Kerr metric (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Kerr metric" in English language version.

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Harrison, B. Kent (1978-10-30). "Bäcklund Transformation for the Ernst Equation of General Relativity". Physical Review Letters. 41 (18): 1197–1200. Bibcode:1978PhRvL..41.1197H. doi:10.1103/PhysRevLett.41.1197. ISSN 0031-9007.

archive.today

Paul Davies: About Time: Einstein's Unfinished Revolution

arxiv.org

Abbot, B.P. (11 February 2016). "Observation of Gravitational Waves from a Binary Black Hole Merger". Physical Review Letters. 116 (6): 061102. arXiv:1602.03837. Bibcode:2016PhRvL.116f1102A. doi:10.1103/PhysRevLett.116.061102. PMID 26918975. S2CID 124959784.
Newman, Ezra; Adamo, Tim (2014). "Kerr–Newman metric". Scholarpedia. 9 (10): 31791. arXiv:1410.6626. Bibcode:2014SchpJ...931791N. doi:10.4249/scholarpedia.31791. ISSN 1941-6016.
Visser, Matt (2007). "The Kerr spacetime: A brief introduction". p. 15, Eq. 60–61, p. 24, p. 35. arXiv:0706.0622v3 [gr-qc].
Balasin, Herbert; Nachbagauer, Herbert (1994). "Distributional energy–momentum tensor of the Kerr–Newman spacetime family". Classical and Quantum Gravity. 11 (6): 1453–1461. arXiv:gr-qc/9312028. Bibcode:1994CQGra..11.1453B. doi:10.1088/0264-9381/11/6/010. S2CID 6041750.
Visser, Matt (14 January 2008). "The Kerr spacetime: A brief introduction". p. 12. arXiv:0706.0622 [gr-qc].
Will, Clifford M. (May 2011). "Finally, results from Gravity Probe B". Physics. 4: 43. arXiv:1106.1198. Bibcode:2011PhyOJ...4...43W. doi:10.1103/Physics.4.43. S2CID 119237335.
The LIGO Scientific Collaboration; the Virgo Collaboration (2007). "The Kerr spacetime: A brief introduction". p. 13, below eq. 52. arXiv:0706.0622v3 [gr-qc].
Frolov, Andrei V.; Frolov, Valeri P. (2014). "Rigidly rotating zero-angular-momentum observer surfaces in the Kerr spacetime". Physical Review D. 90 (12): 124010. arXiv:1408.6316. Bibcode:2014PhRvD..90l4010F. doi:10.1103/PhysRevD.90.124010. S2CID 118417747.)
Riazuelo, Alain (December 2020). "Seeing Relativity -- III. Journeying within the Kerr metric toward the negative gravity region". International Journal of Modern Physics D. 29 (16): 2050109–2050202. arXiv:2008.04384. Bibcode:2020IJMPD..2950109R. doi:10.1142/S0218271820501096. ISSN 0218-2718. S2CID 221095833.

books.google.com

Rezzolla, Luciano; Zanotti, Olindo (2013). Relativistic Hydrodynamics. Oxford University Press. pp. 55–57 [eqns. 1.249 to 1.265]. ISBN 978-0-19-852890-6.
Berman, Marcelo. "Energy of Black Holes and Hawking's Universe" in Trends in Black Hole Research, page 148 (Kreitler ed., Nova Publishers 2006).
Stephani, Hans et al. Exact Solutions of Einstein's Field Equations (Cambridge University Press 2003). See page 485 regarding determinant of metric tensor. See page 325 regarding generalizations.

caltech.edu

tapir.caltech.edu

Christopher M. Hirata: Lecture XXVI: Kerr black holes: I. Metric structure and regularity of particle orbits, p. 1, Eq. 1

cnrs.fr

lapth.cnrs.fr

Thibault Damour: Black Holes: Energetics and Thermodynamics, page 11

colorado.edu

jila.colorado.edu

Andrew Hamilton: Black hole Penrose diagrams (JILA Colorado)

doi.org

Kerr, Roy P. (1963). "Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics". Physical Review Letters. 11 (5): 237–238. Bibcode:1963PhRvL..11..237K. doi:10.1103/PhysRevLett.11.237.
Sneppen, Albert (December 2021). "Divergent reflections around the photon sphere of a black hole". Scientific Reports. 11 (1). Cosmic Dawn Center: 14247. Bibcode:2021NatSR..1114247S. doi:10.1038/s41598-021-93595-w. PMC 8270963. PMID 34244573.
Abbot, B.P. (11 February 2016). "Observation of Gravitational Waves from a Binary Black Hole Merger". Physical Review Letters. 116 (6): 061102. arXiv:1602.03837. Bibcode:2016PhRvL.116f1102A. doi:10.1103/PhysRevLett.116.061102. PMID 26918975. S2CID 124959784.
Newman, E. T.; Janis, A. I. (1965-06-01). "Note on the Kerr Spinning-Particle Metric". Journal of Mathematical Physics. 6 (6): 915–917. Bibcode:1965JMP.....6..915N. doi:10.1063/1.1704350. ISSN 0022-2488.
Newman, Ezra; Adamo, Tim (2014). "Kerr–Newman metric". Scholarpedia. 9 (10): 31791. arXiv:1410.6626. Bibcode:2014SchpJ...931791N. doi:10.4249/scholarpedia.31791. ISSN 1941-6016.
Harrison, B. Kent (1978-10-30). "Bäcklund Transformation for the Ernst Equation of General Relativity". Physical Review Letters. 41 (18): 1197–1200. Bibcode:1978PhRvL..41.1197H. doi:10.1103/PhysRevLett.41.1197. ISSN 0031-9007.
Chou, Yu-Ching (January 2020). "A radiating Kerr black hole and Hawking radiation". Heliyon. 6 (1): e03336. Bibcode:2020Heliy...603336C. doi:10.1016/j.heliyon.2020.e03336. PMC 7002888. PMID 32051884.
Boyer, Robert H.; Lindquist, Richard W. (1967). "Maximal Analytic Extension of the Kerr Metric". J. Math. Phys. 8 (2): 265–281. Bibcode:1967JMP.....8..265B. doi:10.1063/1.1705193.
Debney, G. C.; Kerr, R. P.; Schild, A. (1969). "Solutions of the Einstein and Einstein-Maxwell Equations". Journal of Mathematical Physics. 10 (10): 1842–1854. Bibcode:1969JMP....10.1842D. doi:10.1063/1.1664769. Especially see equations (7.10), (7.11) and (7.14).
Balasin, Herbert; Nachbagauer, Herbert (1994). "Distributional energy–momentum tensor of the Kerr–Newman spacetime family". Classical and Quantum Gravity. 11 (6): 1453–1461. arXiv:gr-qc/9312028. Bibcode:1994CQGra..11.1453B. doi:10.1088/0264-9381/11/6/010. S2CID 6041750.
Bhat, Manjiri; Dhurandhar, Sanjeev; Dadhich, Naresh (1985). "Energetics of the Kerr–Newman black hole by the penrose process". Journal of Astrophysics and Astronomy. 6 (2): 85–100. Bibcode:1985JApA....6...85B. CiteSeerX 10.1.1.512.1400. doi:10.1007/BF02715080. S2CID 53513572.
Will, Clifford M. (May 2011). "Finally, results from Gravity Probe B". Physics. 4: 43. arXiv:1106.1198. Bibcode:2011PhyOJ...4...43W. doi:10.1103/Physics.4.43. S2CID 119237335.
Carter, Brandon (1968). "Global structure of the Kerr family of gravitational fields" (PDF). Physical Review. 174 (5): 1559–1571. Bibcode:1968PhRv..174.1559C. doi:10.1103/PhysRev.174.1559. S2CID 123261579. Archived from the original (PDF) on 2020-02-25.
Bardeen, James M.; Press, William H.; Teukolsky, Saul A. (1972). "Rotating Black Holes: Locally Nonrotating Frames, Energy Extraction, and Scalar Synchrotron Radiation". The Astrophysical Journal. 178: 347. Bibcode:1972ApJ...178..347B. doi:10.1086/151796.
Frolov, Andrei V.; Frolov, Valeri P. (2014). "Rigidly rotating zero-angular-momentum observer surfaces in the Kerr spacetime". Physical Review D. 90 (12): 124010. arXiv:1408.6316. Bibcode:2014PhRvD..90l4010F. doi:10.1103/PhysRevD.90.124010. S2CID 118417747.)
Riazuelo, Alain (December 2020). "Seeing Relativity -- III. Journeying within the Kerr metric toward the negative gravity region". International Journal of Modern Physics D. 29 (16): 2050109–2050202. arXiv:2008.04384. Bibcode:2020IJMPD..2950109R. doi:10.1142/S0218271820501096. ISSN 0218-2718. S2CID 221095833.
Bičák, Jří; Ledvinka, Tomáš (1993). "Relativistic disks as sources of the Kerr metric". Physical Review Letters. 71 (11): 1669–1672. Bibcode:1993PhRvL..71.1669B. doi:10.1103/physrevlett.71.1669. PMID 10054468.

fh-swf.de

haegar.fh-swf.de

de Vries, Andreas. "Shadows of rotating black holes" (PDF). p. 8.

harvard.edu

ui.adsabs.harvard.edu

Kerr, Roy P. (1963). "Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics". Physical Review Letters. 11 (5): 237–238. Bibcode:1963PhRvL..11..237K. doi:10.1103/PhysRevLett.11.237.
Sneppen, Albert (December 2021). "Divergent reflections around the photon sphere of a black hole". Scientific Reports. 11 (1). Cosmic Dawn Center: 14247. Bibcode:2021NatSR..1114247S. doi:10.1038/s41598-021-93595-w. PMC 8270963. PMID 34244573.
Abbot, B.P. (11 February 2016). "Observation of Gravitational Waves from a Binary Black Hole Merger". Physical Review Letters. 116 (6): 061102. arXiv:1602.03837. Bibcode:2016PhRvL.116f1102A. doi:10.1103/PhysRevLett.116.061102. PMID 26918975. S2CID 124959784.
Newman, E. T.; Janis, A. I. (1965-06-01). "Note on the Kerr Spinning-Particle Metric". Journal of Mathematical Physics. 6 (6): 915–917. Bibcode:1965JMP.....6..915N. doi:10.1063/1.1704350. ISSN 0022-2488.
Newman, Ezra; Adamo, Tim (2014). "Kerr–Newman metric". Scholarpedia. 9 (10): 31791. arXiv:1410.6626. Bibcode:2014SchpJ...931791N. doi:10.4249/scholarpedia.31791. ISSN 1941-6016.
Harrison, B. Kent (1978-10-30). "Bäcklund Transformation for the Ernst Equation of General Relativity". Physical Review Letters. 41 (18): 1197–1200. Bibcode:1978PhRvL..41.1197H. doi:10.1103/PhysRevLett.41.1197. ISSN 0031-9007.
Chou, Yu-Ching (January 2020). "A radiating Kerr black hole and Hawking radiation". Heliyon. 6 (1): e03336. Bibcode:2020Heliy...603336C. doi:10.1016/j.heliyon.2020.e03336. PMC 7002888. PMID 32051884.
Boyer, Robert H.; Lindquist, Richard W. (1967). "Maximal Analytic Extension of the Kerr Metric". J. Math. Phys. 8 (2): 265–281. Bibcode:1967JMP.....8..265B. doi:10.1063/1.1705193.
Debney, G. C.; Kerr, R. P.; Schild, A. (1969). "Solutions of the Einstein and Einstein-Maxwell Equations". Journal of Mathematical Physics. 10 (10): 1842–1854. Bibcode:1969JMP....10.1842D. doi:10.1063/1.1664769. Especially see equations (7.10), (7.11) and (7.14).
Balasin, Herbert; Nachbagauer, Herbert (1994). "Distributional energy–momentum tensor of the Kerr–Newman spacetime family". Classical and Quantum Gravity. 11 (6): 1453–1461. arXiv:gr-qc/9312028. Bibcode:1994CQGra..11.1453B. doi:10.1088/0264-9381/11/6/010. S2CID 6041750.
Bhat, Manjiri; Dhurandhar, Sanjeev; Dadhich, Naresh (1985). "Energetics of the Kerr–Newman black hole by the penrose process". Journal of Astrophysics and Astronomy. 6 (2): 85–100. Bibcode:1985JApA....6...85B. CiteSeerX 10.1.1.512.1400. doi:10.1007/BF02715080. S2CID 53513572.
Will, Clifford M. (May 2011). "Finally, results from Gravity Probe B". Physics. 4: 43. arXiv:1106.1198. Bibcode:2011PhyOJ...4...43W. doi:10.1103/Physics.4.43. S2CID 119237335.
Carter, Brandon (1968). "Global structure of the Kerr family of gravitational fields" (PDF). Physical Review. 174 (5): 1559–1571. Bibcode:1968PhRv..174.1559C. doi:10.1103/PhysRev.174.1559. S2CID 123261579. Archived from the original (PDF) on 2020-02-25.
Bardeen, James M.; Press, William H.; Teukolsky, Saul A. (1972). "Rotating Black Holes: Locally Nonrotating Frames, Energy Extraction, and Scalar Synchrotron Radiation". The Astrophysical Journal. 178: 347. Bibcode:1972ApJ...178..347B. doi:10.1086/151796.
Frolov, Andrei V.; Frolov, Valeri P. (2014). "Rigidly rotating zero-angular-momentum observer surfaces in the Kerr spacetime". Physical Review D. 90 (12): 124010. arXiv:1408.6316. Bibcode:2014PhRvD..90l4010F. doi:10.1103/PhysRevD.90.124010. S2CID 118417747.)
Riazuelo, Alain (December 2020). "Seeing Relativity -- III. Journeying within the Kerr metric toward the negative gravity region". International Journal of Modern Physics D. 29 (16): 2050109–2050202. arXiv:2008.04384. Bibcode:2020IJMPD..2950109R. doi:10.1142/S0218271820501096. ISSN 0218-2718. S2CID 221095833.
Bičák, Jří; Ledvinka, Tomáš (1993). "Relativistic disks as sources of the Kerr metric". Physical Review Letters. 71 (11): 1669–1672. Bibcode:1993PhRvL..71.1669B. doi:10.1103/physrevlett.71.1669. PMID 10054468.

livescience.com

Sutter, Paul (22 July 2021). "Black holes warp the universe into a grotesque hall of mirrors". livescience.com.

mobt3ath.com

Belinski, V.; Verdaguer, E. (2001). Gravitational Solitons. Cambridge Monographs on Mathematical Physics. Cambridge University Press. ISBN 978-0521805865. PDF

nih.gov

pubmed.ncbi.nlm.nih.gov

Sneppen, Albert (December 2021). "Divergent reflections around the photon sphere of a black hole". Scientific Reports. 11 (1). Cosmic Dawn Center: 14247. Bibcode:2021NatSR..1114247S. doi:10.1038/s41598-021-93595-w. PMC 8270963. PMID 34244573.
Abbot, B.P. (11 February 2016). "Observation of Gravitational Waves from a Binary Black Hole Merger". Physical Review Letters. 116 (6): 061102. arXiv:1602.03837. Bibcode:2016PhRvL.116f1102A. doi:10.1103/PhysRevLett.116.061102. PMID 26918975. S2CID 124959784.
Chou, Yu-Ching (January 2020). "A radiating Kerr black hole and Hawking radiation". Heliyon. 6 (1): e03336. Bibcode:2020Heliy...603336C. doi:10.1016/j.heliyon.2020.e03336. PMC 7002888. PMID 32051884.
Bičák, Jří; Ledvinka, Tomáš (1993). "Relativistic disks as sources of the Kerr metric". Physical Review Letters. 71 (11): 1669–1672. Bibcode:1993PhRvL..71.1669B. doi:10.1103/physrevlett.71.1669. PMID 10054468.

ncbi.nlm.nih.gov

Sneppen, Albert (December 2021). "Divergent reflections around the photon sphere of a black hole". Scientific Reports. 11 (1). Cosmic Dawn Center: 14247. Bibcode:2021NatSR..1114247S. doi:10.1038/s41598-021-93595-w. PMC 8270963. PMID 34244573.
Chou, Yu-Ching (January 2020). "A radiating Kerr black hole and Hawking radiation". Heliyon. 6 (1): e03336. Bibcode:2020Heliy...603336C. doi:10.1016/j.heliyon.2020.e03336. PMC 7002888. PMID 32051884.

pdf-archive.com

Misner, Thorne & Wheeler: Gravitation Archived 2017-08-22 at the Wayback Machine, pages 899, 900, 908

psu.edu

citeseerx.ist.psu.edu

Bhat, Manjiri; Dhurandhar, Sanjeev; Dadhich, Naresh (1985). "Energetics of the Kerr–Newman black hole by the penrose process". Journal of Astrophysics and Astronomy. 6 (2): 85–100. Bibcode:1985JApA....6...85B. CiteSeerX 10.1.1.512.1400. doi:10.1007/BF02715080. S2CID 53513572.

scitation.org

aip.scitation.org

Newman, E. T.; Janis, A. I. (1965-06-01). "Note on the Kerr Spinning-Particle Metric". Journal of Mathematical Physics. 6 (6): 915–917. Bibcode:1965JMP.....6..915N. doi:10.1063/1.1704350. ISSN 0022-2488.

semanticscholar.org

api.semanticscholar.org

Abbot, B.P. (11 February 2016). "Observation of Gravitational Waves from a Binary Black Hole Merger". Physical Review Letters. 116 (6): 061102. arXiv:1602.03837. Bibcode:2016PhRvL.116f1102A. doi:10.1103/PhysRevLett.116.061102. PMID 26918975. S2CID 124959784.
Balasin, Herbert; Nachbagauer, Herbert (1994). "Distributional energy–momentum tensor of the Kerr–Newman spacetime family". Classical and Quantum Gravity. 11 (6): 1453–1461. arXiv:gr-qc/9312028. Bibcode:1994CQGra..11.1453B. doi:10.1088/0264-9381/11/6/010. S2CID 6041750.
Bhat, Manjiri; Dhurandhar, Sanjeev; Dadhich, Naresh (1985). "Energetics of the Kerr–Newman black hole by the penrose process". Journal of Astrophysics and Astronomy. 6 (2): 85–100. Bibcode:1985JApA....6...85B. CiteSeerX 10.1.1.512.1400. doi:10.1007/BF02715080. S2CID 53513572.
Will, Clifford M. (May 2011). "Finally, results from Gravity Probe B". Physics. 4: 43. arXiv:1106.1198. Bibcode:2011PhyOJ...4...43W. doi:10.1103/Physics.4.43. S2CID 119237335.
Carter, Brandon (1968). "Global structure of the Kerr family of gravitational fields" (PDF). Physical Review. 174 (5): 1559–1571. Bibcode:1968PhRv..174.1559C. doi:10.1103/PhysRev.174.1559. S2CID 123261579. Archived from the original (PDF) on 2020-02-25.
Frolov, Andrei V.; Frolov, Valeri P. (2014). "Rigidly rotating zero-angular-momentum observer surfaces in the Kerr spacetime". Physical Review D. 90 (12): 124010. arXiv:1408.6316. Bibcode:2014PhRvD..90l4010F. doi:10.1103/PhysRevD.90.124010. S2CID 118417747.)
Riazuelo, Alain (December 2020). "Seeing Relativity -- III. Journeying within the Kerr metric toward the negative gravity region". International Journal of Modern Physics D. 29 (16): 2050109–2050202. arXiv:2008.04384. Bibcode:2020IJMPD..2950109R. doi:10.1142/S0218271820501096. ISSN 0218-2718. S2CID 221095833.

pdfs.semanticscholar.org

Carter, Brandon (1968). "Global structure of the Kerr family of gravitational fields" (PDF). Physical Review. 174 (5): 1559–1571. Bibcode:1968PhRv..174.1559C. doi:10.1103/PhysRev.174.1559. S2CID 123261579. Archived from the original (PDF) on 2020-02-25.

uu.nl

staff.science.uu.nl

Stijn van Tongeren: Rotating Black Holes, page 42

web.archive.org

Misner, Thorne & Wheeler: Gravitation Archived 2017-08-22 at the Wayback Machine, pages 899, 900, 908
Carter, Brandon (1968). "Global structure of the Kerr family of gravitational fields" (PDF). Physical Review. 174 (5): 1559–1571. Bibcode:1968PhRv..174.1559C. doi:10.1103/PhysRev.174.1559. S2CID 123261579. Archived from the original (PDF) on 2020-02-25.

worldcat.org

search.worldcat.org

Newman, E. T.; Janis, A. I. (1965-06-01). "Note on the Kerr Spinning-Particle Metric". Journal of Mathematical Physics. 6 (6): 915–917. Bibcode:1965JMP.....6..915N. doi:10.1063/1.1704350. ISSN 0022-2488.
Newman, Ezra; Adamo, Tim (2014). "Kerr–Newman metric". Scholarpedia. 9 (10): 31791. arXiv:1410.6626. Bibcode:2014SchpJ...931791N. doi:10.4249/scholarpedia.31791. ISSN 1941-6016.
Harrison, B. Kent (1978-10-30). "Bäcklund Transformation for the Ernst Equation of General Relativity". Physical Review Letters. 41 (18): 1197–1200. Bibcode:1978PhRvL..41.1197H. doi:10.1103/PhysRevLett.41.1197. ISSN 0031-9007.
Riazuelo, Alain (December 2020). "Seeing Relativity -- III. Journeying within the Kerr metric toward the negative gravity region". International Journal of Modern Physics D. 29 (16): 2050109–2050202. arXiv:2008.04384. Bibcode:2020IJMPD..2950109R. doi:10.1142/S0218271820501096. ISSN 0218-2718. S2CID 221095833.

youtube.com

Roy Kerr (Crafoord Prize Symposium in Astronomy): Spinning Black Holes. (YouTube, Timestamp 26m)