Spinning Black Holes Fall in Love

Tiec, Alexandre Le; Casals, Marc

doi:10.48550/arxiv.2007.00214

Cited by 18 publications

(29 citation statements)

References 52 publications

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“…Conservation of P thus tells us this solution, when extended to the horizon, must approach a constant rather than the divergent logarithm. 13 It is worth emphasizing the vanishing of the Love number follows from two facts: (1) the purely decaying solution (∼ 1/r +1 at large r) is divergent at the horizon, and (2) the solution that is regular at the horizon is a finite polynomial going as 1 + r + • • • + r . The second fact by itself is not sufficient: it does not forbid us from adding to it a decaying tail that goes as 1/r +1 .…”

Section: Ladder In Schwarzschildmentioning

confidence: 99%

“…For black holes, though, such a polarizability, or tidal response, appears to be absent. Let us be more precise: under the influence of a weak static tidal field (spin 0, 1, or 2), black holes have vanishing Love numbers [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The Love numbers quantify the tidal response: suppose the external tidal field goes as r at large distance r ( is the multipole of interest), an object such as a star that gets tidally deformed would source a response field that goes as 1/r +1 far away.…”

Section: Introductionmentioning

confidence: 99%

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Ladder Symmetries of Black Holes: Implications for Love Numbers and No-Hair Theorems

Hui,

Joyce,

Penco

et al. 2021

Preprint

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It is well known that asymptotically flat black holes in general relativity have a vanishing static tidal response and no static hair. We show that both are a result of linearly realized symmetries governing static (spin 0,1,2) perturbations around black holes. The symmetries have a geometric origin: in the scalar case, they arise from the (E)AdS isometries of a dimensionally reduced black hole spacetime. Underlying the symmetries is a ladder structure which can be used to construct the full tower of solutions, and derive their general properties: (1) solutions that decay with radius spontaneously break the symmetries, and must diverge at the horizon; (2) solutions regular at the horizon respect the symmetries, and take the form of a finite polynomial that grows with radius. Property (1) implies no hair; (1) and (2) combined imply that static response coefficients-and in particular Love numbers-vanish. We also discuss the manifestation of these symmetries in the effective point particle description of a black hole, showing explicitly that for scalar probes the worldline couplings associated with a non-trivial tidal response and scalar hair must vanish in order for the symmetries to be preserved.

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Section: Ladder In Schwarzschildmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Ladder Symmetries of Black Holes: Implications for Love Numbers and No-Hair Theorems

Hui,

Joyce,

Penco

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…What are the explicit finite transformations associated with 2 The case of the TNLs of the Kerr black hole has been the subject of debate recently as different claims have been made. See [16][17][18][19][20][21][22][23][24][25] for details. In this work, we shall only focus on the Schwarzschild black hole.…”

Section: Introductionmentioning

confidence: 99%

Hidden symmetry of the static response of black holes: Applications to Love numbers

Achour¹,

Livine²,

Mukohyama³

et al. 2022

Preprint

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We show that any static linear perturbations around a spherically symmetric black hole enjoys a set of conserved charges which forms a centrally extended Schrödinger algebra sh(1) = sl(2, R) ⋉ H. The central charge is given by the black hole mass, echoing results on black hole entropy from near-horizon diffeomorphism symmetry. The finite symmetry transformations generated by these conserved charges correspond to Galilean and conformal transformations of the static field and of the coordinates. This new structure allows one to discuss the static response of a Schwarzschild black hole in the test field approximation from a symmetry-based approach. First we show that the (horizontal) symmetry protecting the vanishing of the Love numbers recently exhibited by Hui et al. coincides with one of the sl(2, R) generators of the Schrödinger group. Then, it is demonstrated that the HJPSS symmetry is selected thanks to the spontaneous breaking of the full Schrödinger symmetry at the horizon down to a simple abelian sub-group. The latter can be understood as the symmetry protecting the regularity of the test field at the horizon. In the 4-dimensional case, this provides a symmetry protection for the vanishing of the Schwarzschild Love numbers. 1

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“…a source distribution that is deformed due to an external tidal field [14] or involve the application of black hole perturbation theory [8][9][10][11][12][13]. A limit of the compactness is then taken to deduce the corresponding Love numbers for black holes.…”

Section: Introductionmentioning

confidence: 99%

Tidal deformation of dynamical horizons in binary black hole mergers

Prasad,

Gupta,

Bose

et al. 2021

Preprint

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An important physical phenomenon that manifests itself during the inspiral of two orbiting compact objects is the tidal deformation of each under the gravitational influence of its companion. In the case of binary neutron star mergers, this tidal deformation and the associated Love numbers have been used to probe properties of dense matter and the nuclear equation of state. Non-spinning black holes on the other hand have a vanishing (field) tidal Love number in General Relativity. This pertains to the deformation of the asymptotic gravitational field. In certain cases, especially in the late stages of the inspiral phase when the black holes get close to each other, the source multipole moments might be more relevant in probing their properties and the No-Hair theorem; contrastingly, these Love numbers do not vanish. In this paper, we track the source multipole moments in simulations of several binary black hole mergers and calculate these Love numbers. We present evidence that, at least for modest mass ratios, the behavior of the source multipole moments is universal. [This manuscript has been assigned the LIGO Preprint number LIGO-P2100109.]

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Spinning Black Holes Fall in Love

Cited by 18 publications

References 52 publications

Ladder Symmetries of Black Holes: Implications for Love Numbers and No-Hair Theorems

Ladder Symmetries of Black Holes: Implications for Love Numbers and No-Hair Theorems

Hidden symmetry of the static response of black holes: Applications to Love numbers

Tidal deformation of dynamical horizons in binary black hole mergers

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