On symmetry operators for the Maxwell equation on the Kerr-NUT-(A)dS spacetime

Houri, Tsuyoshi; Tanahashi, Norihiro; Yasui, Yukinori

doi:10.1088/1361-6382/ab586d

Cited by 14 publications

(18 citation statements)

References 35 publications

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“…The spacetime no longer possesses the hidden symmetry of the principal tensor. However, as shown in [43] a weaker structure of the principal tensor with torsion exists [36]. This is a non-degenerate closed conformal Killing-Yano tensor with torsion, obeying the following generalization of Eq.…”

Section: Kerr-sen Geometrymentioning

confidence: 95%

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Massive vector fields in Kerr-Newman and Kerr-Sen black hole spacetimes

Cayuso

Dias

Gray

et al. 2020

J. High Energ. Phys.

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The superradiant instability modes of ultralight massive vector bosons are studied for weakly charged rotating black holes in Einstein-Maxwell gravity (the Kerr-Newman solution) and low-energy heterotic string theory (the Kerr-Sen black hole). We show that in both these cases, the corresponding massive vector (Proca) equations can be fully separated, exploiting the hidden symmetry present in these spacetimes. The resultant ordinary differential equations are solved numerically to find the most unstable modes of the Proca field in the two backgrounds and compared to the vacuum (Kerr black hole) case. black hole with mass M and U (1) charge Q and contains two extra background fields; the scalar dilaton Φ and the 3-form H. In the limit that these two fields vanish the spacetime reduces to the Kerr black hole. On the other hand, this spacetime should be compared to the Kerr-Newman solution [17] which is the unique stationary black hole solution to the Einstein equations with U (1) charge (it can also be understood as a solution of N = 2, D = 4 supergravity). Both Kerr-Newman and Kerr-Sen black holes are stationary and axisymmetric spacetimes, possessing two Killing vectors which aid in understanding the behaviour of test fields in these backgrounds. In the Kerr-Newman case there exists an additional hidden symmetry of the principal Killing-Yano tensor which gives rise to Carter's constant for charged geodesics [18]. For the Kerr-Sen spacetime only a generalized principal tensor with torsion exists which is a weaker but still rather useful structure [19].The aim of this paper is to study the superradiant instabilities of the Kerr-Sen and Kerr-Newman black holes, as triggered by the ultralight massive bosons. These are well understood in the case of massive scalar fields, see [20] and [21], but the corresponding study for massive vectors is currently missing. The reason is simple. Even for vacuum (Kerr) black holes, the corresponding Proca equations are rather complicated partial differential equations whose direct decoupling and separation à la Teukolsky [22,23] does not work due to the presence of the mass term [24,25]. As a consequence the problem was investigated either using approximations [9,24,25] or employing serious numerical analysis [10,26,27].However, a separability renaissance for vector fields has begun in the last couple of years due to a new ansatz by Lunin [28]. Simplified and written in covariant form by Frolov-Krtouš-Kubizňák [29,30], the new ansatz works for the massive vector field case [31] and can be applied in the Kerr-NUT-AdS spacetimes for all dimensions. Importantly the Lunin-Frolov-Krtouš-Kubizňák (LFKK) ansatz exploits the existence of hidden symmetries in these spacetimes which are encoded in the principal tensor [18] and allows the Proca equations to be decoupled and separated into ordinary differential equations [31]. In four dimensions, the separation equally applies to the non-accelerating electro-vacuum type D Plebański-Demiański spacetimes and thence to the Kerr-Newman black holes. 1...

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Section: Kerr-sen Geometrymentioning

confidence: 95%

“…Despite being a weaker structure, the principal tensor with torsion still gives rise to standard Killing tensor, via (2.8). However, the isometries of the spacetime are no longer straightforwardly generated from h [43].…”

Section: Kerr-sen Geometrymentioning

confidence: 99%

Massive vector fields in Kerr-Newman and Kerr-Sen black hole spacetimes

Cayuso

Dias

Gray

et al. 2020

J. High Energ. Phys.

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“…Unfortunately there are no known procedures for extending these algebraic techniques to vector and tensor fields, especially for finding the eigenfunctions. 2 On the other hand, experience with other backgrounds, such as black hole geometries, shows that separation of variables for a scalar field is often accompanied by separation in the vector and tensor equations [29][30][31][32][33][34][35][36]. Inspired by this success, we focus on the gWZW models which admit separation of variables in the Helmholtz equation for a scalar and demonstrate that separability of the vector equation in all such cases.…”

Section: Introductionmentioning

confidence: 91%

Separation of variables in the WZW models

Lunin

Tian

2021

J. High Energ. Phys.

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We consider dynamics of scalar and vector fields on gravitational backgrounds of the Wess-Zumino-Witten models. For SO(4) and its cosets, we demonstrate full separation of variables for all fields and find a close analogy with a similar separation of vector equations in the backgrounds of the Myers-Perry black holes. For SO(5) and higher groups separation of variables is found only in some subsectors.

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“…In this paper we consider first order symmetry operators for differential p-form fields both for massless and massive cases. For recent related works for p = 1 case see [7,8,9,10,11,12,13,14,15,16], and for arbitrary p see [17]. We do not impose the background equation of motion on the background geometry and the metric can have any signature.…”

Section: Introductionmentioning

confidence: 99%

“…[18].) Indeed the relation between Killing-Yano forms and the separability of the equations of motion for 1-forms in Myers-Perry-(A)dS or Kerr-NUT-(A)dS spacetimes is discussed in [10,11,12,13,15] and for p-forms in [17]. (conformal) Killing-Yano forms also appear in the first order symmetry operators for the equations of motion for spinor fields (See e.g.…”

mentioning

confidence: 99%