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Photon Regions Around Black Holes

  • Arne GrenzebachEmail author
Chapter
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Part of the SpringerBriefs in Physics book series (SpringerBriefs in Physics)

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.

Keywords

Photon region black hole Equations of motion Spherical light-rays Plots photon region Spin Charge NUT charge Cosmological constant Accelerated space-time 

References

  1. Barrow JD, Shaw DJ (2011) The value of the cosmological constant. Gen Relativ Gravit 43(10):2555–2560. doi: 10.1007/s10714-011-1199-1 MathSciNetCrossRefzbMATHADSGoogle Scholar
  2. Carter B (1968) Hamilton-Jacobi and Schrödinger separable solutions of Einstein’s equations. Commun Math Phys 10(4):280–310. http://projecteuclid.org/euclid.cmp/1103841118 Google Scholar
  3. Grenzebach A, Perlick V, Lämmerzahl C (2014) Photon regions and shadows of Kerr–Newman–NUT Black Holes with a cosmological constant. Phys Rev D 89:124,004(12). doi: 10.1103/PhysRevD.89.124004. arXiv:1403.5234
  4. Grenzebach A (2015) Aberrational effects for shadows of black holes. In: Puetzfeld et al Proceedings of the 524th WE-Heraeus-Seminar “Equations of Motion in Relativistic Gravity”, held in Bad Honnef, Germany, 17–23 Feb 2013, pp 823–832. doi: 10.1007/978-3-319-18335-0_25, arXiv:1502.02861 Google Scholar
  5. Grenzebach A, Perlick V, Lämmerzahl C (2015) Photon Regions and shadows of accelerated black holes. Int J Mod Phys D 24(9):1542,024(22). doi: 10.1142/S0218271815420249 (Special Issue “Papers” of the “7th Black Holes Workshop”, Aveiro, Portugal, arXiv:1503.03036)
  6. Hackmann E (2010) Geodesic equations in black hole space-times with cosmological constant. Dissertation, Universität Bremen, Bremen. http://nbn-resolving.de/urn:nbn:de:gbv:46-diss000118806
  7. Hackmann E, Kagramanova V, Kunz J, Lämmerzahl C (2009) Analytic solutions of the geodesic equation in axially symmetric space-times. Europhys Lett 88(3):30,008(5). doi: 10.1209/0295-5075/88/30008 Google Scholar
  8. Hartle JB (2003) Gravity: An Introduction to Einstein’s General Relativity. Pearson Education (Addison-Wesley), San FranciscoGoogle Scholar
  9. Kagramanova V, Kunz J, Hackmann E, Lämmerzahl C (2010) Analytic treatment of complete and incomplete geodesics in Taub–NUT space-times. Phys Rev D 81(12):124,044(17). doi: 10.1103/PhysRevD.81.124044
  10. Perlick V (2004) Gravitational lensing form a spacetime perspective. Living Rev Relativ 7(9). doi: 10.12942/lrr-2004-9
  11. Perlmutter S, Aldering G, Goldhaber G, Knop RA, Nugent P, Castro PG, Deustua S, Fabbro S, Goobar A, Groom DE, Hook IM, Kim AG, Kim MY, Lee JC, Nunes NJ, Pain R, Pennypacker CR, Quimby R, Lidman C, Ellis RS, Irwin M, McMahon RG, Ruiz-Lapuente P, Walton N, Schaefer B, Boyle BJ, Filippenko AV, Matheson T, Fruchter AS, Panagia N, Newberg HJM, Couch WJ, Project TSC (1999) Measurements of \(\varOmega \) and \(\varLambda \) from 42 High-Redshift Supernovae. Astrophys J 517(2):565. doi: 10.1086/307221 Google Scholar
  12. Riess AG, Filippenko AV, Challis P, Clocchiatti A, Diercks A, Garnavich PM, Gilliland RL, Hogan CJ, Jha S, Kirshner RP, Leibundgut B, Phillips MM, Reiss D, Schmidt BP, Schommer RA, Smith RC, Spyromilio J, Stubbs C, Suntzeff NB, Tonry J (1998) Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron J 116(3):1009. doi: 10.1086/300499 Google Scholar
  13. Teo E (2003) Spherical Photon Orbits around a Kerr Black Hole. Gen Relativ Gravit 35(11):1909–1926. doi: 10.1023/A:1026286607562 Google Scholar
  14. Unsöld A, Baschek B (2005) Der neue Kosmos, 7th edn. Springer, HeidelbergGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.ZARM—Zentrum für angewandte Raumfahrttechnologie und MikrogravitationUniversität BremenBremenGermany

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