General parametrization of axisymmetric black holes in metric theories of gravity

By R. Konoplya, Luciano Rezzolla, A. Zhidenko. 2016

172 citations recorded by the source corpus.

Following previous work of ours in spherical symmetry, we here propose a new parametric framework to describe the spacetime of axisymmetric black holes in generic metric theories of gravity. In this case, the metric components are functions of both the radial and the polar angular coordinates, forcing a double expansion to obtain a generic axisymmetric metric expression. In particular, we use a continued-fraction expansion in terms of a compactified radial coordinate to express the radial dependence, while we exploit a Taylor expansion in terms of the cosine of the polar angle for the polar dependence. These choices lead to a superior convergence in the radial direction and to an exact limit on the equatorial plane. As a validation of our approach, we build parametrized representations of Kerr, rotating dilaton, and Einstein-dilaton-Gauss-Bonnet black holes. The match is already very good at lowest order in the expansion and improves as new orders are added. We expect a similar behavior for any stationary and axisymmetric black-hole metric.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b903478c7baa0b73adae232c2c6d30ceafff0226

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Citations in the corpus

Shadow casted by a Konoplya-Zhidenko rotating non-Kerr black hole (2017, background): “Recently, Konoplya and Zhidenko [34] have proposed recently a rotating non-Kerr black hole metric beyond General Relativity through adding a static deformation, which can be looked as an axisymmetric vacuum solution of a unknown alternative theory of gravity [35].”
Testing black hole candidates with electromagnetic radiation (2015, background): “Rezzolla & Zhidenko (2014) and Konoplya et al. (2016) suggested a parametrization that seems to fairly well reproduce some known non-Kerr BH solutions in alternative theories of gravity with a small number of deformation parameters.”
Black Hole Parameter Estimation from Its Shadow (2018, background): “Black hole shadows have been investigated for a parameterized axisymmetric rotating black hole, which generalizes all stationary and axisymmetric black holes in any metric theory of gravity (Rezzolla & Zhidenko 2014; Konoplya et al. 2016; Younsi et al. 2016).”
Gravitational Lensing in Presence of Plasma: Strong Lens Systems, Black Hole Lensing and Shadow (2017, background): “Numerous analytical investigations and numerical simulations of the shadow are presented in literature (for example, see [90, 101, 95, 85, 86, 103, 104, 105, 94, 98, 99, 91, 106, 102, 97, 87, 88, 89, 93, 92, 96, 100, 110, 107, 108, 109, 111]).”
Calculating black hole shadows: Review of analytical studies (2021, background): “A Carter constant also exists for some other black-hole metrics: Konoplya, Rezzolla and Zhidenko [109] had introduced a certain class of parametrized metrics for which the shadow was discussed by Younsi et al. [110].”
The current ability to test theories of gravity with black hole shadows (2018, background): “Furthermore, the radial coordinate is compactified through a dimensionless variable x := 1− r0 r , (2) where x = 0 corresponds to the position of the event horizon and x = 1 to spatial infinity.”