Relativistic images

{{Short description|Images of gravitational lensing}}

File:BlackHole Lensing.gif

Relativistic images are images of gravitational lensing which result due to light deflections by angles $\backslash hat\{\backslash alpha\}\; >\; 3\; \backslash pi/2$.

This term was coined by Virbhadra and Ellis{{cite journal | last1=Virbhadra | first1=K. S. | last2=Ellis | first2=George F. R. | title=Schwarzschild black hole lensing | journal=Physical Review D | publisher=American Physical Society (APS) | volume=62 | issue=8 | date=2000-09-08 | issn=0556-2821 | doi=10.1103/physrevd.62.084003 |arxiv=astro-ph/9904193 | page=084003| bibcode=2000PhRvD..62h4003V | s2cid=15956589 }} in the year 2000 and is used by many researchers working in this fieldSee:

• {{cite journal | last=Bin-Nun | first=Amitai Y. | title=Relativistic images in Randall-Sundrum II braneworld lensing | journal=Physical Review D | volume=81 | issue=12 | date=2010-06-16 | issn=1550-7998 | doi=10.1103/physrevd.81.123011 | page=123011| arxiv=0912.2081 | bibcode=2010PhRvD..81l3011B | s2cid=5704419 }}
• {{cite journal | last1=Tsupko | first1=O. Yu. | last2=Bisnovatyi-Kogan | first2=G. S. | title=Relativistic rings due to Schwarzschild gravitational lensing | journal=Gravitation and Cosmology | publisher=Pleiades Publishing Ltd | volume=15 | issue=2 | year=2009 | issn=0202-2893 | doi=10.1134/s0202289309020182 | pages=184–187| bibcode=2009GrCo...15..184T | s2cid=120088537 }}
• {{cite journal | last1=Eiroa | first1=Ernesto F. | last2=Romero | first2=Gustavo E. | last3=Torres | first3=Diego F. | title=Reissner-Nordström black hole lensing | journal=Physical Review D | volume=66 | issue=2 | date=2002-07-02 | issn=0556-2821 | doi=10.1103/physrevd.66.024010 | page=024010| arxiv=gr-qc/0203049 | bibcode=2002PhRvD..66b4010E | s2cid=12504121 }}
• {{cite journal | last1=DEY | first1=TUSHAR KANTI | last2=SEN | first2=SURAJIT | title=Gravitational Lensing by Wormholes | journal=Modern Physics Letters A | volume=23 | issue=13 | date=2008-04-30 | issn=0217-7323 | doi=10.1142/s0217732308025498 | pages=953–962| arxiv=0806.4059 | bibcode=2008MPLA...23..953D | s2cid=7909286 }}
• {{cite journal | last=Eiroa | first=Ernesto F. | title=Braneworld black hole gravitational lens: Strong field limit analysis | journal=Physical Review D | publisher=American Physical Society (APS) | volume=71 | issue=8 | date=2005-04-12 | issn=1550-7998 | doi=10.1103/physrevd.71.083010 | page=083010| arxiv=gr-qc/0410128 | bibcode=2005PhRvD..71h3010E | s2cid=14585512 }}
• {{cite journal | last=Bozza | first=V. | title=Quasiequatorial gravitational lensing by spinning black holes in the strong field limit | journal=Physical Review D | volume=67 | issue=10 | date=2003-05-22 | issn=0556-2821 | doi=10.1103/physrevd.67.103006 | page=103006| arxiv=gr-qc/0210109 | bibcode=2003PhRvD..67j3006B | s2cid=119397160 }}
• {{cite journal | last=Bhadra | first=A. | title=Gravitational lensing by a charged black hole of string theory | journal=Physical Review D | publisher=American Physical Society (APS) | volume=67 | issue=10 | date=2003-05-27 | issn=0556-2821 | doi=10.1103/physrevd.67.103009 | page=103009| s2cid=33555724 | url=https://cds.cern.ch/record/620006 | arxiv=gr-qc/0306016 | bibcode=2003PhRvD..67j3009B }}
• {{cite journal | last1=Sarkar | first1=Kabita | last2=Bhadra | first2=Arunava | title=Strong field gravitational lensing in scalar–tensor theories | journal=Classical and Quantum Gravity | volume=23 | issue=22 | date=2006-10-06 | issn=0264-9381 | doi=10.1088/0264-9381/23/22/002 | pages=6101–6113| arxiv=gr-qc/0602087 | bibcode=2006CQGra..23.6101S | s2cid=10741616 }}
• {{cite journal | last1=Liu | first1=Yue | last2=Chen | first2=Songbai | last3=Jing | first3=Jiliang | title=Strong gravitational lensing in a squashed Kaluza-Klein black hole spacetime | journal=Physical Review D | volume=81 | issue=12 | date=2010-06-07 | issn=1550-7998 | doi=10.1103/physrevd.81.124017 | page=124017| arxiv=1003.1429 | bibcode=2010PhRvD..81l4017L | s2cid=118842469 }}
• {{cite journal | last1=Gyulchev | first1=Galin N. | last2=Yazadjiev | first2=Stoytcho S. | title=Kerr-Sen dilaton-axion black hole lensing in the strong deflection limit | journal=Physical Review D | volume=75 | issue=2 | date=2007-01-17 | issn=1550-7998 | doi=10.1103/physrevd.75.023006 | page=023006| arxiv=gr-qc/0611110 | bibcode=2007PhRvD..75b3006G | s2cid=52211738 }}
• {{cite journal | last1=Chen | first1=Songbai | last2=Jing | first2=Jiliang | title=Strong field gravitational lensing in the deformed Hořava-Lifshitz black hole | journal=Physical Review D | volume=80 | issue=2 | date=2009-07-27 | issn=1550-7998 | doi=10.1103/physrevd.80.024036 | page=024036| arxiv=0905.2055 | bibcode=2009PhRvD..80b4036C | s2cid=119251399 }}
• {{cite journal | last1=Gyulchev | first1=Galin N. | last2=Yazadjiev | first2=Stoytcho S. | title=Gravitational lensing by rotating naked singularities | journal=Physical Review D | volume=78 | issue=8 | date=2008-10-10 | issn=1550-7998 | doi=10.1103/physrevd.78.083004 | page=083004| arxiv=0806.3289 | bibcode=2008PhRvD..78h3004G | s2cid=118616129 }}
• {{cite journal | last=Petters | first=A. O. | title=On relativistic corrections to microlensing effects: applications to the Galactic black hole | journal=Monthly Notices of the Royal Astronomical Society | publisher=Oxford University Press (OUP) | volume=338 | issue=2 | date=2003-01-11 | issn=0035-8711 | doi=10.1046/j.1365-8711.2003.06065.x|arxiv=astro-ph/0208500 | pages=457–464| bibcode=2003MNRAS.338..457P | doi-access=free }}
• {{cite journal | last1=MAJUMDAR | first1=A. S. | last2=MUKHERJEE | first2=N. | title=Braneworld Black Holes in Cosmology and Astrophysics | journal=International Journal of Modern Physics D | publisher=World Scientific Pub Co Pte Lt | volume=14 | issue=7 | year=2005 | issn=0218-2718 | doi=10.1142/s0218271805006948 |arxiv=astro-ph/0503473 | pages=1095–1129| bibcode=2005IJMPD..14.1095M | s2cid=119530457 | url=https://cds.cern.ch/record/828833 }}
• {{cite journal | last=Sereno | first=Mauro | title=Weak field limit of Reissner-Nordström black hole lensing | journal=Physical Review D | publisher=American Physical Society (APS) | volume=69 | issue=2 | date=2004-01-13 | issn=1550-7998 | doi=10.1103/physrevd.69.023002 | page=023002| arxiv=gr-qc/0310063 | bibcode=2004PhRvD..69b3002S | s2cid=119333514 }}
• {{cite journal | last1=Stefanov | first1=Ivan Zh. | last2=Yazadjiev | first2=Stoytcho S. | last3=Gyulchev | first3=Galin G. | title=Connection between Black-Hole Quasinormal Modes and Lensing in the Strong Deflection Limit | journal=Physical Review Letters | volume=104 | issue=25 | date=2010-06-25 | issn=0031-9007 | doi=10.1103/physrevlett.104.251103 | page=251103| pmid=20867359 |arxiv=1003.1609| bibcode=2010PhRvL.104y1103S | s2cid=16644240 }}
• {{cite journal | last1=Mukherjee | first1=Nupur | last2=Majumdar | first2=A. S. | title=Particle motion and gravitational lensing in the metric of a dilaton black hole in a de Sitter universe | journal=General Relativity and Gravitation | volume=39 | issue=5 | date=2007-02-21 | issn=0001-7701 | doi=10.1007/s10714-007-0407-5 | pages=583–600| arxiv=astro-ph/0605224 | bibcode=2007GReGr..39..583M | s2cid=50992892 }}
• {{cite journal | last1=Claudel | first1=Clarissa-Marie | last2=Virbhadra | first2=K. S. | last3=Ellis | first3=G. F. R. | title=The geometry of photon surfaces | journal=Journal of Mathematical Physics | volume=42 | issue=2 | year=2001 | pages=818–838 | issn=0022-2488 | doi=10.1063/1.1308507 | arxiv=gr-qc/0005050 | bibcode=2001JMP....42..818C | s2cid=119457077 }}
• {{cite journal | last1=Virbhadra | first1=K. S. | last2=Ellis | first2=G. F. R. | title=Gravitational lensing by naked singularities | journal=Physical Review D | publisher=American Physical Society (APS) | volume=65 | issue=10 | date=2002-05-10 | issn=0556-2821 | doi=10.1103/physrevd.65.103004 | page=103004| bibcode=2002PhRvD..65j3004V }}
• {{cite journal | last=Virbhadra | first=K. S. | title=Relativistic images of Schwarzschild black hole lensing | journal=Physical Review D | volume=79 | issue=8 | date=2009-04-09 | issn=1550-7998 | doi=10.1103/physrevd.79.083004 | page=083004| arxiv=0810.2109 | bibcode=2009PhRvD..79h3004V | s2cid=119232496 }}
• {{cite journal | last1=Ghosh | first1=Tanwi | last2=SenGupta | first2=Soumitra | title=Strong gravitational lensing across a dilaton anti–de Sitter black hole | journal=Physical Review D | volume=81 | issue=4 | date=2010-02-10 | issn=1550-7998 | doi=10.1103/physrevd.81.044013 | page=044013| arxiv=1001.5129 | bibcode=2010PhRvD..81d4013G | s2cid=119243456 }}
• {{cite journal | last=Whisker | first=Richard | title=Strong gravitational lensing by braneworld black holes | journal=Physical Review D | publisher=American Physical Society (APS) | volume=71 | issue=6 | date=2005-03-03 | issn=1550-7998 | doi=10.1103/physrevd.71.064004| arxiv=astro-ph/0411786 | page=064004| bibcode=2005PhRvD..71f4004W | s2cid=118977836 | url=https://cds.cern.ch/record/808155 }}
• {{cite journal | last1=Rahvar | first1=S. | last2=Mehrabi | first2=A. | last3=Dominik | first3=M. | title=Compact object detection in self-lensing binary systems with a main-sequence star | journal=Monthly Notices of the Royal Astronomical Society | publisher=Oxford University Press (OUP) | volume=410 | issue=2 | date=2010-09-22 | issn=0035-8711 | doi=10.1111/j.1365-2966.2010.17490.x | pages=912–918|doi-access=free|arxiv=1008.1033}}
• {{cite journal | last1=LEIVA | first1=CARLOS | last2=SAAVEDRA | first2=JOEL | last3=VILLANUEVA | first3=JOSÉ | title=Geodesic Structure of the Schwarzschild Black Hole in Rainbow Gravity | journal=Modern Physics Letters A | volume=24 | issue=18 | date=2009-06-14 | issn=0217-7323 | doi=10.1142/s0217732309029983 | pages=1443–1451| arxiv=0808.2601 | bibcode=2009MPLA...24.1443L | s2cid=119216773 }}
• R. Sosnovskiy, {{arxiv|0806.4379}}
• {{cite journal | last1=Keeton | first1=Charles R. | last2=Petters | first2=A. O. | title=Formalism for testing theories of gravity using lensing by compact objects. II. Probing post-post-Newtonian metrics | journal=Physical Review D | publisher=American Physical Society (APS) | volume=73 | issue=4 | date=2006-02-21 | issn=1550-7998 | doi=10.1103/physrevd.73.044024 | page=044024| arxiv=gr-qc/0601053 | bibcode=2006PhRvD..73d4024K | s2cid=56001059 }}
• {{cite journal | last1=Nandi | first1=Kamal K. | last2=Zhang | first2=Yuan-Zhong | last3=Zakharov | first3=Alexander V. | title=Gravitational lensing by wormholes | journal=Physical Review D | publisher=American Physical Society (APS) | volume=74 | issue=2 | date=2006-07-20 | issn=1550-7998 | doi=10.1103/physrevd.74.024020 | page=024020| arxiv=gr-qc/0602062 | bibcode=2006PhRvD..74b4020N | s2cid=119454982 }}
• {{cite journal | last1=Sereno | first1=Mauro | last2=De Luca | first2=Fabiana | title=Primary caustics and critical points behind a Kerr black hole | journal=Physical Review D | publisher=American Physical Society (APS) | volume=78 | issue=2 | date=2008-07-09 | issn=1550-7998 | doi=10.1103/physrevd.78.023008 | page=023008| arxiv=0710.5923 | bibcode=2008PhRvD..78b3008S | s2cid=119197253 | url=https://www.zora.uzh.ch/id/eprint/16760/1/0710.5923v2.pdf }}
• {{cite journal | last1=De Paolis | first1=F. | last2=Geralico | first2=A. | last3=Ingrosso | first3=G. | last4=Nucita | first4=A. A. | last5=Qadir | first5=A. | title=Kerr black holes as retro-MACHOs | journal=Astronomy & Astrophysics | publisher=EDP Sciences | volume=415 | issue=1 | year=2004 | issn=0004-6361 | doi=10.1051/0004-6361:20034587 | arxiv=astro-ph/0401384 | pages=1–7| bibcode=2004A&A...415....1D |doi-access=free}}
• {{cite journal | last=Stornaiolo | first=Cosimo | title=Cosmological Black Holes | journal=General Relativity and Gravitation | volume=34 | issue=12 | year=2002 | issn=0001-7701 | doi=10.1023/a:1021183417872 | pages=2089–2099| arxiv=gr-qc/0101120 | bibcode=2002GReGr..34.2089S | s2cid=17640392 }}
• {{cite journal | last1=Keeton | first1=Charles R. | last2=Petters | first2=A. O. | title=Formalism for testing theories of gravity using lensing by compact objects: Static, spherically symmetric case | journal=Physical Review D | publisher=American Physical Society (APS) | volume=72 | issue=10 | date=2005-11-04 | issn=1550-7998 | doi=10.1103/physrevd.72.104006 | page=104006| arxiv=gr-qc/0511019 | bibcode=2005PhRvD..72j4006K | s2cid=119035986 }}
• {{cite journal | last1=Harko | first1=Tiberiu | last2=Kovács | first2=Zoltan | last3=Lobo | first3=Francisco S. N. | title=Solar System tests of Hořava–Lifshitz gravity | journal=Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | volume=467 | issue=2129 | year=2011 | issn=1364-5021 | doi=10.1098/rspa.2010.0477 | pages=1390–1407|arxiv=0908.2874| bibcode=2011RSPSA.467.1390H | s2cid=2412476 }}
• {{cite journal | last=Sereno | first=M. | title=Aberration in gravitational lensing | journal=Physical Review D | publisher=American Physical Society (APS) | volume=78 | issue=8 | date=2008-10-08 | issn=1550-7998 | doi=10.1103/physrevd.78.083003 | page=083003| s2cid=119215266 | url=https://www.zora.uzh.ch/id/eprint/16581/3/Sereno_PhysRevD_2008_AM_V.pdf | arxiv=0809.3900 | bibcode=2008PhRvD..78h3003S }}
• {{cite journal | last=Sereno | first=Mauro | title=Influence of the cosmological constant on gravitational lensing in small systems | journal=Physical Review D | publisher=American Physical Society (APS) | volume=77 | issue=4 | date=2008-02-15 | issn=1550-7998 | doi=10.1103/physrevd.77.043004 | page=043004| arxiv=0711.1802 | bibcode=2008PhRvD..77d3004S | s2cid=39617618 | url=https://www.zora.uzh.ch/id/eprint/16762/4/0711.1802v1.pdf }}
• {{cite journal | last1=Iyer | first1=S. V. | last2=Petters | first2=A. O. | title=Light's bending angle due to black holes: from the photon sphere to infinity | journal=General Relativity and Gravitation | volume=39 | issue=10 | date=2007-07-11 | issn=0001-7701 | doi=10.1007/s10714-007-0481-8 | pages=1563–1582| arxiv=gr-qc/0611086 | bibcode=2007GReGr..39.1563I | s2cid=119007619 }}
• {{cite journal | last1=Harko | first1=Tiberiu | last2=Kovács | first2=Zoltán | last3=Lobo | first3=Francisco S. N. | title=Testing Hořava-Lifshitz gravity using thin accretion disk properties | journal=Physical Review D | publisher=American Physical Society (APS) | volume=80 | issue=4 | date=2009-08-24 | issn=1550-7998 | doi=10.1103/physrevd.80.044021 | page=044021| arxiv=0907.1449 | bibcode=2009PhRvD..80d4021H | hdl=10722/91855 | s2cid=118616205 | hdl-access=free }}
• {{cite journal | last=Sereno | first=M. | title=Gravitational lensing by stars with angular momentum | journal=Monthly Notices of the Royal Astronomical Society | publisher=Oxford University Press (OUP) | volume=344 | issue=3 | year=2003 | issn=0035-8711 | doi=10.1046/j.1365-8711.2003.06881.x|arxiv=astro-ph/0307243 | pages=942–950| bibcode=2003MNRAS.344..942S | doi-access=free }}
• {{cite journal | last1=Böhmer | first1=C G | last2=Harko | first2=T | title=Galactic dark matter as a bulk effect on the brane | journal=Classical and Quantum Gravity | volume=24 | issue=13 | date=2007-06-12 | issn=0264-9381 | doi=10.1088/0264-9381/24/13/004 | pages=3191–3209| arxiv=0705.2496 | bibcode=2007CQGra..24.3191B | s2cid=119315095 }}
• {{cite journal | last1=Aliev | first1=Alikram N. | last2=Talazan | first2=Pamir | title=Gravitational effects of rotating braneworld black holes | journal=Physical Review D | volume=80 | issue=4 | date=2009-08-24 | issn=1550-7998 | doi=10.1103/physrevd.80.044023 | page=044023| arxiv=0906.1465 | bibcode=2009PhRvD..80d4023A | s2cid=119306508 }}
• {{cite conference | last=PERLICK | first=VOLKER | title=The Eleventh Marcel Grossmann Meeting | chapter=THEORETICAL GRAVITATIONAL LENSING – BEYOND THE WEAK-FIELD SMALL-ANGLE APPROXIMATION | publisher=World Scientific Publishing Company | year=2008 | isbn=978-981-283-426-3 | doi=10.1142/9789812834300_0030 | pages=680–699|arxiv=0708.0178}}
• {{cite journal | last=Bozza | first=Valerio | title=Gravitational lensing by black holes | journal=General Relativity and Gravitation | volume=42 | issue=9 | date=2010-05-05 | issn=0001-7701 | doi=10.1007/s10714-010-0988-2 | pages=2269–2300|arxiv=0911.2187| bibcode=2010GReGr..42.2269B | s2cid=118635353 }}

(see also in [http://search.arxiv.org:8081/?query=%22relativistic+images%22&qid=null [a]], [http://www.google.com/search?client=firefox-a&rls=org.mozilla%3Aen-US%3Aofficial&channel=s&hl=en&source=hp&q=%22relativistic+images%22&btnG=Google+Search [b]], and [http://search.yahoo.com/search;_ylt=A0geuz.5ynlMd2MBXD9XNyoA?p=%22relativistic+images%22&fr=sfp&xargs=0&pstart=1&b=1&xa=OsEZ9USraQ7tMnfDVpvwPg--,1283136569 [c]].)

They further defined a term relativistic Einstein rings.