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Photon Regions Around Black Holes

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The Shadow of Black Holes

Part of the book series: SpringerBriefs in Physics ((SpringerBriefs in Physics))

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Abstract

The existence of a photon region, a region that contains spherical lightlike geodesics, is crucial for determining the shadow of a black hole. Here, their characterizing inequality is derived. The photon regions are visualized together with ergoregions and regions with causality violation for various values of the parameters.

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Notes

  1. 1.

    Large parts of this section are based on [1, 3] while parts of the Sects. 3.1, 3.2 and 3.3 can be found in [1] or [3].

  2. 2.

    There are other definitions of the Carter constant which differ in additive constants.

  3. 3.

    This is also possible for matter if \(\alpha =0\) since \(\varSigma \) has no term depending on both r and \(\vartheta \).

  4. 4.

    As realistic value of \(\varLambda \) one finds \(\varLambda \approx +{10}^{-52} \) m\(^{-2}\) (Unsöld and Baschek 2005) which corresponds to \(\varLambda \approx {10}^{-122}\) measured in Planck units (Barrow and Shaw 2011; Riess et al. 1998; Perlmutter et al. 1999).

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Authors and Affiliations

  1. ZARM—Zentrum für angewandte Raumfahrttechnologie und Mikrogravitation, Universität Bremen, Am Fallturm, Bremen, Germany

    Arne Grenzebach

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  1. Arne Grenzebach
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Correspondence to Arne Grenzebach .

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Grenzebach, A. (2016). Photon Regions Around Black Holes. In: The Shadow of Black Holes. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-30066-5_3

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