Vanishing Love numbers of black holes in general relativity: From spacetime conformal symmetry of a two-dimensional reduced geometry

We study the underlying structure of the vanishing of the Love numbers of both Schwarzschild and Kerr black holes in terms of spacetime conformal symmetry in a unified manner for the static spin-$s$ fields. The perturbations can be reduced with the harmonic decomposition to a set of infinite static scalar fields in a two-dimensional anti-de Sitter spacetime~$({\rm AdS}_2)$. In the reduced system, each scalar field is paired with another, implying that all multipole modes of the perturbation can be regarded as symmetric partners, which can be understood from the property of the supersymmetry algebra. The generator of the supersymmetric structure is constructed from a closed conformal Killing vector field of ${\rm AdS}_2$. The associated conserved quantity allows one to show no static response, i.e., vanishing of the Love and dissipation numbers. We also discuss the vanishing Love numbers of the Kerr black hole with the nonzero dissipation numbers for the non-axisymmetric perturbations in terms of a radial constant found in a parallel manner as the axisymmetric field case even though the interpretation for the structure is controversial. The symmetric structure corresponds to the ``ladder'' symmetry in Hui et al. [JCAP 01, no.01, 032 (2022)] although the geometrical origin is different. Our ladder operator includes the generators of hidden symmetries in previous works.

[1]  S. Dubovsky,et al.  Love symmetry , 2022, Journal of High Energy Physics.

[2]  M. Kimura,et al.  Ladder operators and quasinormal modes in Bañados-Teitelboim-Zanelli black holes , 2022, Physical Review D.

[3]  L. Hui,et al.  Near-zone symmetries of Kerr black holes , 2022, Journal of High Energy Physics.

[4]  E. Livine,et al.  Hidden symmetry of the static response of black holes: applications to Love numbers , 2022, Journal of High Energy Physics.

[5]  M. Kimura,et al.  Aretakis constants and instability in general spherically symmetric extremal black hole spacetimes: Higher multipole modes, late-time tails, and geometrical meanings , 2021, Physical Review D.

[6]  M. Kimura,et al.  Spectral Problems for Quasinormal Modes of Black Holes , 2021, Universe.

[7]  V. Cardoso,et al.  Black holes in galaxies: Environmental impact on gravitational-wave generation and propagation , 2021, Physical Review D.

[8]  P. Pani,et al.  Tidal deformability of dressed black holes and tests of ultralight bosons in extended mass ranges , 2021, 2106.14428.

[9]  G. Bonelli,et al.  Exact solution of Kerr black hole perturbations via CFT2 and instanton counting: Greybody factor, quasinormal modes, and Love numbers , 2021, Physical Review D.

[10]  L. Hui,et al.  Ladder symmetries of black holes. Implications for love numbers and no-hair theorems , 2021, Journal of Cosmology and Astroparticle Physics.

[11]  S. Dubovsky,et al.  Hidden Symmetry of Vanishing Love Numbers. , 2021, Physical review letters.

[12]  S. Dubovsky,et al.  On the vanishing of Love numbers for Kerr black holes , 2021, Journal of High Energy Physics.

[13]  M. Kimura,et al.  Revisiting the Aretakis constants and instability in two-dimensional anti–de Sitter spacetimes , 2021, 2101.03479.

[14]  M. Casals,et al.  Tidal Love numbers of Kerr black holes , 2020, 2010.15795.

[15]  H. Chia Tidal deformation and dissipation of rotating black holes , 2020, Physical Review D.

[16]  L. Hui,et al.  Static response and Love numbers of Schwarzschild black holes , 2020, Journal of Cosmology and Astroparticle Physics.

[17]  Yasuyuki Hatsuda,et al.  An alternative to the Teukolsky equation , 2020, General Relativity and Gravitation.

[18]  M. Casals,et al.  Spinning Black Holes Fall in Love. , 2020, Physical review letters.

[19]  V. Cardoso,et al.  Environmental effects in gravitational-wave physics: Tidal deformability of black holes immersed in matter , 2019, Physical Review D.

[20]  Y. N. Liu,et al.  Multi-messenger Observations of a Binary Neutron Star Merger , 2019, Proceedings of Multifrequency Behaviour of High Energy Cosmic Sources - XIII — PoS(MULTIF2019).

[21]  Yasuyuki Hatsuda Quasinormal modes of black holes and Borel summation , 2019, Physical Review D.

[22]  V. Cardoso,et al.  Testing the nature of dark compact objects: a status report , 2019, Living Reviews in Relativity.

[23]  R. Penna Near-horizon Carroll symmetry and black hole Love numbers , 2018, 1812.05643.

[24]  N. Yunes,et al.  Can We Probe Planckian Corrections at the Horizon Scale with Gravitational Waves? , 2018, Physical review letters.

[25]  L. Senatore,et al.  Black Holes in an Effective Field Theory Extension of General Relativity. , 2018, Physical review letters.

[26]  S. Gralla On the ambiguity in relativistic tidal deformability , 2017, 1710.11096.

[27]  The Ligo Scientific Collaboration,et al.  GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral , 2017, 1710.05832.

[28]  V. Cardoso,et al.  General first-order mass ladder operators for Klein–Gordon fields , 2017, 1707.08534.

[29]  V. Cardoso,et al.  Mass Ladder Operators from Spacetime Conformal Symmetry , 2017, 1706.07339.

[30]  V. Cardoso,et al.  Testing strong-field gravity with tidal Love numbers , 2017, 1701.01116.

[31]  Rafael A. Porto The tune of love and the nature(ness) of spacetime , 2016, 1606.08895.

[32]  D. Reitze The Observation of Gravitational Waves from a Binary Black Hole Merger , 2016 .

[33]  B. Kleihaus,et al.  Spinning black holes in Einstein–Gauss-Bonnet–dilaton theory: Nonperturbative solutions , 2015, 1511.05513.

[34]  C. Brans Gravity: Newtonian, Post-Newtonian, Relativistic , 2015 .

[35]  Marco O. P. Sampaio,et al.  Testing general relativity with present and future astrophysical observations , 2015, 1501.07274.

[36]  G. Gibbons,et al.  Conformal Carroll groups , 2014, 1403.4213.

[37]  M. Smolkin,et al.  Black hole stereotyping: induced gravito-static polarization , 2011, 1110.3764.

[38]  D. Klemm,et al.  Conformal structure of the Schwarzschild black hole , 2011, 1106.0999.

[39]  B. Kleihaus,et al.  Rotating black holes in dilatonic Einstein-Gauss-Bonnet theory. , 2011, Physical review letters.

[40]  T. Hinderer,et al.  Post-1-Newtonian tidal effects in the gravitational waveform from binary inspirals , 2011, 1101.1673.

[41]  A. Maloney,et al.  Hidden Conformal Symmetry of the Kerr Black Hole , 2010, 1004.0996.

[42]  D. Marolf,et al.  Uniqueness of extremal Kerr and Kerr-Newman black holes , 2009, 0906.2367.

[43]  T. Damour,et al.  Relativistic tidal properties of neutron stars , 2009, 0906.0096.

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

[45]  E. Poisson,et al.  Relativistic theory of tidal Love numbers , 2009, 0906.1366.

[46]  M. Visser Black holes in general relativity , 2009, 0901.4365.

[47]  T. Hinderer Tidal Love Numbers of Neutron Stars , 2007, 0711.2420.

[48]  T. Hinderer,et al.  Constraining neutron-star tidal Love numbers with gravitational-wave detectors , 2007, 0709.1915.

[49]  C. Will,et al.  Gravitational-wave spectroscopy of massive black holes with the space interferometer LISA , 2005, gr-qc/0512160.

[50]  I. Rothstein,et al.  Dissipative effects in the worldline approach to black hole dynamics , 2005, hep-th/0511133.

[51]  I. Rothstein,et al.  Effective field theory of gravity for extended objects , 2004, hep-th/0409156.

[52]  H. Kodama,et al.  A Master Equation for Gravitational Perturbations of Maximally Symmetric Black Holes in Higher Dimensions , 2003, hep-th/0305147.

[53]  G. Valent The hydrogen atom in electric and magnetic fields: Pauli’s 1926 article , 2002, quant-ph/0212010.

[54]  A. Higuchi Erratum: “Symmetric tensor spherical harmonics on the N-sphere and their application to the de Sitter group SO(N,1)” [J. Math. Phys. 28, 1553 (1987)] , 2002 .

[55]  Takahiro Tanaka,et al.  Improvement on the metric reconstruction scheme in the Regge-Wheeler-Zerilli formalism , 2002, gr-qc/0211060.

[56]  A. Khare,et al.  Supersymmetry and quantum mechanics , 1994, hep-th/9405029.

[57]  Zaslavskii Ob Black-hole normal modes and quantum anharmonic oscillator. , 1991 .

[58]  B. Whiting Mode stability of the Kerr black hole. , 1989 .

[59]  Atsushi Higuchi,et al.  Symmetric tensor spherical harmonics on the N‐sphere and their application to the de Sitter group SO(N,1) , 1987 .

[60]  V. Ferrari,et al.  New approach to the quasinormal modes of a black hole , 1984 .

[61]  V. Ferrari,et al.  Oscillations of a Black Hole , 1984 .

[62]  Takashi Nakamura,et al.  A class of new perturbation equations for the Kerr geometry , 1982 .

[63]  S. Chandrasekhar,et al.  The quasi-normal modes of the Schwarzschild black hole , 1975, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[64]  D. C. Robinson Uniqueness of the Kerr black hole , 1975 .

[65]  Brandon Carter,et al.  Axisymmetric Black Hole Has Only Two Degrees of Freedom , 1971 .

[66]  David M. Miller,et al.  Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) , 1965 .

[67]  P. C. Peters Gravitational Radiation and the Motion of Two Point Masses , 1964 .

[68]  F. Tangherlini Schwarzschild field inn dimensions and the dimensionality of space problem , 1963 .

[69]  John Archibald Wheeler,et al.  Stability of a Schwarzschild singularity , 1957 .

[70]  Zaslavskii Black-hole normal modes and quantum anharmonic oscillator. , 1991, Physical review. D, Particles and fields.

[71]  J. W. Humberston Classical mechanics , 1980, Nature.

[72]  J. Bekenstein Nonexistence of Baryon Number for Black Holes. II , 1972 .

[73]  S. Teukolsky ROTATING BLACK HOLES: SEPARABLE WAVE EQUATIONS FOR GRAVITATIONAL AND ELECTROMAGNETIC PERTURBATIONS. , 1972 .

[74]  A. G. Greenhill,et al.  Handbook of Mathematical Functions with Formulas, Graphs, , 1971 .

[75]  F. Zerilli Gravitational field of a particle falling in a schwarzschild geometry analyzed in tensor harmonics , 1969 .