Principal tensor strikes again: Separability of vector equations with torsion

Cayuso, Ramiro; Gray, Finnian; Kubizňák, David; Margalit, Aoibheann; Souza, Renato Gomes; Thiele, Leander

doi:10.1016/j.physletb.2019.07.007

Cited by 10 publications

(11 citation statements)

References 32 publications

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“…Nevertheless, our problem presents an extra difficulty related to the presence of µ in the radial and angular equations, which is not the case in four dimensions where the separation parameter µ can be absorbed by a redefinition of the separation constant C m , as can be seen in [13,20]. See also [35] for a similar discussion.…”

Section: Quasinormal Modes From the Radial Systemmentioning

confidence: 87%

Vector perturbations of Kerr-AdS5 and the Painlevé VI transcendent

Amado

Cunha

Pallante

2020

J. High Energ. Phys.

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We analyze the Ansatz of separability for Maxwell equations in generically spinning, five-dimensional Kerr-AdS black holes. We find that the parameter µ introduced in [1] can be interpreted as apparent singularities of the resulting radial and angular equations. Using isomonodromy deformations, we describe a non-linear symmetry of the system, under which µ is tied to the Painlevé VI transcendent. By translating the boundary conditions imposed on the solutions of the equations for quasinormal modes in terms of monodromy data, we find a procedure to fix µ and study the behavior of the quasinormal modes in the limit of fast spinning small black holes.

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Section: Quasinormal Modes From the Radial Systemmentioning

confidence: 87%

Vector perturbations of Kerr-AdS5 and the Painlevé VI transcendent

Amado

Cunha

Pallante

2020

J. High Energ. Phys.

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“…However, the existence of torsion could be obstacle for this method. In [20], this method was applied on the Cvetič-Lü-Page-Pope spacetime in five dimensions, where the Maxwell equation is modified by adding the Chern-Simons term that arises naturally in the equation of motion in the supergravity theory, and the additional term is realized by means of the torsion. For now, we have no reason on the Wahlquist spacetime to modify the Maxwell equation by torsion, but it would be fruitful to pursue this issue and clarify the applicability of this method.…”

Section: Summary and Discussionmentioning

confidence: 99%

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

Houri

Tanahashi

Yasui

2020

Class. Quantum Grav.

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We examine hidden symmetry and its relation to the separability of the Maxwell equation on the Wahlquist spacetime. After seeing that the Wahlquist spacetime is a type-D spacetime whose repeated principal null directions are shear-free and geodesic, we show that the spacetime admits three gauged conformal Killing-Yano (GCKY) tensors which are in a relation with torsional conformal Killing-Yano tensors. As a by-product, we obtain an ordinary CKY tensor. We also show that thanks to the GCKY tensors, the Maxwell equation reduces to three Debye equations, which are scalar-type equations, and two of them can be solved by separation of variables. I. INTRODUCTIONHidden symmetry of spacetime has played an important role in the study of black hole physics. In particular, conformal Killing-Yano symmetry, known as hidden symmetry of the Kerr spacetime, has received special attention since it has been crucial to understanding the separability of various equations on a curved spacetime.On the Kerr spacetime, the Hamilton-Jacobi equation for geodesics, the Klein-Gordon equation, and the Dirac equation can be solved by separation of variables, and these separabilities have been understood in terms of a Killing-Yano tensor. For electromagnetic and gravitational perturbations, Teukolsky [1, 2] provided the scalar-type master equations, which can be solved by separation of variables. Cohen and Kegeles [3] showed that, if a spacetime is algebraically special and its repeated principal null direction (PND) is shear-free and geodesic, 1 the Maxwell equation reduces to a scalar-type master equation called the Debye equation. They also showed that when their method is applied to the Kerr spacetime, the Debye equation coincides with the Teukolsky equation. Moreover, they extended their results to massless Dirac fields on algebraically special spacetimes and gravitational perturbations on vacuum spacetimes [4]. After a while, Benn, Charlton, and Kress [5] unveiled the underlying structure of the works by Cohen and Kegeles from the viewpoint of GCKY symmetry. So far, while the GCKY symmetry has been related to obtaining the scalar-type master equations from the Dirac, Maxwell, and linearized Einstein equations, the separability of those equations has not been well understood. To fill the gap is one of the aims in this paper.In this paper, we examine hidden symmetry of the Wahlquist spacetime [6][7][8][9][10][11][12], which is a stationary, axially symmetric solution to the Einstein equation with rigidly rotating perfect fluids. According to the Goldberg-Sachs theorem, the repeated PNDs on a type-D vacuum spacetime are shear-free and geodesic. However, since the Wahlquist metric is a non-vacuum type-D spacetime, it is interesting to ask if the repeated PNDs are shear-free and geodesic. According to [3,5], if they are so, we obtain GCKY tensors with a certain condition and hence the Maxwell equation reduces to the Debye equation. Since the Wahlquist spacetime is known to admit a torsional conformal Killing-Yano (TCKY) tensor [12], there may...

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“…To motivate the generalized Proca equation, we assume that the massive vector field P couples to the background fields Φ and H in analogy to the massless Maxwell field already present in the Kerr-Sen action (2.9). As in [38], we also demand that the modified Proca is linear in P , reduces to the Proca equation in the absence of the background fields, and obeys current conservation in the presence of sources. It follows that there are two key modifications to the Proca equation in the Kerr-Sen background.…”

Section: Generalized Proca In Kerr-sen Spacetimementioning

confidence: 99%

“…In this case, the torsion is naturally identified with the Maxwell 3-form present in the spacetime, and both the principal tensor and the Proca equations pick up a corresponding torsion modification. Despite these significant differences, the LFKK ansatz still applies and the (torsion) modified Proca equations decouple and separate [38].In this work, we will apply the LFKK ansatz to separate the Proca equations in the Kerr-Sen black hole background. Similar to the black hole of minimal gauged supergravity, the corresponding Proca equations have to be modified by the presence of torsion, now naturally identified with the 3-form field H. To account for the dilaton field Φ, we work in 1 See [31][32][33] for further discussions of the LFKK ansatz in four dimensions, and [34] for an alternative way of separating the Maxwell equations in the Wahlquist metrics.…”

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confidence: 99%

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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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Principal tensor strikes again: Separability of vector equations with torsion

Cited by 10 publications

References 32 publications

Vector perturbations of Kerr-AdS5 and the Painlevé VI transcendent

Vector perturbations of Kerr-AdS5 and the Painlevé VI transcendent

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

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

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