A new method for shadow calculations: application to parameterised axisymmetric black holes (1607.05767v2)

Abstract: Collaborative international efforts under the name of the Event Horizon Telescope project, using sub- mm very long baseline interferometry, are soon expected to provide the first images of the shadow cast by the candidate supermassive black hole in our Galactic center, Sagittarius A*. Observations of this shadow would provide direct evidence of the existence of astrophysical black holes. Although it is expected that astrophysical black holes are described by the axisymmetric Kerr solution, there also exist many other black hole solutions, both in general relativity and in other theories of gravity, which cannot presently be ruled out. To this end, we present calculations of black hole shadow images from various metric theories of gravity as described by our recent work on a general parameterisation of axisymmetric black holes [R. Konoplya, L. Rezzolla and A. Zhidenko, Phys. Rev. D 93, 064015 (2016)]. An algorithm to perform general ray-tracing calculations for any metric theory of gravity is first outlined and then employed to demonstrate that even for extremal metric deformation parameters of various black hole spacetimes, this parameterisation is both robust and rapidly convergent to the correct solution.

Overview of New Method for Black Hole Shadow Calculations

The paper "New method for shadow calculations: Application to parameterised axisymmetric black holes" presents a paper on computing black hole shadow images via a novel parameterisation method applicable to any stationary and axisymmetric black hole metric in various theories of gravity. The significance of this research lies in its potential to elucidate the strong-gravity environments around black holes, as anticipated observations from the Event Horizon Telescope (EHT) will be capable of imaging these shadow silhouettes.

Black hole shadows are defined as the silhouette or dark region formed on the background of the luminous material emitted in the vicinity of a black hole. The shape and size of these shadows are highly sensitive to the parameters of the black hole, notably its mass, spin, and potentially any deviations from the standard Kerr solution described by general relativity.

Numerical Methodology and Parameterisation

The paper outlines an algorithmic approach based on general ray-tracing calculations that operate without assumptions tied to a particular gravitational theory. This approach depends on the development of a general parameterisation framework, first established in prior work by some of the authors, which expresses the black hole metric in terms of series expansions in radial and polar coordinates. The parameterisation can reproduce known solutions, such as the Kerr metric, while allowing flexibility for other possible solutions predicted by alternative theories of gravity.

The research focuses on three distinct metrics: the Kerr-Sen metric, Einstein-Dilaton-Gauss-Bonnet (EDGB) metric, and the Johannsen-Psaltis phenomenological metric. For each of these, the paper performs a detailed assessment of shadow calculations, considering various combinations of metric expansion orders. The paper also evaluates the robustness and convergence of the parameterisation method by comparing shadow images calculated at various expansion orders against their exact or analytically deduced counterparts.

Results and Implications

Key numerical results demonstrate the efficacy of the parameterisation. For extreme parameter values, often beyond expected astrophysical relevance, the parameterisation remains effective, offering accurate shadow predictions. The Kerr-Sen metric, representing a charged black hole with a dilaton field, is successfully parameterised within extreme spin and charge values. The EDGB metric, a representative of non-Einsteinian theories, shows excellent convergence properties despite the coupling between scalar fields and higher curvature terms. Finally, the Johannsen-Psaltis metric further validates the method's utility for exploring gravitational theories beyond general relativity by capturing significant deviations in horizon shapes due to deformation parameters.

Future Directions

The outlined framework and results have significant theoretical and practical implications for the field of astrophysics and gravity. The ability to parameterise any axisymmetric black hole allows researchers to span a broad range of theories and make precise predictions about shadow features, which could be detected or inferred from EHT or similar telescopic data. This work thus paves the way for more comprehensive tests of the Kerr hypothesis and the nature of black holes within different gravitational paradigms. The framework could potentially constrain or even refute alternative gravitational theories by matching predictions with upcoming empirical observations of black hole shadows.

In future applications, this method may facilitate more advanced ray-tracing simulations incorporating full electromagnetic spectra and enabling comparisons with high-quality observational data. This could in turn lead to new insights into black hole environments and contribute to broader gravitational theory tests. Additionally, coupling this parameterisation strategy with numerical solutions of the Einstein equations may further enhance its utility in modeling more complex scenarios involving dynamic, multi-body systems within strong gravity fields.