A bstract In holography, the IR behavior of a quantum system at nonzero density is described by the near horizon geometry of an extremal charged black hole. It is commonly believed that for systems on S 3 , this near horizon geometry is AdS 2 × S 3 . We show that this is not the case: generic static, nonspherical perturbations of AdS 2 × S 3 blow up at the horizon, showing that it is not a stable IR fixed point. We then construct a new near horizon geometry which is invariant under only SO(3) (and not SO(4)) symmetry and show that it is stable to SO(3)-preserving perturbations (but not in general). We also show that an open set of nonextremal, SO(3)-invariant charged black holes develop this new near horizon geometry in the limit T → 0. Our new IR geometry still has AdS 2 symmetry, but it is warped over a deformed sphere. We also construct many other near horizon geometries, including some with no rotational symmetries, but expect them all to be unstable IR fixed points.
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Near-zone symmetries of Kerr black holes
A bstract 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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- Award ID(s):
- 1915611
- NSF-PAR ID:
- 10388686
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2022
- Issue:
- 9
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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A bstract Perturbations of massless fields in the Kerr-Newman black hole background enjoy a (“Love”) SL(2 , ℝ) symmetry in the suitably defined near zone approximation. We present a detailed study of this symmetry and show how the intricate behavior of black hole responses in four and higher dimensions can be understood from the SL(2 , ℝ) representation theory. In particular, static perturbations of four-dimensional black holes belong to highest weight SL(2 , ℝ) representations. It is this highest weight properety that forces the static Love numbers to vanish. We find that the Love symmetry is tightly connected to the enhanced isometries of extremal black holes. This relation is simplest for extremal charged spherically symmetric (Reissner-Nordström) solutions, where the Love symmetry exactly reduces to the isometry of the near horizon AdS 2 throat. For rotating (Kerr-Newman) black holes one is lead to consider an infinite-dimensional SL(2 , ℝ) ⋉ $$ \hat{\textrm{U}}{(1)}_{\mathcal{V}} $$ U ̂ 1 V extension of the Love symmetry. It contains three physically distinct subalgebras: the Love algebra, the Starobinsky near zone algebra, and the near horizon algebra that becomes the Bardeen-Horowitz isometry in the extremal limit. We also discuss other aspects of the Love symmetry, such as the geometric meaning of its generators for spin weighted fields, connection to the no-hair theorems, non-renormalization of Love numbers, its relation to (non-extremal) Kerr/CFT correspondence and prospects of its existence in modified theories of gravity.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP09(2022)049
