Fetching the paper…

Reading the bibliography…

2020

Darboux diagonalization of the spatial 3-metric in Kerr spacetime

Baines, Joshua, Berry, Thomas, Simpson, Alex et al.

Original
PDF
Post on X

Understand

The astrophysical importance of the Kerr spacetime cannot be overstated.

Of the currently known exact solutions to the Einstein field equations, the Kerr spacetime stands out in terms of its direct applicability to describing astronomical black hole candidates.
In counterpoint, purely mathematically, there is an old classical result of differential geometry, due to Darboux, that all 3-manifolds can have their metrics recast into diagonal form.
In the case of the Kerr spacetime the Boyer-Lindquist coordinates provide an explicit example of a diagonal spatial 3-metric.

Darboux diagonalization of the spatial 3-metric in Kerr spacetime · Around

Built on

A. Simpson, P. Martín-Moruno and M. Visser, “Vaidya spacetimes, black-bounces, and traversable wormholes”, Class. Quant. Grav. 36
Original
1902
Earlier work this paper cites.
R. Carballo-Rubio, F. Di Filippo, S. Liberati and M. Visser, “Opening the Pandora’s box at the core of black holes”, Class. Quant. Grav. 37
Original
1908
Earlier work this paper cites.
R. Carballo-Rubio, F. Di Filippo, S. Liberati and M. Visser, “Geodesically complete black holes”, Phys. Rev. D 101
Original
1911
Earlier work this paper cites.
A. Simpson and M. Visser, “Regular black holes with asymptotically Minkowski cores”, Universe 6
Original
1911
Earlier work this paper cites.
Paul Painlevé, “La mécanique classique et la théorie de la relativité ”, C. R. Acad. Sci. (Paris) 173, 677?680(1921)
1921
Earlier work this paper cites.
Paul Painlevé, ‘‘La gravitation dans la mécanique de Newton et dans la mécanique d’Einstein”, C.R Acad. Sci. (Paris) 173, 873--886(1921)
1921
Earlier work this paper cites.
Gullstrand, Allvar (1922). “Allgemeine Lösung des statischen Einkörperproblems in der Einsteinschen Gravitationstheorie”. Arkiv för Matematik, Astronomi och Fysik. 16 (8): 1–15
1922
Earlier work this paper cites.
Luther Pfahler Eisenhart, “Fields of parallel vectors in a Riemannian geometry”, Trans. Amer. Math. Soc. 27 (1925), no. 4, 563–573
1925
Earlier work this paper cites.
Roy Kerr, “Gravitational field of a spinning mass as an example of algebraically special metrics”, Physical Review Letters 11
1963
Earlier work this paper cites.
Roy Kerr, “Gravitational collapse and rotation”, published in: Quasi-stellar sources and gravitational collapse: Including the proceedings of the First Texas Symposium on Relativistic Astrophysics
1963
Earlier work this paper cites.
Ronald J. Adler, Maurice Bazin, and Menahem Schiffer, Introduction to General Relativity
1965
Earlier work this paper cites.
J. M. Bardeen, “Non-singular general-relativistic gravitational collapse”, in Proceedings of International Conference GR5, 1968, Tbilisi, USSR, p. 174
1968
Earlier work this paper cites.
Steven Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity , (Wiley, Hoboken, 1972)
1972
Earlier work this paper cites.
Charles Misner, Kip Thorne, and John Archibald Wheeler, Gravitation
1973
Earlier work this paper cites.
Robert Wald, General relativity , (University of Chicago Press, Chicago, 1984)
1984
Earlier work this paper cites.
Hans Thirring and Josef Lense, “Über den Einfluss der Eigenrotation der Zentralkörperauf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie”, Physikalische Zeitschrift, Leipzig Jg. 19
1984
Earlier work this paper cites.
D. M. DeTurck and D. Yang, “Existence of elastic deformations with prescribed principal strains and triply orthogonal systems”, Duke Math. J. 51 (1984), no. 2, 243–260
1984
Earlier work this paper cites.
R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmidt and P. A. Griths, “Exterior differential systems”, Mathematical Sciences Research Institute Publications, 18. (Springer-Verlag, New York, 1991)
1991
Earlier work this paper cites.
Ray D’Inverno, Introducing Einstein’s Relativity
1992
Earlier work this paper cites.
K. P. Tod, “On choosing coordinates to diagonalize the metric”, Classical Quantum Gravity 9 (1992), no. 7, 1693–1705
1992
Earlier work this paper cites.
M. Visser, “Acoustic black holes: Horizons, ergospheres, and Hawking radiation”, Class. Quant. Grav. 15
1998
Earlier work this paper cites.
G. Volovik, “Simulation of Painlevé-Gullstrand black hole in thin He-3-A film”, JETP Lett. 69
1999
Earlier work this paper cites.

Similar

C. Doran, “A New form of the Kerr solution”, Phys. Rev. D 61
2000
Cited alongside, same era.
K. Martel and E. Poisson, “Regular coordinate systems for Schwarzschild and other spherical space-times”, Am. J. Phys. 69
2001
Cited alongside, same era.
E. Barausse, E. Berti, T. Hertog, S. A. Hughes, P. Jetzer, P. Pani, T. P. Sotiriou, N. Tamanini, H. Witek, K. Yagi, N. Yunes, et al. , “Prospects for Fundamental Physics with LISA”, doi:10.1007/s10714-020-02691-1 (GRG in press). [ arXiv:2001.09793 [gr-qc]]
Original
2001
Cited alongside, same era.
M. Visser, C. Barceló and S. Liberati, “Analog models of and for gravity”, Gen. Rel. Grav. 34
2002
Cited alongside, same era.
M. Novello, M. Visser and G. Volovik, Artificial black holes
2002
Cited alongside, same era.

Then

Joshua Baines, Thomas Berry, Alex Simpson, and Matt Visser, “Unit-lapse forms of the Kerr spacetime”, arXiv:2008.03817 [gr-qc]
Original
2008
Later among the works it cites.
M. Visser, C. Barceló, S. Liberati and S. Sonego, “Small, dark, and heavy: But is it a black hole?”, PoS BHGRS
Original
2008
Later among the works it cites.
M. Visser, “Black holes in general relativity”, PoS BHGRS
Original
2008
Later among the works it cites.
T. Berry, F. S. N. Lobo, A. Simpson and M. Visser, “Thin-shell traversable wormhole crafted from a regular black hole with asymptotically Minkowski core,” [ arXiv:2008.07046 [gr-qc]]
Original
2008
Later among the works it cites.
T. Berry, A. Simpson and M. Visser, “Photon spheres, ISCOs, and OSCOs: Astrophysical observables for regular black holes with asymptotically Minkowski cores,” [ arXiv:2008.13308 [gr-qc]]

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

James Hartle, Gravity: An introduction to Einstein’s general relativity

2003

Cited alongside, same era.

S. E. Perez-Bergliaffa, K. Hibberd, M. Stone and M. Visser, “Wave equation for sound in fluids with vorticity”, Physica D 191

2003

Cited alongside, same era.

U. R. Fischer and M. Visser, “On the space-time curvature experienced by quasiparticle excitations in the Painlevé–Gullstrand effective geometry”, Annals Phys. 304

2003

Cited alongside, same era.

C. Barceló, S. Liberati and M. Visser, “Probing semiclassical analog gravity in Bose-Einstein condensates with widely tune-able interactions”, Phys. Rev. A 68

2003

Cited alongside, same era.

F. S. N. Lobo, A. Simpson and M. Visser, “Dynamic thin-shell black-bounce traversable wormholes”, Phys. Rev. D 101

2003

Cited alongside, same era.

Sean Carroll, An introduction to general relativity: Spacetime and Geometry

2004

Cited alongside, same era.

J. A. Valiente Kroon, “On the nonexistence of conformally flat slices in the Kerr and other stationary space-times,” Phys. Rev. Lett. 92

2004

Cited alongside, same era.

2008

Later among the works it cites.

D. L. Wiltshire, M. Visser and S. M. Scott, The Kerr spacetime: Rotating black holes in general relativity , (Cambridge University Press, Cambridge, 2009)

2009

Later among the works it cites.

J. Natario, “Painlevé-Gullstrand Coordinates for the Kerr Solution”, Gen. Rel. Grav. 41

2009

Later among the works it cites.

J. D. E. Grant and J. A. Vickers, “Block diagonalization of four-dimensional metrics,” Class. Quant. Grav. 26

2009

Later among the works it cites.

M. Visser and C. Molina-París, “Acoustic geometry for general relativistic barotropic irrotational fluid flow”, New J. Phys. 12

2010

Later among the works it cites.

Oldřich Kowalski and Masami Sekizawa, “Diagonalization of three-dimensional pseudo-Riemannian metrics”, Journal of Geometry and Physics, 74

2013

Later among the works it cites.

M. Visser, “Survey of analogue spacetimes”, Lect. Notes Phys. 870

2013

Later among the works it cites.

Barrett O’Neill, The geometry of Kerr black holes , (Peters, Wellesley, 1995). Reprinted (Dover, Mineloa, 2014)

2014

Later among the works it cites.

V. P. Frolov, “Information loss problem and a black hole model with a closed apparent horizon”, JHEP 1405

2014

Later among the works it cites.

D. Rajan and M. Visser, “Cartesian Kerr–Schild variation on the Newman–Janis trick”, Int. J. Mod. Phys. D 26

2017

Later among the works it cites.

V. P. Frolov and A. Zelnikov, “Quantum radiation from an evaporating nonsingular black hole”, Phys. Rev. D 95

2017

Later among the works it cites.

S. Liberati, G. Tricella and M. Visser, “Towards a Gordon form of the Kerr spacetime”, Class. Quant. Grav. 35

2018

Later among the works it cites.

R. Carballo-Rubio, F. Di Filippo, S. Liberati and M. Visser, “Phenomenological aspects of black holes beyond general relativity”, Phys. Rev. D 98

2018

Later among the works it cites.

R. Carballo-Rubio, F. Di Filippo, S. Liberati, C. Pacilio and M. Visser, “On the viability of regular black holes”, J. High Energ. Phys. 2018

2018

Later among the works it cites.

P. Boonserm, T. Ngampitipan, A. Simpson and M. Visser, “Exponential metric represents a traversable wormhole”, Phys. Rev. D 98

2018

Later among the works it cites.

S. Liberati, S. Schuster, G. Tricella and M. Visser, “Vorticity in analogue spacetimes”, Phys. Rev. D 99

2019

Later among the works it cites.

A. Simpson and M. Visser, “Black-bounce to traversable wormhole”, JCAP 02

Original

2019

Later among the works it cites.