Hidden symmetry and the separability of the Maxwell equation on the Wahlquist spacetime

Houri, Tsuyoshi; Tanahashi, Norihiro; Yasui, Yukinori

doi:10.1088/1361-6382/ab6e8a

Cited by 10 publications

(10 citation statements)

References 34 publications

(158 reference statements)

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“…One can verify that the Wahlquist metric satisfies N µν = 0 (and M µνρ = 0 [49]) only on-shell. This traces back to the fact that the Wahlquist metric belongs to type I for off-shell, whereas to type D for on-shell [50]. It would be an interesting future direction to explore the relation to the (torsionful) Killing-Yano tensor and the tensor N µν and to the quotient space interpretation.…”

Section: Discussionmentioning

confidence: 86%

An alternative to the Simon tensor

Nozawa

2021

Preprint

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The Simon tensor gives rise to a local characterization of the Kerr-NUT family in the stationary class of vacuum spacetimes. We find that a symmetric and traceless tensor in the quotient space of the stationary Killing trajectory offers a useful alternative to the Simon tensor. Our tensor is distinct from the spatial dual of the Simon tensor and illustrates the geometric property of the three dimensional quotient space more manifest. The reconstruction procedure of the metric for which the generalized Simon tensor vanishes is spelled out in detail. We give a four dimensional description of this tensor in terms of the Coulomb part of the imaginary selfdual Weyl tensor, which corresponds to the generalization of the three-index tensor defined by Mars. This allows us to establish a new and simple criterion for the Kerr-NUT family: the gradient of the Ernst potential becomes the non-null eigenvector of the Coulomb part of the imaginary selfdual Weyl tensor. We also discuss the SU(1, 2) covariant extension of the obstruction tensor into the Einstein-Maxwell system as an intrinsic characterization of the Kerr-Newman-NUT family.

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Section: Discussionmentioning

confidence: 86%

An alternative to the Simon tensor

Nozawa

2021

Preprint

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“…Second, the principal tensor explicitly enters the separation ansatz (3.3) via the polarization tensor (3.4). Third, the principal tensor gives rise to a complete set of mutually commuting operators that guarantee this separability [29,34,43]. Namely, apart from the (trivial) ones connected with Killing vectors, the following two (2nd order) operators directly link to the separation ansatz:…”

Section: Proca In Kerr-newman Spacetimementioning

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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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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“…Mars also states that the space-time admits a Killing tensor as shown in [12]. More recent work in this field exists, "where the existence of a rank-2 generalized closed conformal Killing-Yano tensor with a a e-mail: hortacsu@itu.edu.tr (corresponding author) skew-symmetric torsion" [13], and "the separability of the Maxwell equation on the Wahlquist spacetime" are shown [14].…”

Section: Introductionmentioning

confidence: 99%

A massless scalar particle coupled to the Wahlquist metric

Birkandan

Hortaçsu

2021

Eur. Phys. J. C

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We study the solutions of the wave equation where a massless scalar field is coupled to the Wahlquist metric, a type-D solution. We first take the full metric, and then write simplifications of the metric by taking some of the constants in the metric null. When we do not equate any of the arbitrary constants in the metric to zero, we find the solution is given in terms of the general Heun function, apart from some simple functions multiplying this solution. This is also true, if we equate one of the constants $$Q_0$$ Q 0 or $$a_1$$ a 1 to zero. When both the NUT related constant $$a_1$$ a 1 and $$Q_0$$ Q 0 are zero, the singly confluent Heun function is the solution. When we also equate the constant $$\nu _0$$ ν 0 to zero, we get the double confluent Heun-type solution. In the latter two cases, we have an exponential and two monomials raised to powers multiplying the Heun type function. Thus, we generalize the Batic et al. result for type-D metrics for this metric and show that all variations of the Wahlquist metric give Heun type solutions.

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Hidden symmetry and the separability of the Maxwell equation on the Wahlquist spacetime

Cited by 10 publications

References 34 publications

An alternative to the Simon tensor

An alternative to the Simon tensor

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

A massless scalar particle coupled to the Wahlquist metric

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