Abstract
In this Chapter we thoroughly review the geometry of extremal Reissner–Nordström black holes. We also present the main results on the asymptotics of linear perturbations on such backgrounds.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
It is the function t that is singular at these points.
- 2.
With respect to the coordinate system \((\rho =r,\theta ,\varphi )\) on \(\Sigma _0\).
- 3.
See also Sect. 2.6 for a discussion on the interior of dynamical extremal black holes.
References
H. Reissner, Über die eigengravitation des elektrischen feldes nach der Einstein’schen theorie. Annalen der Physik
G. Nordström, On the energy of the gravitational field in Einstein’s theory, in Verhandl. Koninkl. Ned. Akad. Wetenschap. (1918), pp. 1201–1208
J. Sbierski, The \(C^0\)-inextendibility of the Schwarzschild spacetime and the spacelike diameter in lorentzian geometry (2015), arXiv:1507.00601
D. Marolf, The danger of extremes. Gen. Relativ. Gravit. 42, 2337–2343 (2010)
K. Murata, H.S. Reall, N. Tanahashi, What happens at the horizon(s) of an extreme black hole? Class. Quantum Gravity 30, 235007 (2013)
J. Sbierski, Characterisation of the energy of Gaussian beams on Lorentzian manifolds with applications to black hole spacetimes. Anal. Part. Diff. Eq. 8, 1379–1420 (2015)
W. Couch, R. Torrence, Conformal invariance under spatial inversion of extreme Reissner–Nordström black holes. Gen. Rel. Gravity 16, 789–792 (1984)
H. Godazgar, M. Godazgar, C.N. Pope, Aretakis charges and asymptotic null infinity. Phys. Rev. D 96, 084055 (2017)
S. Aretakis, Stability and instability of extreme Reissner–Nordström black hole spacetimes for linear scalar perturbations I. Commun. Math. Phys. 307, 17–63 (2011)
S. Aretakis, Stability and instability of extreme Reissner–Nordström black hole spacetimes for linear scalar perturbations II. Annales Henri Poincaré 12, 1491–1538 (2011)
S. Aretakis, The wave equation on extreme Reissner–Nordström black hole spacetimes: stability and instability results (2010), arXiv:1006.0283
Y. Angelopoulos, S. Aretakis, D. Gajic, The trapping effect on degenerate horizons. Annales Henri Poincaré 18(5), 1593–1633 (2017)
J. Lucietti, K. Murata, H.S. Reall, N. Tanahashi, On the horizon instability of an extreme Reissner–Nordström black hole. JHEP 1303, 035 (2013), arXiv:1212.2557
O. Sela, Late-time decay of coupled electromagnetic and gravitational perturbations outside an extremal charged black hole. Phys. Rev. D 94, 084006 (2016)
S. Aretakis, On a non-linear instability of extremal black holes. Phys. Rev. D 87, 084052 (2013)
P. Bizon, M. Kahl, A Yang–Mills field on the extremal Reissner–Nordström black hole. Class. Quantum Gravity 33, 175013 (2016)
Y. Angelopoulos, S. Aretakis, D. Gajic, Asymptotic blow-up for a class of semi-linear wave equations on extremal Reissner–Nordström spacetimes (2016), arXiv:1612.01562
Y. Angelopoulos, Global spherically symmetric solutions of non-linear wave equations with null condition on extremal Reissner–Nordström spacetimes. Int. Math. Res. Not. 11, 3279–3355 (2016)
S. Hadar, H.S. Reall, Is there a breakdown of effective field theory at the horizon of an extremal black hole? J. High Energy Phys. 2017(12), 62 (2017)
K. Murata, Instability of higher dimensional extreme black holes. Class. Quantum Gravity 30, 075002 (2013)
N. Tsukamoto, M. Kimura, T. Harada, High energy collision of particles in the vicinity of extremal black holes in higher dimensions: Banados–Silk–West process as linear instability of extremal black holes. Phys. Rev. D 89, 024020 (2014)
J. Bičák, Gravitational collapse with charge and small asymmetries I: scalar perturbations. Gen. Relativ. Gravit. 3, 331–349 (1972)
H. Onozawa, T. Mishima, T. Okamura, H. Ishihara, Quasinormal modes of maximally charged black holes. Phys. Rev. D 53, 7033 (1996)
C.J. Blaksley, L.M. Burko, Late-time tails in the Reissner–Nordström spacetime revisited. Phys. Rev. D 76, 104035 (2007)
A. Ori, Late-time tails in extremal Reissner–Nordström spacetime (2013), arXiv:1305.1564
O. Sela, Late-time decay of perturbations outside extremal charged black hole. Phys. Rev. D 93, 024054 (2016)
M. Casals, S.E. Gralla, P. Zimmerman, Horizon instability of extremal Kerr black holes: nonaxisymmetric modes and enhanced growth rate. Phys. Rev. D 94, 064003 (2016)
Y. Angelopoulos, S. Aretakis, D. Gajic, Late-time asymptotics for the wave equation on extremal Reissner–Nordström backgrounds, preprint (2018)
J. Bičák, Gravitational collapse with charge and small asymmetries I. Scalar perturbations. Gen. Relativ. Gravit. 3, 331–349 (1972)
P. Bizon, H. Friedrich, A remark about the wave equations on the extreme Reissner–Nordström black hole exterior. Class. Quantum Gravity 30, 065001 (2013)
S. Aretakis, A note on instabilities of extremal black holes from afar. Class. Quantum Gravity 30, 095010 (2013)
H. Koyama, A. Tomimatsu, Asymptotic power-law tails of massive scalar fields in a Reissner–Nordström background. Phys. Rev. D 63, 064032 (2001)
S. Bhattacharjee, B. Chakrabarty, D. D. K. Chow, P. Paul, and A. Virmani, On late time tails in an extreme Reissner–Nordström black hole: Frequency domain analysis (2018), arxiv: 1805.10655
J. Lucietti, H. Reall, Gravitational instability of an extreme Kerr black hole. Phys. Rev. D 86, 104030 (2012)
L.M. Burko, G. Khanna, Linearized stability of extreme black holes. Phys. Rev. D 97, 061502 (2018)
S.E. Gralla, P. Zimmerman, Critical exponents of extremal Kerr perturbations. Class. Quantum Gravity 35(9) (2018)
Y. Angelopoulos, S. Aretakis, D. Gajic, Horizon hair of extremal black holes and measurements at null infinity. Phys. Rev. Lett. 121, 131102 (2018)
D. Gajic, Linear waves in the interior of extremal black holes I. Commun. Math. Phys. 353, 717–770 (2017)
D. Gajic, Linear waves in the interior of extremal black holes II. Annales Henri Poincaré 18, 4005–4081 (2017)
A. Franzen, Boundedness of massless scalar waves on Reissner–Nordström interior backgrounds. Commun. Math. Phys. 343, 601–650 (2014)
J. Luk, S.-J. Oh, Proof of linear instability of the Reissner–Nordström Cauchy horizon under scalar perturbations. Duke Math. J. 166(3), 437–493 (2017)
P. Hintz, Boundedness and decay of scalar waves at the Cauchy horizon of the Kerr spacetime (2015), arXiv:1512.08003
J. Luk, J. Sbierski, Instability results for the wave equation in the interior of Kerr black holes. J. Funct. Anal. 271(7), 1948–1995 (2016)
M. Dafermos, Y. Shlapentokh-Rothman, Time-translation invariance of scattering maps and blue-shift instabilities on Kerr black hole spacetimes. Commun. Math. Phys. 350, 985–1016 (2016)
G. Fournodavlos, J. Sbierski, Generic blow-up results for the wave equation in the interior of a Schwarzschild black hole (2018), arXiv:1804.01941
D. Christodoulou, The Formation of Black Holes in General Relativity (European Mathematical Society Publishing House, 2009)
D. Gajic, J. Luk, The interior of dynamical extremal black holes in spherical symmetry (2017), arXiv:1709.09137
M. Dafermos, J. Luk, The interior of dynamical vacuum black holes I: the \(C^0\)-stability of the Kerr Cauchy horizon (2017), arXiv:1710.01722
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 The Author(s)
About this chapter
Cite this chapter
Aretakis, S. (2018). Extremal Reissner–Nordström Black Holes. In: Dynamics of Extremal Black Holes. SpringerBriefs in Mathematical Physics, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-319-95183-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-95183-6_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-95182-9
Online ISBN: 978-3-319-95183-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)