Abstract
Abstract The Event Horizon Telescope (EHT) is taking the first images of black holes resolved at horizon scales to measure their shadows and probe accretion physics. A promising avenue for testing the hypothesis that astrophysical black holes are described by the Kerr solution to Einstein’s equations is to compare the size and shape of the shadow a black hole casts on the surrounding emission to the predictions of the Kerr metric. We develop here an efficient parametric framework to perform this test. We carry out ray-tracing simulations for several parameterized non-Kerr metrics to create a large data set of non-Kerr shadows that probe the allowed parameter space for the free parameters of each metric. We then perform principal components analysis (PCA) on this set of shadows and show that only a small number of components are needed to accurately reconstruct all shadows within the set. We further show that the amplitude of the PCA components are smoothly related to the free parameters in the metrics and, therefore, that these PCA components can be fit to EHT observations in order to place constraints on the free parameters of these metrics that will help quantify any potential deviations from the Kerr solution.
Highlights
Much of our current understanding of black holes relies on the assumption that they are described by the Kerr solution to the Einstein equations
We use Principal Component Analysis to show that the shapes of all black hole shadows generated by several of the parameterized metrics mentioned above can be represented by a small set of functions. This allows us to generate a general parametric model for shadow shapes that is largely agnostic of the underlying spacetime metric, is more compact than a general polynomial expansion, and can be used to derive metric constraints from the Event Horizon Telescope (EHT) data
We simulate a large set of black hole shadows that probe the allowed parameter space of the metrics described in the previous section
Summary
Much of our current understanding of black holes relies on the assumption that they are described by the Kerr solution to the Einstein equations. The second primary target of the EHT is the Galactic Center black hole, Sgr A* This has the largest angular size on the sky of any currently known black hole (e.g., Johannsen et al 2012) and well constrained mass and distance (Ghez et al 2008; Gillessen et al 2009; Gravity Collaboration et al 2018); measuring the shape and size of its shadow is expected to provide a precise test of the Kerr metric. We use Principal Component Analysis to show that the shapes of all black hole shadows generated by several of the parameterized metrics mentioned above can be represented by a small set of functions This allows us to generate a general parametric model for shadow shapes that is largely agnostic of the underlying spacetime metric, is more compact than a general polynomial expansion, and can be used to derive metric constraints from the EHT data.
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