On the integrability of Einstein–Maxwell–(A)dS gravity in the presence of Killing vectors

Klemm, Dietmar; Nozawa, Masato; Rabbiosi, Marco

doi:10.1088/0264-9381/32/20/205008

Cited by 14 publications

(24 citation statements)

References 73 publications

(152 reference statements)

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“…One might ask whether this PSL(2, R) is related to the Ehlers transformations for the (electro)vacuum solutions to Einstein's equations. The latter symmetry is, however, broken in the presence of a cosmological constant [44]. Thus, the remarkable symmetry (3.29) is not related to Ehlers transformations and is intrinsic to supersymmetric solutions.…”

Section: Non-null Classmentioning

confidence: 98%

Geometry of Killing spinors in neutral signature

Klemm

Nozawa

2015

Class. Quantum Grav.

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We classify the supersymmetric solutions of minimal N = 2 gauged supergravity in four dimensions with neutral signature. They are distinguished according to the sign of the cosmological constant and whether the vector field constructed as a bilinear of the Killing spinor is null or non-null. In neutral signature the bilinear vector field can be spacelike, which is a new feature not arising in Lorentzian signature. In the Λ < 0 non-null case, the canonical form of the metric is described by a fibration over a threedimensional base space that has U(1) holonomy with torsion. We find that a generalized monopole equation determines the twist of the bilinear Killing field, which is reminiscent of an Einstein-Weyl structure. If, moreover, the electromagnetic field strength is self-dual, one gets the Kleinian signature analogue of the Przanowski-Tod class of metrics, namely a pseudo-hermitian spacetime determined by solutions of the continuous Toda equation, conformal to a scalar-flat pseudo-Kähler manifold, and admitting in addition a charged conformal Killing spinor. In the Λ < 0 null case, the supersymmetric solutions define an integrable null Kähler structure. In the Λ > 0 non-null case, the manifold is a fibration over a Lorentzian Gauduchon-Tod base space. Finally, in the Λ > 0 null class, the metric is contained in the Kundt family, and it turns out that the holonomy is reduced to Sim(1) × Sim(1). There appear no self-dual solutions in the null class for either sign of the cosmological constant.

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Section: Non-null Classmentioning

confidence: 98%

Geometry of Killing spinors in neutral signature

Klemm

Nozawa

2015

Class. Quantum Grav.

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“…Q I = 0 this leads to the Ercolani-Sinha solution [35], which is given in terms of elliptic functions. (6.4) can be written as 8) and thus its symmetries are determined by the transformations that leave the tensor C I JK invariant, T −1 CT T = C. Unfortunately this implies T = 1. The discrete symmetry group of (6.8), which is easily shown to be (Z 2 ) 6 × Z 3 , is not very useful for generating new solutions from known ones.…”

Section: Solutions With Running Scalarsmentioning

confidence: 99%

“…For the simple example quoted above, the addition of a cosmological constant breaks three of the eight SU(2, 1) symmetries, corresponding to the generalized Ehlers and the two Harrison transformations. This leaves a semidirect product of a one-dimensional Heisenberg group and a translation group R 2 as residual symmetry [8], that cannot be used to generate new solutions.…”

Section: Introductionmentioning

confidence: 99%

AdS5 black strings in the stu model of FI-gauged N = 2 supergravity

Azzola

Klemm

Rabbiosi

2018

J. High Energ. Phys.

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We analytically construct asymptotically AdS 5 black string solutions starting from the four-dimensional domain wall black hole of [1]. It is shown that its uplift gives a black string in d = 5 minimal gauged supergravity, with momentum along the string. Applying instead the residual symmetries of N = 2, d = 4 Fayet-Iliopoulosgauged supergravity discovered in [2] to the domain wall seed leads, after uplifting, to a dyonic black string that interpolates between AdS 5 and AdS 3 × H 2 at the horizon. A Kaluza-Klein reduction of the latter along an angular Killing direction φ followed by a duality transformation yields, after going back to five dimensions, a black string with both momentum along the string and rotation along φ. This is the first instance of using solution-generating techniques in gauged supergravity to add rotation to a given seed. These solutions all have constant scalar fields. As was shown in [3], the construction of supersymmetric static magnetic black strings in the FI-gauged stu model amounts to solving the SO(2, 1) spinning top equations, which descend from an inhomogeneous version of the Nahm equations. We are able to solve these in a particular case, which leads to a generalization of the Maldacena-Nuñez solution.

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“…This was recently extended to include a non-zero cosmological constant by Leigh et al [6], where they traced the symmetries broken by the presence of the cosmological constant and recast the equations of motion as a one-dimensional system which was solved using the Hamilton-Jacobi method. A further generalisation of this method to include electromagnetic fields was done by Klemm et al [7]. In higher dimensional vacuum gravity, D-dimensional static spacetimes with (D − 2)…”

Section: Introductionmentioning

confidence: 99%

Cohomogeneity-one solutions in Einstein-Maxwell-dilaton gravity

Lim

2017

Phys. Rev. D

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The field equations for Einstein-Maxwell-dilaton gravity in D dimensions are reduced to an effective one-dimensional system under the influence of exponential potentials. Various cases where exact solutions can be found are explored. With this procedure, we present interesting solutions such as a one-parameter generalisation of the dilaton-Melvin spacetime and a three-parameter solution that interpolates between the Reissner-Nordström and Bertotti-Robinson solutions. This procedure also allows simple, alternative derivations of known solutions such as the Lifshitz spacetime and the planar Anti-de Sitter naked singularity. In the latter case, the metric is cast in a simpler form which reveals the presence of an additional curvature

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On the integrability of Einstein–Maxwell–(A)dS gravity in the presence of Killing vectors

Cited by 14 publications

References 73 publications

Geometry of Killing spinors in neutral signature

Geometry of Killing spinors in neutral signature

AdS5 black strings in the stu model of FI-gauged N = 2 supergravity

Cohomogeneity-one solutions in Einstein-Maxwell-dilaton gravity

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