![]() As a result, measuring the shadow shape leads to a test of the general relativistic no-hair theorem (Psaltis et al. For a general spacetime, the shape of the shadow depends primarily on the deviation of the spacetime quadrupole from its Kerr value (Johannsen & Psaltis 2010b). At the same time, the shape of the shadow for a Kerr black hole is nearly circular for all but the highest spins. ![]() Therefore, measuring the size of the shadow of a black hole of known mass constitutes a null hypothesis test of the Kerr metric (Psaltis et al. For a Kerr black hole, the shadow has a radius of 5 ± 0.2 GMc −2 for all spins and observer inclinations (see, e.g., de Vries 2000 Johannsen & Psaltis 2010b Chan et al. The black hole shadow depends only on the geometry of the spacetime and not on the astrophysics of the accretion process. One possible avenue for conducting a test of this assumption with observations in the electromagnetic spectrum is by measuring the size and shape of the shadow a black hole casts on the surrounding emission (Johannsen & Psaltis 2010b Psaltis 2018). ![]() 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 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. 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 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 develop here an efficient parametric framework to perform this test. 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. 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.
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