Photon regions and shadows of accelerated black holes

By A. Grenzebach, V. Perlick, C. Lammerzahl. 2015

136 citations recorded by the source corpus.

In an earlier paper, we have analytically determined the photon regions and the shadows of black holes of the Plebanski class of metrics which are also known as the Kerr–Newman–NUT–(anti-)de Sitter metrics. These metrics are characterized by six parameters: Mass, spin, electric and magnetic charges, gravitomagnetic NUT charge and the cosmological constant. Here, we extend this analysis to the Plebanski–Demianski class of metrics which contains, in addition to these six parameters, the so-called acceleration parameter. All these metrics are axially symmetric and stationary type D solutions to the Einstein–Maxwell equations with a cosmological constant. We derive analytical formulas for the photon regions (i.e. for the regions that contain spherical lightlike geodesics) and for the boundary curve of the shadow as it is seen by an observer at Boyer–Lindquist coordinates (rO, ϑO) in the domain of outer communication. Whereas all relevant formulas are derived for the whole Plebanski–Demianski class, we concentrate on the accelerated Kerr metric (i.e. only mass, spin and acceleration parameter are different from zero) when discussing the influence of the acceleration parameter on the photon region and on the shadow in terms of pictures. The accelerated Kerr metric is also known as the rotating C-metric. We discuss how our analytical formulas can be used for calculating the horizontal and vertical angular diameters of the shadow and we estimate these values for the black holes at the center of our Galaxy and at the center of M87.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/72099491f7ccc0b88345061eedd669de3bae3b75

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Citations in the corpus

Black hole shadow in an expanding universe with a cosmological constant (2018, methodology): “More generally, an analytical formula for the shape and the size of the shadow of a black hole of the Plebański-Demiański class, for an observer anywhere in the domain of outer communication, was derived by Grenzebach et al.[3, 4].”
Black Hole Parameter Estimation from Its Shadow (2018, background): “We can also characterize the shadow of a rotating black hole through its oblateness (Takahashi 2004; Grenzebach et al. 2015; Tsupko 2017), the measure of distortion (circular asymmetry) in a shadow, by defining the dimensionless parameter D as the ratio of horizontal and vertical diameters: a a b b…”
Calculating black hole shadows: Review of analytical studies (2021, methodology): “Bardeen [29] and Chandrasekhar [30] Grenzebach, Perlick and Lämmerzahl [40, 41]”
A coordinate-independent characterization of a black hole shadow (2015, background): “In most cases, the expression of the shadow as a closed polar curve is not known analytically, but for the Plebański-Demiański class of space-times, the shadow has been cast in an analytic form (Grenzebach et al. 2014, 2015).”
Gravitational Lensing in Presence of Plasma: Strong Lens Systems, Black Hole Lensing and Shadow (2017, methodology): “This method of plotting the shadow, which was used in [55,85,86], is to be distinguished from the one introduced by Bardeen [84] and used subsequently by many authors.”