for Horndeski gravity
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