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Abstract We introduce new methods to numerically construct for the first time stationary axisymmetric black hole solutions in Einstein-aether theory and study their properties. The key technical challenge is to impose regularity at the spin-2, 1, and 0 wave mode horizons. Interestingly we find the metric horizon, and various wave mode horizons, are not Killing horizons, having null generators to which no linear combination of Killing vectors is tangent, and which spiral from pole to equator or vice versa. Existing phenomenological constraints result in two regions of coupling parameters where the theory is viable and some couplings are large; region I with a large twist coupling and region II with also a (somewhat) large expansion coupling. Currently these constraints do not include tests from strong field dynamics, such as observations of black holes and their mergers. Given the large aether coupling(s) one might expect such dynamics to deviate significantly from general relativity (GR), and hence to further constrain the theory. Here we argue this is not the case, since for these parameter regions solutions exist where the aether is ‘painted’ onto a metric background that is very close to that of GR. This painting for region I is approximately independent of the large twist coupling, and for region II is also approximately independent of the large expansion coupling and normal to a maximal foliation of the spacetime. We support this picture analytically for weak fields, and numerically for rotating black hole solutions, which closely approximate the Kerr metric. 

Abstract We demonstrate the flexibility and utility of the Berger–Rigoutsos adaptive mesh refinement (AMR) algorithm used in the open-source numerical relativity (NR) code GRC hombo for generating gravitational waveforms from binary black-hole (BH) inspirals, and for studying other problems involving non-trivial matter configurations. We show that GRC hombo can produce high quality binary BH waveforms through a code comparison with the established NR code L ean . We also discuss some of the technical challenges involved in making use of full AMR (as opposed to, e.g. moving box mesh refinement), including the numerical effects caused by using various refinement criteria when regridding. We suggest several ‘rules of thumb’ for when to use different tagging criteria for simulating a variety of physical phenomena. We demonstrate the use of these different criteria through example evolutions of a scalar field theory. Finally, we also review the current status and general capabilities of GRC hombo .