Papapetrou Field Research Articles

Boosted Kerr–Newman black holes

Abstract In this paper we obtain a new solution of Einstein field equations which describes a boosted Kerr–Newman black hole relative to a Lorentz frame at future null infinity. To simplify our analysis we consider a particular configuration in which the boost is aligned with the black hole angular momentum. The boosted Kerr–Newman black hole is obtained considering the complete asymptotic Lorentz transformations of Robinson–Trautman coordinates to Bondi–Sachs, including the perturbation term of the boosted Robinson–Trautman metric. To verify that the final form of the metric is indeed a solution of Einstein field equations, we evaluate the corresponding energy–momentum tensor the boosted Kerr–Newman solution. To this end, we consider the electromagnetic energy–momentum tensor built with the Kerr boosted metric together with its timelike killing vector. We show that the Papapetrou field thus obtained engender an energy–momentum tensor which satisfies Einstein field equations up to 4th order for the Kerr–Newman metric. To proceed, we examine the causal structure of the boosted Kerr–Newman black hole in Bondi–Sachs coordinates as in a preferred timelike foliation. We show that the ultimate effect of a nonvanishing charge is to shrink the overall size of the event horizon and ergosphere areas when compared to the neutral boosted Kerr black holes. Considering the preferred timelike foliation we obtain the electromagnetic fields for a proper nonrotating frame of reference. We show that while the electric field displays a pure radial behavior, the magnetic counterpart develops an involved structure with two intense lobes of the magnetic field observed in the direction opposite to the boost.

Particle dynamics on test papapetrou fields of vacuum spacetimes

In this paper we examine the dynamics of test particles subjected to Papapetrou fields which emerge from vacuum spacetimes isometries. Assuming that the background geometry is described by a Kerr metric whose timelike Killing vector satisfies Maxwell equations, we evaluate the electromagnetic fields—Papapetrou fields—by fixing a locally non-rotating (LNR) frame of reference. We also evaluate such the electromagnetic fields for a vanishing rotation parameter assuming a timelike frame of reference for a Schwarzschild background. In order to probe for the effect of the test Papapetrou fields we study the motion of charged particles in a Kerr background. Restricting ourselves to orbits in the equatorial plane with LNR initial conditions we show that there is an explicit deviation between orbits of neutral and charged particles in the case of repulsive electromagnetic configurations. For critical charge-mass ratios ζ * test particles can be found in the Kerr retrograde photon sphere. For static configurations we show that massive/charged test particles may populate the unstable Schwarzschild photon sphere for given domain of the parameter space.

Papapetrou field as the gravitoelectromagnetic field tensor in stationary spacetimes

Introducing the well known Papapetrou field as the gravitoelectromagnetic field tensor, we express the Maxwell-type part of the 3-dimensional quasi-Maxwell form of the {\it vacuum} Einstein field equations in terms of differential forms, analogous to their electromagnetic counterparts in curved spacetimes. Using the same formalism we introduce the junction conditions on non-null hypersurfaces in terms of the introduced gravitoelectromagnetic 4-vector fields and apply them to the case of the Van Stockum interior and exterior solutions.

On the invariant symmetries of the D-metrics

We analyze the symmetries and other invariant qualities of the D-metrics (type D aligned Einstein-Maxwell solutions with cosmological constant whose Debever null principal directions determine shear-free geodesic null congruences). We recover some properties and deduce new ones about their isometry group and about their quadratic first integrals of the geodesic equation, and we analyze when these invariant symmetries characterize the family of metrics. We show that the subfamily of the Kerr-NUT solutions are those admitting a Papapetrou field aligned with the Weyl tensor.

Type I vacuum solutions with aligned Papapetrou fields: An intrinsic characterization

We show that Petrov type I vacuum solutions admitting a Killing vector whose Papapetrou field is aligned with a principal bivector of the Weyl tensor are the Kasner and Taub metrics, their counterpart with timelike orbits and their associated windmill-like solutions, as well as the Petrov homogeneous vacuum solution. We recover all these metrics by using an integration method based on an invariant classification which allows us to characterize every solution. In this way we obtain an intrinsic and explicit algorithm to identify them.

The Simon and Simon–Mars tensors for stationary Einstein–Maxwell fields

Modulo conventional scale factors, the Simon and Simon–Mars tensors are defined for stationary vacuum spacetimes so that their equality follows from the Bianchi identities of the second kind. In the nonvacuum case one can absorb additional source terms into a redefinition of the Simon tensor so that this equality is maintained. Among the electrovacuum class of solutions of the Einstein–Maxwell equations, the expression for the Simon tensor in the Kerr–Newman–Taub–NUT spacetime in terms of the Ernst potential is formally the same as in the vacuum case (modulo a scale factor), and its vanishing guarantees the simultaneous alignment of the principal null directions of the Weyl tensor, the Papapetrou field associated with the timelike Killing vector field, the electromagnetic field of the spacetime and even the Killing–Yano tensor.

Vacuum type I spacetimes and aligned Papapetrou fields: symmetries

We analyse type I vacuum solutions admitting an isometry whose Killing 2-form is aligned with a principal bivector of the Weyl tensor, and we show that these solutions belong to a family of type I metrics which admit a group G3 of isometries. We give a classification of this family and study the Bianchi type for each class. The classes compatible with an aligned Killing 2-form are also determined. The Szekeres–Brans theorem is extended to non-vacuum spacetimes with vanishing Cotton tensor.

The Cotton, Simon–Mars and Cotton–York tensors in stationary spacetimes

The Cotton–York and Simon–Mars tensors in stationary vacuum spacetimes are studied in the language of the congruence approach pioneered by Hawking and Ellis. Their relationships with the Papapetrou field defined by the stationary Killing congruence and with a recent characterization of the Kerr spacetime in terms of the alignment between the principal null directions of the Weyl tensor with those of the Papapetrou field are also investigated in a more transparent language.

General approach to the study of vacuum spacetimes with an isometry

In vacuum spacetimes the exterior derivative of a Killing vector field is a2-form (called here the Papapetrou field) that satisfies Maxwell'sequations without electromagnetic sources. In this paper, using thealgebraic structure of the Papapetrou field, we will set up a newformalism for the study of vacuum spacetimes with an isometry, which issuitable to investigate the connections between the isometry and thePetrov type of the spacetime. This approach has some advantages, amongwhich are that it leads to a new classification of these spacetimes andtheintegrability conditions provide expressions that determinethe Weyl curvature completely.These facts make the formalism useful for applicationto any problem or situation with an isometry and requiring the knowledgeof the curvature.

On the Papapetrou field in vacuum

In this paper we study the electromagnetic fields generated by a Killing vector field in vacuum spacetimes (Papapetrou fields). The motivation of this work is to provide new tools for the resolution of Maxwell's equations as well as for the search, characterization, and study of exact solutions of Einstein's equations. The first part of this paper is devoted to an algebraic study in which we give an explicit and covariant procedure to construct the principal null directions of a Papapetrou field. In the second part, we focus on the main differential properties of the principal directions, studying when they are geodesic, and in that case we compute their associated optical scalars. With this information we get the conditions that a principal direction of the Papapetrou field must satisfy in order to be aligned with a multiple principal direction of the Weyl tensor in the case of algebraically special vacuum spacetimes. Finally, we illustrate this study using the Kerr, Kasner and pp waves spacetimes.

Do Harrison transformations possess any physical meaning?

We propose to give a physical interpretation of the Harrison transformations, so far considered merely as generation techniques of exact solutions of the Einstein-Maxwell equations, as the mechanism which makes a certain class of electrovacuum test fields (Papapetrou fields) gravitate themselves.