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Richterek, Lukáš; Novotný, Jan; Horský, Jan

doi:10.1023/a:1020581415399

Cited by 12 publications

(20 citation statements)

References 8 publications

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“…Eqs. (31) and (32) of [11], respectively). To which extend is this a property of the γ A -solution alone or a general rule of the E-M theory itself -i.e., a Kinnersley V transformation with timelike (spacelike) Killing vector always leads to solutions with electric (magnetic) field -is an intriguing question, which we will attempt to address in a future work.…”

Section: Discussionmentioning

confidence: 99%

“…The so called Horsky-Mitskievich conjecture, outlines an efficient and fruitful way to obtain solutions to the E-M equations, as a generalization of some already known vacuum seed metrics. In this context, taking the γ-solution as a seed vacuum spacetime, they have obtained two classes of E-M fields, the main properties of which are discussed extensively in [10] and [11].…”

Section: Introductionmentioning

confidence: 99%

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Generating solutions to the Einstein–Maxwell equations

Contopoulos

Esposito

Kleidis

et al. 2015

Int. J. Mod. Phys. D

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The Einstein-Maxwell (E-M) equations in a curved spacetime that admits at least one Killing vector are derived, from a Lagrangian density adapted to symmetries. In this context, an auxiliary space of potentials is introduced, in which, the set of potentials associated to an original (seed) solution of the E-M equations are transformed to a new set, either by continuous transformations or by discrete transformations. In this article, continuous transformations are considered. Accordingly, originating from the so-called γA-metric, other exact solutions to the E-M equations are recovered and discussed.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generating solutions to the Einstein–Maxwell equations

Contopoulos

Esposito

Kleidis

et al. 2015

Int. J. Mod. Phys. D

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show abstract

“…Upon consideration of the quaternionic version of the Ernst formalism, Hallilsoy [13] found a generalized version of the ZV metric. On the other hand, by treating the γ-solution as a seed (vacuum) metric, Richterek et al [14], [15] obtained two new classes of solutions to the Einstein -Maxwell equations with interesting properties.…”

Section: New Solutions Generated From Schwarzschildmentioning

confidence: 99%

Generating solutions to the Einstein field equations

Contopoulos

Esposito

Kleidis

et al. 2016

Int. J. Mod. Phys. D

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Exact solutions to the Einstein field equations may be generated from already existing ones (seed solutions), that admit at least one Killing vector. In this framework, a space of potentials is introduced. By the use of symmetries in this space, the set of potentials associated to a known solution are transformed into a new set, either by continuous transformations or by discrete transformations. In view of this method, and upon consideration of continuous transformations, we arrive at some exact, stationary axisymmetric solutions to the Einstein field equations in vacuum, that may be of geometrical or/and physical interest.

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“…As can be verified directly by substitution, the metric given by (24)- (32) does solve the f (R) field equations (3) with R = 0 for any constant σ, but has nonvanishing Ricci tensor unless σ = 0. In the zero ellipticity limit, ǫ → 0, we obtain the Reissner-Nordström metric [57]. A physical interpretation of σ is not readily available without performing some additional analysis, i.e.…”

Section: Worked Example: Ellipsoidal Neutron Starsmentioning

confidence: 99%

Ernst formulation of axisymmetric fields inf(R)gravity: Applications to neutron stars and gravitational waves

Suvorov

Melatos

2016

Phys. Rev. D

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The Ernst formulation of the Einstein equations is generalised to accommodate f (R) theories of gravity. It is shown that, as in general relativity, the axisymmetric f (R) field equations for a vacuum spacetime that is either stationary or cylindrically symmetric reduce to a single, non-linear differential equation for a complex-valued scalar function. As a worked example, we apply the generalised Ernst equations to derive a f (R) generalisation of the Zipoy-Voorhees metric, which may be used to describe the gravitational field outside of an ellipsoidal neutron star. We also apply the theory to investigate the phase speed of large-amplitude gravitational waves in f (R) gravity in the context of soliton-like solutions that display shock-wave behaviour across the causal boundary.

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Cited by 12 publications

References 8 publications

Generating solutions to the Einstein–Maxwell equations

Generating solutions to the Einstein–Maxwell equations

Generating solutions to the Einstein field equations

Ernst formulation of axisymmetric fields inf(R)gravity: Applications to neutron stars and gravitational waves

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