Separability of the Klein-Gordon equation for rotating spacetimes obtained from Newman-Janis algorithm

Chen, Che-Yu; Chen, Pisin

doi:10.1103/PhysRevD.100.104054

Title: Separability of the Klein-Gordon equation for rotating spacetimes obtained from Newman-Janis algorithm

Abstract

In the literature, the Newman-Janis algorithm (NJA) has been widely used to construct stationary and axisymmetric spacetimes to describe rotating black holes. In addition, it has been recently shown that the general stationary and axisymmetric spacetime generated through NJA allows the complete separability of the null geodesic equations. In fact, the Hamilton-Jacobi equation in this spacetime is also separable if one of the metric functions is additively separable. In this work, we further study the conditions for a separable Klein-Gordon equation in such a general spacetime. Here, the relations between the NJA spacetime and other parametrized axially symmetric spacetimes in the literature are also discussed.

Authors:

^[1]; Chen, Pisin ^[2]

National Taiwan Univ., Taipei (Taiwan)
National Taiwan Univ., Taipei (Taiwan); Stanford Univ., CA (United States)

Publication Date:: 2019-11-15

Research Org.:: SLAC National Accelerator Lab., Menlo Park, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1596304

Grant/Contract Number:: AC02-76SF00515; 107-2119-M-002-005; 108-2811-M-002-682

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review D

Additional Journal Information:: Journal Volume: 100; Journal Issue: 10; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 79 ASTRONOMY AND ASTROPHYSICS; Alternative gravity theories; General relativity equations & solutions; Classical black holes

Citation Formats


                    Chen, Che-Yu, and Chen, Pisin. Separability of the Klein-Gordon equation for rotating spacetimes obtained from Newman-Janis algorithm.  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevD.100.104054.

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                    Chen, Che-Yu, & Chen, Pisin. Separability of the Klein-Gordon equation for rotating spacetimes obtained from Newman-Janis algorithm.  United States.  https://doi.org/10.1103/PhysRevD.100.104054

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                    Chen, Che-Yu, and Chen, Pisin. Fri .  
"Separability of the Klein-Gordon equation for rotating spacetimes obtained from Newman-Janis algorithm".  United States.  https://doi.org/10.1103/PhysRevD.100.104054.  https://www.osti.gov/servlets/purl/1596304.

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@article{osti_1596304,

  title        = {Separability of the Klein-Gordon equation for rotating spacetimes obtained from Newman-Janis algorithm},

  author       = {Chen, Che-Yu and Chen, Pisin},

  abstractNote = {In the literature, the Newman-Janis algorithm (NJA) has been widely used to construct stationary and axisymmetric spacetimes to describe rotating black holes. In addition, it has been recently shown that the general stationary and axisymmetric spacetime generated through NJA allows the complete separability of the null geodesic equations. In fact, the Hamilton-Jacobi equation in this spacetime is also separable if one of the metric functions is additively separable. In this work, we further study the conditions for a separable Klein-Gordon equation in such a general spacetime. Here, the relations between the NJA spacetime and other parametrized axially symmetric spacetimes in the literature are also discussed.},

  doi          = {10.1103/PhysRevD.100.104054},

  journal      = {Physical Review D},

  number       = 10,

  volume       = 100,

  place        = {United States},

  year         = {2019},

  month        = {11}

}

Copy to clipboard

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https://doi.org/10.1103/PhysRevD.100.104054

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Works referenced in this record:

Black hole space-time in dark matter halo
journal, September 2018

Xu, Zhaoyi; Hou, Xian; Gong, Xiaobo
Journal of Cosmology and Astroparticle Physics, Vol. 2018, Issue 09
DOI: 10.1088/1475-7516/2018/09/038

Testing the Kerr metric with the iron line and the KRZ parametrization
journal, September 2016

Ni, Yueying; Jiang, Jiachen; Bambi, Cosimo
Journal of Cosmology and Astroparticle Physics, Vol. 2016, Issue 09
DOI: 10.1088/1475-7516/2016/09/014

Metric for rapidly spinning black holes suitable for strong-field tests of the no-hair theorem
journal, June 2011

Johannsen, Tim; Psaltis, Dimitrios
Physical Review D, Vol. 83, Issue 12
DOI: 10.1103/PhysRevD.83.124015

Note on a new parametrization for testing the Kerr metric
journal, May 2016

Ghasemi-Nodehi, M.; Bambi, Cosimo
The European Physical Journal C, Vol. 76, Issue 5
DOI: 10.1140/epjc/s10052-016-4137-2

Preserving Kerr symmetries in deformed spacetimes
journal, August 2018

Papadopoulos, Georgios O.; Kokkotas, Kostas D.
Classical and Quantum Gravity, Vol. 35, Issue 18
DOI: 10.1088/1361-6382/aad7f4

Black hole shadow in a general rotating spacetime obtained through Newman-Janis algorithm
journal, July 2019

Shaikh, Rajibul
Physical Review D, Vol. 100, Issue 2
DOI: 10.1103/PhysRevD.100.024028

Solution of the Scalar Wave Equation in a Kerr Background by Separation of Variables
journal, April 1972

Brill, Dieter R.; Chrzanowski, Paul L.; Pereira, C. Martin
Physical Review D, Vol. 5, Issue 8
DOI: 10.1103/PhysRevD.5.1913

Shadows of CPR black holes and tests of the Kerr metric
journal, July 2015

Ghasemi-Nodehi, M.; Li, Zilong; Bambi, Cosimo
The European Physical Journal C, Vol. 75, Issue 7
DOI: 10.1140/epjc/s10052-015-3539-x

Generating rotating regular black hole solutions without complexification
journal, September 2014

Azreg-Aïnou, Mustapha
Physical Review D, Vol. 90, Issue 6
DOI: 10.1103/PhysRevD.90.064041

Rotating regular black holes
journal, April 2013

Bambi, Cosimo; Modesto, Leonardo
Physics Letters B, Vol. 721, Issue 4-5
DOI: 10.1016/j.physletb.2013.03.025

On generic parametrizations of spinning black-hole geometries
journal, March 2014

Cardoso, Vitor; Pani, Paolo; Rico, João
Physical Review D, Vol. 89, Issue 6
DOI: 10.1103/PhysRevD.89.064007

Note on the Kerr Spinning‐Particle Metric
journal, June 1965

Newman, E. T.; Janis, A. I.
Journal of Mathematical Physics, Vol. 6, Issue 6
DOI: 10.1063/1.1704350

Metric of a Rotating, Charged Mass
journal, June 1965

Newman, E. T.; Couch, E.; Chinnapared, K.
Journal of Mathematical Physics, Vol. 6, Issue 6
DOI: 10.1063/1.1704351

Black hole shadow in an asymptotically flat, stationary, and axisymmetric spacetime: The Kerr-Newman and rotating regular black holes
journal, March 2018

Tsukamoto, Naoki
Physical Review D, Vol. 97, Issue 6
DOI: 10.1103/PhysRevD.97.064021

Janis–Newman Algorithm: Generating Rotating and NUT Charged Black Holes
journal, March 2017

Erbin, Harold
Universe, Vol. 3, Issue 1
DOI: 10.3390/universe3010019

Testing general relativity with present and future astrophysical observations
journal, December 2015

Berti, Emanuele; Barausse, Enrico; Cardoso, Vitor
Classical and Quantum Gravity, Vol. 32, Issue 24
DOI: 10.1088/0264-9381/32/24/243001

Charged rotating noncommutative black holes
journal, November 2010

Modesto, Leonardo; Nicolini, Piero
Physical Review D, Vol. 82, Issue 10
DOI: 10.1103/PhysRevD.82.104035

Applicability of the Newman-Janis algorithm to black hole solutions of modified gravity theories
journal, November 2013

Hansen, Devin; Yunes, Nicolás
Physical Review D, Vol. 88, Issue 10
DOI: 10.1103/PhysRevD.88.104020

Rotating black hole in Rastall theory
journal, September 2018

Kumar, Rahul; Ghosh, Sushant G.
The European Physical Journal C, Vol. 78, Issue 9
DOI: 10.1140/epjc/s10052-018-6206-1

Mapping spacetimes with LISA: inspiral of a test body in a ‘quasi-Kerr’ field
journal, May 2006

Glampedakis, Kostas; Babak, Stanislav
Classical and Quantum Gravity, Vol. 23, Issue 12
DOI: 10.1088/0264-9381/23/12/013

Post-Kerr black hole spectroscopy
journal, September 2017

Glampedakis, Kostas; Pappas, George; Silva, Hector O.
Physical Review D, Vol. 96, Issue 6
DOI: 10.1103/PhysRevD.96.064054

Uniqueness of the Newman–Janis Algorithm in Generating the Kerr–Newman Metric
journal, March 2000

Drake, S. P.; Szekeres, Peter
General Relativity and Gravitation, Vol. 32, Issue 3
DOI: 10.1023/A:1001920232180

Hamilton-Jacobi and Schrodinger Separable Solutions of Einstein’s Equations
journal, December 1968

Carter, Brandon
Communications in Mathematical Physics, Vol. 10, Issue 4
DOI: 10.1007/BF03399503

Photon Rings Around kerr and Kerr-Like Black Holes
journal, October 2013

Johannsen, Tim
The Astrophysical Journal, Vol. 777, Issue 2
DOI: 10.1088/0004-637X/777/2/170

Cosmic censorship and parametrized spinning black-hole geometries
journal, November 2015

Cardoso, Vitor; Queimada, Leonel
General Relativity and Gravitation, Vol. 47, Issue 12
DOI: 10.1007/s10714-015-1990-5

General parametrization of axisymmetric black holes in metric theories of gravity
journal, March 2016

Konoplya, Roman; Rezzolla, Luciano; Zhidenko, Alexander
Physical Review D, Vol. 93, Issue 6
DOI: 10.1103/PhysRevD.93.064015

Comment on ‘Spinning loop black holes’
journal, June 2011

Azreg-Aïnou, Mustapha
Classical and Quantum Gravity, Vol. 28, Issue 14
DOI: 10.1088/0264-9381/28/14/148001

Regular black hole metric with three constants of motion
journal, August 2013

Johannsen, Tim
Physical Review D, Vol. 88, Issue 4
DOI: 10.1103/PhysRevD.88.044002

Axisymmetric black holes allowing for separation of variables in the Klein-Gordon and Hamilton-Jacobi equations
journal, April 2018

Konoplya, R. A.; Stuchlík, Z.; Zhidenko, A.
Physical Review D, Vol. 97, Issue 8
DOI: 10.1103/PhysRevD.97.084044

Astrophysical signatures of black holes in generalized Proca theories
journal, January 2019

Rahman, Mostafizur; Sen, Anjan A.
Physical Review D, Vol. 99, Issue 2
DOI: 10.1103/PhysRevD.99.024052

New method for shadow calculations: Application to parametrized axisymmetric black holes
journal, October 2016

Younsi, Ziri; Zhidenko, Alexander; Rezzolla, Luciano
Physical Review D, Vol. 94, Issue 8
DOI: 10.1103/PhysRevD.94.084025

Charged rotating noncommutative black holes
text, January 2010

Modesto, Leonardo; Nicolini, Piero
arXiv
DOI: 10.48550/arxiv.1005.5605

A Metric for Rapidly Spinning Black Holes Suitable for Strong-Field Tests of the No-Hair Theorem
text, January 2011

Johannsen, Tim; Psaltis, Dimitrios
arXiv
DOI: 10.48550/arxiv.1105.3191

Rotating regular black holes
text, January 2013

Bambi, Cosimo; Modesto, Leonardo
arXiv
DOI: 10.48550/arxiv.1302.6075

Applicability of the Newman-Janis Algorithm to Black Hole Solutions of Modified Gravity Theories
text, January 2013

Hansen, Devin; Yunes, Nicolas
arXiv
DOI: 10.48550/arxiv.1308.6631

Generating rotating regular black hole solutions without complexification
text, January 2014

Azreg-Aïnou, Mustapha
arXiv
DOI: 10.48550/arxiv.1405.2569

Regular Black Hole Metric with Three Constants of Motion
text, January 2015

Johannsen, Tim
arXiv
DOI: 10.48550/arxiv.1501.02809

Photon Rings around Kerr and Kerr-like Black Holes
text, January 2015

Johannsen, Tim
arXiv
DOI: 10.48550/arxiv.1501.02814

Testing General Relativity with Present and Future Astrophysical Observations
text, January 2015

Berti, Emanuele; Barausse, Enrico; Cardoso, Vitor
arXiv
DOI: 10.48550/arxiv.1501.07274

Cosmic Censorship and parametrized spinning black-hole geometries
text, January 2015

Cardoso, Vitor; Queimada, Leonel
arXiv
DOI: 10.48550/arxiv.1511.00690

Note on a new parametrization for testing the Kerr metric
text, January 2016

Ghasemi-Nodehi, M.; Bambi, Cosimo
arXiv
DOI: 10.48550/arxiv.1604.07032

Testing the Kerr metric with the iron line and the KRZ parametrization
text, January 2016

Ni, Yueying; Jiang, Jiachen; Bambi, Cosimo
arXiv
DOI: 10.48550/arxiv.1607.04893

A new method for shadow calculations: application to parameterised axisymmetric black holes
text, January 2016

Younsi, Ziri; Zhidenko, Alexander; Rezzolla, Luciano
arXiv
DOI: 10.48550/arxiv.1607.05767

Post-Kerr black hole spectroscopy
text, January 2017

Glampedakis, Kostas; Pappas, George; Silva, Hector O.
arXiv
DOI: 10.48550/arxiv.1706.07658

Black hole shadow in an asymptotically-flat, stationary, and axisymmetric spacetime: The Kerr-Newman and rotating regular black holes
text, January 2017

Tsukamoto, Naoki
arXiv
DOI: 10.48550/arxiv.1708.07427

Axisymmetric black holes allowing for separation of variables in the Klein-Gordon and Hamilton-Jacobi equation
text, January 2018

Konoplya, R. A.; Stuchlík, Z.; Zhidenko, A.
arXiv
DOI: 10.48550/arxiv.1801.07195

Astrophysical Signatures of Black holes in Generalized Proca Theories
text, January 2018

Rahman, Mostafizur; Sen, Anjan A.
arXiv
DOI: 10.48550/arxiv.1810.09200

Mapping spacetimes with LISA: inspiral of a test-body in a `quasi-Kerr' field
text, January 2005

Glampedakis, Kostas; Babak, Stanislav
arXiv
DOI: 10.48550/arxiv.gr-qc/0510057

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Title: Separability of the Klein-Gordon equation for rotating spacetimes obtained from Newman-Janis algorithm

Abstract

Citation Formats

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Testing the Kerr metric with the iron line and the KRZ parametrization journal, September 2016

Metric for rapidly spinning black holes suitable for strong-field tests of the no-hair theorem journal, June 2011

Note on a new parametrization for testing the Kerr metric journal, May 2016

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Black hole shadow in an asymptotically flat, stationary, and axisymmetric spacetime: The Kerr-Newman and rotating regular black holes journal, March 2018

Janis–Newman Algorithm: Generating Rotating and NUT Charged Black Holes journal, March 2017

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Applicability of the Newman-Janis algorithm to black hole solutions of modified gravity theories journal, November 2013

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Hamilton-Jacobi and Schrodinger Separable Solutions of Einstein’s Equations journal, December 1968

Photon Rings Around kerr and Kerr-Like Black Holes journal, October 2013

Cosmic censorship and parametrized spinning black-hole geometries journal, November 2015

General parametrization of axisymmetric black holes in metric theories of gravity journal, March 2016

Comment on ‘Spinning loop black holes’ journal, June 2011

Regular black hole metric with three constants of motion journal, August 2013

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Astrophysical signatures of black holes in generalized Proca theories journal, January 2019

New method for shadow calculations: Application to parametrized axisymmetric black holes journal, October 2016

Charged rotating noncommutative black holes text, January 2010

A Metric for Rapidly Spinning Black Holes Suitable for Strong-Field Tests of the No-Hair Theorem text, January 2011

Rotating regular black holes text, January 2013

Applicability of the Newman-Janis Algorithm to Black Hole Solutions of Modified Gravity Theories text, January 2013

Generating rotating regular black hole solutions without complexification text, January 2014

Regular Black Hole Metric with Three Constants of Motion text, January 2015

Photon Rings around Kerr and Kerr-like Black Holes text, January 2015

Testing General Relativity with Present and Future Astrophysical Observations text, January 2015

Cosmic Censorship and parametrized spinning black-hole geometries text, January 2015

Note on a new parametrization for testing the Kerr metric text, January 2016

Testing the Kerr metric with the iron line and the KRZ parametrization text, January 2016

A new method for shadow calculations: application to parameterised axisymmetric black holes text, January 2016

Post-Kerr black hole spectroscopy text, January 2017

Black hole shadow in an asymptotically-flat, stationary, and axisymmetric spacetime: The Kerr-Newman and rotating regular black holes text, January 2017

Axisymmetric black holes allowing for separation of variables in the Klein-Gordon and Hamilton-Jacobi equation text, January 2018

Astrophysical Signatures of Black holes in Generalized Proca Theories text, January 2018

Mapping spacetimes with LISA: inspiral of a test-body in a `quasi-Kerr' field text, January 2005

Black hole space-time in dark matter halo
journal, September 2018

Testing the Kerr metric with the iron line and the KRZ parametrization
journal, September 2016

Metric for rapidly spinning black holes suitable for strong-field tests of the no-hair theorem
journal, June 2011

Note on a new parametrization for testing the Kerr metric
journal, May 2016

Preserving Kerr symmetries in deformed spacetimes
journal, August 2018

Black hole shadow in a general rotating spacetime obtained through Newman-Janis algorithm
journal, July 2019

Solution of the Scalar Wave Equation in a Kerr Background by Separation of Variables
journal, April 1972

Shadows of CPR black holes and tests of the Kerr metric
journal, July 2015

Generating rotating regular black hole solutions without complexification
journal, September 2014

Rotating regular black holes
journal, April 2013

On generic parametrizations of spinning black-hole geometries
journal, March 2014

Note on the Kerr Spinning‐Particle Metric
journal, June 1965

Metric of a Rotating, Charged Mass
journal, June 1965

Black hole shadow in an asymptotically flat, stationary, and axisymmetric spacetime: The Kerr-Newman and rotating regular black holes
journal, March 2018

Janis–Newman Algorithm: Generating Rotating and NUT Charged Black Holes
journal, March 2017

Testing general relativity with present and future astrophysical observations
journal, December 2015

Charged rotating noncommutative black holes
journal, November 2010

Applicability of the Newman-Janis algorithm to black hole solutions of modified gravity theories
journal, November 2013

Rotating black hole in Rastall theory
journal, September 2018

Mapping spacetimes with LISA: inspiral of a test body in a ‘quasi-Kerr’ field
journal, May 2006

Post-Kerr black hole spectroscopy
journal, September 2017

Uniqueness of the Newman–Janis Algorithm in Generating the Kerr–Newman Metric
journal, March 2000

Hamilton-Jacobi and Schrodinger Separable Solutions of Einstein’s Equations
journal, December 1968

Photon Rings Around kerr and Kerr-Like Black Holes
journal, October 2013

Cosmic censorship and parametrized spinning black-hole geometries
journal, November 2015

General parametrization of axisymmetric black holes in metric theories of gravity
journal, March 2016

Comment on ‘Spinning loop black holes’
journal, June 2011

Regular black hole metric with three constants of motion
journal, August 2013

Axisymmetric black holes allowing for separation of variables in the Klein-Gordon and Hamilton-Jacobi equations
journal, April 2018

Astrophysical signatures of black holes in generalized Proca theories
journal, January 2019

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journal, October 2016

Charged rotating noncommutative black holes
text, January 2010

A Metric for Rapidly Spinning Black Holes Suitable for Strong-Field Tests of the No-Hair Theorem
text, January 2011

Rotating regular black holes
text, January 2013

Applicability of the Newman-Janis Algorithm to Black Hole Solutions of Modified Gravity Theories
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Generating rotating regular black hole solutions without complexification
text, January 2014

Regular Black Hole Metric with Three Constants of Motion
text, January 2015

Photon Rings around Kerr and Kerr-like Black Holes
text, January 2015

Testing General Relativity with Present and Future Astrophysical Observations
text, January 2015

Cosmic Censorship and parametrized spinning black-hole geometries
text, January 2015

Note on a new parametrization for testing the Kerr metric
text, January 2016

Testing the Kerr metric with the iron line and the KRZ parametrization
text, January 2016

A new method for shadow calculations: application to parameterised axisymmetric black holes
text, January 2016

Post-Kerr black hole spectroscopy
text, January 2017

Black hole shadow in an asymptotically-flat, stationary, and axisymmetric spacetime: The Kerr-Newman and rotating regular black holes
text, January 2017

Axisymmetric black holes allowing for separation of variables in the Klein-Gordon and Hamilton-Jacobi equation
text, January 2018

Astrophysical Signatures of Black holes in Generalized Proca Theories
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Mapping spacetimes with LISA: inspiral of a test-body in a `quasi-Kerr' field
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