Can one hear the Riemann zeros in black hole ringing?

Aros, Rodrigo; Bugini, F.; Díaz, D. E.

doi:10.1088/1742-6596/720/1/012009

Cited by 3 publications

(4 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(A. 21) In the context of the BTZ black hole, we see that the identification (t E , φ) ∼ (t E , φ+2π) can be understood as the transformation generated by the elements of Γ BTZ with a = πr + and b = π|r − |. Meanwhile, the identification (τ, φ) ∼ (τ + β 0 , φ + Φ), an identity transformation, has a = 0, and b = 2π, in which case the associated γ is not loxodromic.…”

Section: Discussionmentioning

confidence: 99%

“…The relationship between the heat kernel and the Selberg zeta function was presented in [13], and [18] (in the context of the static BTZ black hole). The relationship between quasinormal modes and the Patterson-Selberg 2 zeta function was presented in [20,21]. We build on these previous works constructing a connection between the heat kernel and quasinormal methods.…”

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

Connecting quasinormal modes and heat kernels in 1-loop determinants

2020

View full text Add to dashboard Cite

We connect two different approaches for calculating functional determinants on quotients of hyperbolic spacetime: the heat kernel method and the quasinormal mode method. For the example of a rotating BTZ background, we show how the image sum in the heat kernel method builds up the logarithms in the quasinormal mode method, while the thermal sum in the quasinormal mode method builds up the integrand of the heat kernel. More formally, we demonstrate how the heat kernel and quasinormal mode methods are linked via the Selberg zeta function. We show that a 1-loop partition function computed using the heat kernel method may be cast as a Selberg zeta function whose zeros encode quasinormal modes. We discuss how our work may be used to predict quasinormal modes on more complicated spacetimes. arXiv:1811.08433v2 [hep-th]

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Connecting quasinormal modes and heat kernels in 1-loop determinants

2020

View full text Add to dashboard Cite

show abstract

“…Moreover, scattering situations familiar from the chaotic scattering literature featuring cusps, can in principle be embedded into these scenarios via extremal black holes [21,22]. This scattering language has also been used for expressing various thermodynamic quantities of the BTZ black hole in terms of the Selberg zeta function [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Berry curvature, horocycles and scattering states in $AdS_3/CFT_2$

Lévay

2019

Preprint

View full text Add to dashboard Cite

By studying the space of geodesics in ADS3/CF T2 and quantizing the geodesic motion, we relate scattering data to boundary entanglement of the CFT vacuum. The basic idea is to use a family of plane waves parametrized by coordinates of the space of geodesics i.e. kinematic space. This idea enables a simple calculation of the Berry curvature living on kinematic space. As a result we recover the Crofton form with a coefficient depending on the scattering energy. In arriving at these results the space of horocycles is used. We show that this new space used in concert with kinematic space incorporates naturally the gauge degrees of freedom responsible for an analogue of Berry's Phase. Horocycles also give a new geometric look to the strong subadditivity relation in terms of lambda lengths giving rise to shear coordinates of geodesic quadrangles. A generalization for geodesic polygons then reveals an interesting connection with An cluster algebras. Here the cluster variables are the lambda lengths related to the regularized entropies of the boundary via the Ryu-Takayanagi relation. An elaboration of this idea indicates that cluster algebras might provide a natural algebraic means for encoding the gauge invariant entanglement patterns of certain boundary entangled states in the geometry of bulk geodesics. Finally using the language of integral geometry we show how certain propagators connected to the bulk, boundary and kinematic spaces are related to data of elementary scattering problems. We also present some hints how these ideas might be generalized for more general holographic scenarios.

show abstract

Section: Introductionmentioning

confidence: 99%

Berry curvature, horocycles, and scattering states in AdS3/CFT2

Lévay

2019

Phys. Rev. D

View full text Add to dashboard Cite

By studying the space of geodesics in AdS 3 =CFT 2 and quantizing the geodesic motion, we relate scattering data to boundary entanglement of the CFT vacuum. The basic idea is to use a family of plane waves parametrized by coordinates of the space of geodesics i.e., kinematic space. This idea enables a simple calculation of the Berry curvature living on kinematic space. As a result we recover the Crofton form with a coefficient depending on the scattering energy. In arriving at these results the space of horocycles is used. We show that this new space used in concert with kinematic space incorporates naturally the gauge degrees of freedom responsible for an analog of Berry's phase. Horocycles also give a new geometric look to the strong subadditivity relation in terms of lambda lengths giving rise to shear coordinates of geodesic quadrangles. A generalization for geodesic polygons then reveals an interesting connection with A n cluster algebras. Here the cluster variables are the lambda lengths related to the regularized entropies of the boundary via the Ryu-Takayanagi relation. An elaboration of this idea indicates that cluster algebras might provide a natural algebraic means for encoding the gauge invariant entanglement patterns of certain boundary entangled states in the geometry of bulk geodesics. Finally using the language of integral geometry we show how certain propagators connected to the bulk, boundary and kinematic spaces are related to data of elementary scattering problems. We also present some hints how these ideas might be generalized for more general holographic scenarios.

show abstract

Can one hear the Riemann zeros in black hole ringing?

Cited by 3 publications

References 4 publications

Connecting quasinormal modes and heat kernels in 1-loop determinants

Connecting quasinormal modes and heat kernels in 1-loop determinants

Berry curvature, horocycles and scattering states in $AdS_3/CFT_2$

Berry curvature, horocycles, and scattering states in AdS3/CFT2

Contact Info

Product

Resources

About