SPECIAL ISSUE – VII Black Holes Workshop; Guest Editors: Carlos A. R. Herdeiro, Vitor Cardoso, José P. S. Lemos and Filipe C. MenaNo Access

Photon regions and shadows of accelerated black holes

Arne Grenzebach

ZARM, University of Bremen, Am Fallturm, 28359 Bremen, Germany

Corresponding author.

Search for more papers by this author

Volker Perlick

ZARM, University of Bremen, Am Fallturm, 28359 Bremen, Germany

Search for more papers by this author

, and

Claus Lämmerzahl

ZARM, University of Bremen, Am Fallturm, 28359 Bremen, Germany

Search for more papers by this author

https://doi.org/10.1142/S0218271815420249Cited by:133 (Source: Crossref)

Abstract

In an earlier paper, we have analytically determined the photon regions and the shadows of black holes of the Plebański 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 Plebański–Demiański 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 (r_O, ϑ_O) in the domain of outer communication. Whereas all relevant formulas are derived for the whole Plebański–Demiański 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.

Keywords:

PACS: 04.70.-s, 95.30.Sf, 98.35.Jk

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

A. Grenzebach , V. Perlick and C. Lämmerzahl , Phys. Rev. D 89 , 124004 ( 2014 ) . Web of Science, ADS, Google Scholar
O. James et al. , Class. Quantum Grav. 32 , 065001 ( 2015 ) . Web of Science, Google Scholar
S. S. Doeleman et al. , Nature 455 , 78 ( 2008 ) . Web of Science, ADS, Google Scholar
A. Eckart and R. Genzel , Nature 383 , 415 ( 1996 ) . Web of Science, ADS, Google Scholar
S. Gillessen et al. , Astrophys. J. 692 , 1075 ( 2009 ) . Web of Science, ADS, Google Scholar
A. M. Ghez et al. , Astrophys. J. 689 , 1044 ( 2008 ) . Web of Science, ADS, Google Scholar
L. Huang et al. , Mon. Not. R. Astron. Soc. 379 , 833 ( 2007 ) . Web of Science, ADS, Google Scholar
H. Falcke , F. Melia and E. Agol , Astrophys. J. 528 , L13 ( 2000 ) . Web of Science, ADS, Google Scholar
N. S. Kardashev et al. , Usp. Fiz. Nauk 184 , 1319 ( 2014 ) , arXiv:1502.06071 . Google Scholar
T. Levi-Civita , Rend. Accad. Lincei 28 , 3 ( 1919 ) . Google Scholar
H. Weyl , Ann. Phys. 54 , 117 ( 1917 ) . ADS, Google Scholar
H. Weyl , Ann. Phys. 59 , 185 ( 1919 ) . Google Scholar
J. Ehlers and W. Kundt , Gravitation: An Introduction to Current Research , ed. L. Witten ( John Wiley & Sons , New York , 1962 ) . Google Scholar
K. Hong and E. Teo , Class. Quantum Grav. 22 , 109 ( 2005 ) . Web of Science, ADS, Google Scholar
J. B. Griffiths and J. Podolský , Exact Space-Times in Einstein's General Relativity ( Cambridge University Press , Cambridge , 2009 ) . Google Scholar
K. Hong and E. Teo , Class. Quantum Grav. 20 , 3269 ( 2003 ) . Web of Science, ADS, Google Scholar
W. Kinnersley and M. Walker , Phys. Rev. D 2 , 1359 ( 1970 ) . Web of Science, ADS, Google Scholar
W. B. Bonnor , Gen. Relativ. Gravit. 15 , 535 ( 1983 ) . Web of Science, ADS, Google Scholar
W. B. Bonnor and W. Davidson , Class. Quantum Grav. 9 , 2065 ( 1992 ) . Web of Science, ADS, Google Scholar
J. L. Synge , Mon. Not. R. Astron. Soc. 131 , 463 ( 1966 ) . ADS, Google Scholar
J. M. Bardeen, Black Holes (Les Astres Occlus), eds. C. DeWitt and B. S. DeWitt (Gordon and Breach, New York, 1973) p. 215. Google Scholar
K. Hioki and K.-I. Maeda , Phys. Rev. D 80 , 024042 ( 2009 ) . Web of Science, ADS, Google Scholar
J. M. Bardeen and C. T. Cunningham , Astrophys. J. 183 , 237 ( 1973 ) . Web of Science, ADS, Google Scholar
J.-P. Luminet , Astron. Astrophys. 75 , 228 ( 1979 ) . Web of Science, ADS, Google Scholar
J. Dexter et al. , J. Phys., Conf. Ser. 372 , 012023 ( 2012 ) . ADS, Google Scholar
Z. Younsi , K. Wu and S. V. Fuerst , Aatron. Astrophys. 545 , A13 ( 2012 ) . Web of Science, ADS, Google Scholar
M. Mościbrodzka et al. , Aatron. Astrophys. 570 , A7 ( 2014 ) . Web of Science, ADS, Google Scholar
M. Mościbrodzka et al. , Astrophys. J. Lett. 752 , L1 ( 2012 ) . Web of Science, ADS, Google Scholar
J. Dexter and P. C. Fragile , Mon. Not. R. Astron. Soc. 432 , 2252 ( 2013 ) . Web of Science, ADS, Google Scholar
R. Debever , Bull. Soc. Math. Belgique 23 , 360 ( 1971 ) . Google Scholar
J. F. Plebański and M. Demiański , Ann. Phys. 98 , 98 ( 1976 ) . Web of Science, ADS, Google Scholar
H. Stephani et al. , Exact Solutions of Einstein's Field Equations ( Cambridge University Press , Cambridge , 2003 ) . Google Scholar
A. N. Aliev and A. E. Gümrükçüoğlu , Phys. Rev. D 71 , 104027 ( 2005 ) . Web of Science, ADS, Google Scholar
V. S. Manko and E. Ruiz , Class. Quantum Grav. 22 , 3555 ( 2005 ) . Web of Science, ADS, Google Scholar
J. F. Plebański , Ann. Phys. 90 , 196 ( 1975 ) . Web of Science, ADS, Google Scholar
B. Carter , Commun. Math. Phys. 10 , 280 ( 1968 ) . ADS, Google Scholar
V. Perlick , Living Rev. Rel. 7 , 9 ( 2004 ) . Web of Science, ADS, Google Scholar
B. O'Neill , The Geometry of Kerr Black Holes ( A.K. Peters , Wellesley , 1995 ) . Google Scholar
A. Grenzebach , Aberrational effects for shadows of black holes , Proc. 524th WE-Heraeus-Seminar: Equations of Motion in Relativistic Gravity , eds. D. Puetzfeld , C. Lämmerzahl and B. F. Schutz ( Springer , Heidelberg , 2015 ) . Google Scholar
A. Broderick et al. , Astrophys. J. 805 , 179 ( 2015 ) . Web of Science, ADS, Google Scholar
J. Kormendy and L. C. Ho , Annu. Rev. Astron. Astrophys. 51 , 511 ( 2013 ) . Web of Science, ADS, Google Scholar
K. Gebhardt et al. , Astrophys. J. 729 , 119 ( 2011 ) . Web of Science, ADS, Google Scholar
J. L. Walsh et al. , Astrophys. J. 770 , 86 ( 2013 ) . Web of Science, ADS, Google Scholar