Calculating quasinormal modes of Schwarzschild anti–de Sitter black holes using the continued fraction method

We investigate the scalar, gravitational, and electromagnetic quasinormal mode spectra of Schwarzschild anti-de Sitter black holes using the numerical continued fraction method. The spectra have similar, almost linear structures. With a few exceptions, the low overtone quasinormal modes are consistent with previously obtained results in the literature that use other numerical techniques. The intermediate and high overtone quasinormal modes, in comparison to the Schwarzschild case, converge very quickly to the asymptotic formulas previously obtained by analytic monodromy techniques. In addition, we find a connection between the analytic asymptotic formulas and the purely imaginary modes. In particular, these formulas can be used to predict the bifurcation of the lowest damped electromagnetic modes. Finally, we find no high overtone quasinormal modes with high oscillation frequency and low damping, which had been previously predicted.

[1]  I. Vega,et al.  Electromagnetic quasinormal modes of Schwarzschild–anti–de Sitter black holes: Bifurcations, spectral similarity, and exact solutions in the large black hole limit , 2022, Physical Review D.

[2]  E. Berti,et al.  Destabilizing the Fundamental Mode of Black Holes: The Elephant and the Flea. , 2021, Physical review letters.

[3]  J. Jaramillo,et al.  Energy scales and black hole pseudospectra: the structural role of the scalar product , 2021, Classical and Quantum Gravity.

[4]  E. Berti,et al.  Pseudospectrum of Reissner-Nordström black holes: Quasinormal mode instability and universality , 2021, Physical Review D.

[5]  A. Cornell,et al.  Asymptotic quasinormal frequencies of different spin fields in d-dimensional spherically-symmetric black holes , 2021, Classical and Quantum Gravity.

[6]  J. Jaramillo,et al.  Gravitational Wave Signatures of Black Hole Quasinormal Mode Instability. , 2021, Physical review letters.

[7]  Jiliang Jing,et al.  Bifurcation of the Maxwell quasinormal spectrum on asymptotically anti–de Sitter black holes , 2021, Physical Review D.

[8]  Bin Wang,et al.  Asymptotical quasinormal mode spectrum for piecewise approximate effective potential , 2020, Physical Review D.

[9]  Rodrigo Panosso Macedo,et al.  Pseudospectrum and Black Hole Quasinormal Mode Instability , 2020, Physical Review X.

[10]  Michael D. Green,et al.  Significance of black hole quasinormal modes: A closer look , 2020, Physical Review D.

[11]  V. Zanchin,et al.  Electromagnetic quasinormal modes of rotating black strings and the AdS/CFT correspondence , 2013, 1302.0536.

[12]  R. Konoplya,et al.  Quasinormal modes of black holes: From astrophysics to string theory , 2011, 1102.4014.

[13]  V. Cardoso,et al.  Gravitational quasinormal modes of AdS black branes in d spacetime dimensions , 2009, 0907.5011.

[14]  Vitor Cardoso,et al.  Quasinormal modes of black holes and black branes , 2009, 0905.2975.

[15]  R. G. Daghigh,et al.  The highly real quasinormal modes of Schwarzschild-Anti de Sitter black holes , 2009, 0901.2353.

[16]  V. Zanchin,et al.  Quasinormal modes of plane-symmetric black holes according to the AdS/CFT correspondence , 2008, 0809.0297.

[17]  Michael D. Green,et al.  A detailed analytic study of the asymptotic quasinormal modes of Schwarzschild–anti de Sitter black holes , 2008, 0808.1596.

[18]  A. López-Ortega.  Electromagnetic quasinormal modes of D-dimensional black holes II , 2007, 0706.2933.

[19]  G. Siopsis.  Low frequency quasi-normal modes of AdS black holes ∗ , 2007, hep-th/0702079.

[20]  S. Pufu,et al.  Low-lying gravitational modes in the scalar sector of the global AdS 4 black hole , 2006, hep-th/0612065.

[21]  S. Gubser,et al.  Expanding plasmas and quasinormal modes of anti-de Sitter black holes , 2006, hep-th/0611005.

[22]  A. López-Ortega.  Electromagnetic quasinormal modes of D-dimensional black holes , 2006, gr-qc/0605034.

[23]  G. Siopsis,et al.  Perturbative calculation of quasinormal modes of AdS schwarzschild black holes , 2005, hep-th/0511113.

[24]  V. Zanchin,et al.  Quasinormal modes of plane-symmetric anti-de Sitter black holes: A Complete analysis of the gravitational perturbations , 2005, gr-qc/0510066.

[25]  José Natário,et al.  On the classification of asymptotic quasinormal frequencies for $d$-dimensional black holes and quantum gravity , 2004, hep-th/0411267.

[26]  G. Siopsis.  On quasi-normal modes and the AdS5/CFT4 correspondence , 2004, Nuclear Physics B.

[27]  V. Cardoso,et al.  Asymptotic quasinormal frequencies for black holes in nonasymptotically flat space¿times , 2004, hep-th/0403132.

[28]  Jiliang Jing,et al.  Dirac quasinormal frequencies in Schwarzschild-AdS space-time , 2004, gr-qc/0403030.

[29]  G. Siopsis.  Large mass expansion of quasi-normal modes in AdS5 , 2004, hep-th/0402083.

[30]  G. Siopsis,et al.  Asymptotic form of quasi-normal modes of large AdS black holes , 2003, hep-th/0308196.

[31]  N. Andersson,et al.  The asymptotic quasinormal mode spectrum of non-rotating black holes , 2003, gr-qc/0307020.

[32]  V. Cardoso,et al.  Quasinormal frequencies of Schwarzschild black holes in anti–de Sitter spacetimes: A complete study of the overtone asymptotic behavior , 2003, gr-qc/0305037.

[33]  E. Berti,et al.  Quasinormal modes of Reissner-Nordstrom-anti-de Sitter black holes: Scalar, electromagnetic and gravitational perturbations , 2003, gr-qc/0301052.

[34]  G. Siopsis,et al.  Quasinormal modes of large AdS black holes , 2003, hep-th/0301081.

[35]  L. Motl.  An Analytical computation of asymptotic Schwarzschild quasinormal frequencies , 2002, gr-qc/0212096.

[36]  D.T.Son,et al.  From AdS/CFT correspondence to hydrodynamics. II. Sound waves , 2002, hep-th/0210220.

[37]  C. Herzog.  The Hydrodynamics of M-Theory , 2002, hep-th/0210126.

[38]  D. Son,et al.  From AdS/CFT correspondence to hydrodynamics , 2002 .

[39]  R. Konoplya.  On quasinormal modes of small Schwarzschild-anti-de Sitter black hole , 2002 .

[40]  A. Starinets.  Quasinormal modes of near extremal black branes , 2002, hep-th/0207133.

[41]  James P. Norman,et al.  Gravitational quasinormal modes for anti-de Sitter black holes , 2002, gr-qc/0201016.

[42]  V. Cardoso,et al.  Quasinormal modes of Schwarzschild anti-de Sitter black holes: Electromagnetic and gravitational perturbations , 2001 .

[43]  T. R. Govindarajan,et al.  Quasi-normal modes of AdS black holes: a superpotential approach , 2001 .

[44]  Bin Wang,et al.  Object picture of quasinormal ringing on the background of small Schwarzschild anti-de Sitter black holes , 2001, hep-th/0101133.

[45]  V. Hubeny,et al.  Quasinormal modes of AdS black holes and the approach to thermal equilibrium , 1999, hep-th/9909056.

[46]  R. Mann,et al.  Scalar wave falloff in topological black hole backgrounds , 1999 .

[47]  J. Maldacena.  The Large-N Limit of Superconformal Field Theories and Supergravity , 1997, hep-th/9711200.

[48]  R. Mann,et al.  Scalar wave falloff in asymptotically anti-de Sitter backgrounds , 1996, gr-qc/9612026.

[49]  H. Nollert,et al.  Quasinormal modes of Schwarzschild black holes: The determination of quasinormal frequencies with very large imaginary parts. , 1993, Physical review. D, Particles and fields.

[50]  E. W. Leaver,et al.  An analytic representation for the quasi-normal modes of Kerr black holes , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[51]  D. Page,et al.  Thermodynamics of black holes in anti-de Sitter space , 1983 .

[52]  A. Ghosh,et al.  High frequency quasi-normal modes for black holes with generic singularities: II. Asymptotically non-flat spacetimes , 2006 .