Hidden symmetries for transparent de Sitter space

Compton, Garrett; Morrison, Ian A.

doi:10.1088/1361-6382/ab8c98

Cited by 6 publications

(10 citation statements)

References 46 publications

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“…The connection between the two is an interesting question which we hope to explore in the future. Another influential paper is by Compton and Morrison [44]. The ladder structure we find for black holes mirrors the one they discovered for de Sitter space.…”

Section: Introductionsupporting

confidence: 72%

“…Note that the arbitrary scale L disappears from δφ, as it should. Decomposing φ into spherical harmonics, it can be shown that this symmetry acts on the various components as [44]…”

Section: Discussionmentioning

confidence: 99%

“…8 Instead we take a different tack: let us delve deeper into the symmetries behind the ladder structure. Here, we follow the strategy of [44] who pointed out an analogous ladder in de Sitter space. 9 We can use the algebraic structure to construct conserved quantities for each .…”

Section: Ladder In Schwarzschildmentioning

confidence: 99%

“…The vanishing of a black hole's tidal response is essentially a zero-frequency version of this reflectionless property: the physically relevant solution has only a single fall-off in both asymptotic regions. Interestingly the Pöschl-Teller potential also plays a prominent role in discussions of the transparency of odd-dimensional de Sitter spaces [44,60], revealing a surprising mathematical connection between black hole physics and de Sitter space. 25 The transformation to the z variable also makes manifest some features of the solutions.…”

Section: B Pöschl-teller Potentialmentioning

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: Introductionsupporting

confidence: 72%

“…Note that the arbitrary scale L disappears from δφ, as it should. Decomposing φ into spherical harmonics, it can be shown that this symmetry acts on the various components as [44]…”

Section: Discussionmentioning

confidence: 99%

Section: Ladder In Schwarzschildmentioning

confidence: 99%

Section: B Pöschl-teller Potentialmentioning

confidence: 99%

See 2 more Smart Citations

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

Hui,

Joyce,

Penco

et al. 2021

Preprint

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“…Corresponding to each of these charges is an off-shell symmetry of the action, which can be inferred as described in [4] (see also [29] for a similar construction on de Sitter backgrounds).…”

Section: Jhep09(2022)049 6 Ladder Symmetries and Tidal Responsementioning

confidence: 99%

Near-zone symmetries of Kerr black holes

Hui

Joyce

Penco

et al. 2022

J. High Energ. Phys.

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We study the near-zone symmetries of a massless scalar field on four-dimensional black hole backgrounds. We provide a geometric understanding that unifies various recently discovered symmetries as part of an SO(4, 2) group. Of these, a subset are exact symmetries of the static sector and give rise to the ladder symmetries responsible for the vanishing of Love numbers. In the Kerr case, we compare different near-zone approximations in the literature, and focus on the implementation that retains the symmetries of the static limit. We also describe the relation to spin-1 and 2 perturbations.

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Polarisability and magnetisation of electrically K-mouflaged objects: the Born-Infeld ModMax case study

Jiménez

Bettoni

Brax

2023

J. High Energ. Phys.

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We consider a family of non-linear theories of electromagnetism that interpolate between Born-Infeld at small distances and the recently introduced ModMax at large distances. These models are duality invariant and feature a K-mouflage screening in the Born-Infeld regime. We focus on computing the static perturbations around a point-like screened charge in terms of two decoupled scalar potentials describing the polar and the axial sectors respectively. Duality invariance imposes that the propagation speed of the odd perturbations goes to zero as fast as the effective screened charge of the object, potentially leading to strong coupling and an obstruction to the viability of the EFT below the screened radius. We then consider the linear response to external fields and compute the electric polarisability and the magnetic susceptibility. Imposing regularity of the perturbations at the position of the particle, we find that the polarisability for the odd multipoles vanishes whilst for the magnetisation Born-Infeld emerges as the only theory with vanishing susceptibility for even multipoles. The perturbation equations factorise in terms of ladder operators connecting different multipoles. There are two such ladder structures for the even sector: one that acts as an automorphism between the first four multipoles and another one that connects multipoles separated by four units. When requiring a similar ladder structure for the odd sector, Born-Infeld arises again as the unique theory. We use this ladder structure to relate the vanishing of the polarisability and the susceptibility to the values of conserved charges. Finally the perturbation equations correspond to a supersymmetric quantum mechanical system such that the polar sector can be described in terms of Schrödinger’s equations with four generalised hyperbolic Pösch-Teller potentials whose eigenfunctions are in correspondence with the multipoles.

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Hidden symmetries for transparent de Sitter space

Cited by 6 publications

References 46 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

Near-zone symmetries of Kerr black holes

Polarisability and magnetisation of electrically K-mouflaged objects: the Born-Infeld ModMax case study

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