Stationary Electrovacuum Research Articles

Cylindrical spacetimes due to radial magnetic fields

We continue our previous study of cylindrically symmetric, static electrovacuum spacetimes generated by a magnetic field, involving optionally the cosmological constant, and investigate several classes of exact solutions. These spacetimes are due to magnetic fields that are perpendicular to the axis of symmetry.

Cosmological magnetic field: The boost-symmetric case

We find a class of cylindrically symmetric, static electrovacuum spacetimes generated by a non-homogeneous magnetic field and involving the cosmological constant and one additional parameter, which determine uniquely the strength of the magnetic field. We provide a simple model of a source producing the field.

On the Local Extension of Killing Vector Fields in Electrovacuum Spacetimes

We revisit the problem of extension of a Killing vector field in a spacetime which is solution to the Einstein-Maxwell equation. This extension has been proved to be unique in the case of a Killing vector field which is normal to a bifurcate horizon by Yu. Here we generalize the extension of the vector field to a strong null convex domain in an electrovacuum spacetime, inspired by the same technique used by Ionescu-Klainerman in the setting of Ricci flat manifolds. We also prove a result concerning non-extendibility: we show that one can find local, stationary electrovacuum extension of a Kerr-Newman solution in a full neighborhood of a point of the horizon (that is not on the bifurcation sphere) which admits no extension of the Hawking vector field. This generalizes the construction by Ionescu-Klainerman to the electrovacuum case.

Uniqueness of photon spheres in electro-vacuum spacetimes

In a recent paper (Cederbaum C and Galloway G J 2015 Commun. Analysis Geom. at press), the authors established the uniqueness of photon spheres in static vacuum asymptotically flat spacetimes by adapting Bunting and Masood-ul-Alam’s proof of static vacuum black hole uniqueness. Here, we establish uniqueness of suitably defined sub-extremal photon spheres in static electro-vacuum asymptotically flat spacetimes by adapting the argument of Masood-ul-Alam (1992 Class. Quantum Grav. 9 L53-5). As a consequence of our result, we can rule out the existence of electrostatic configurations involving multiple ‘very compact’ electrically charged bodies and sub-extremal black holes.

Static black holes with axial symmetry in asymptoticallyAdS4spacetime

The known static electrovacuum black holes in a globally ${\mathrm{AdS}}_{4}$ background have an event horizon which is geometrically a round sphere. In this work we argue that the situation is different in models with matter fields possessing an explicit dependence on the azimuthal angle $\ensuremath{\varphi}$, which, however, does not manifest at the level of the energy-momentum tensor. As a result, the full solutions are axially symmetric only, possessing a single (timelike) Killing vector field. Explicit examples of such static black holes are constructed in Einstein--(complex) scalar field and Einstein--Yang-Mills theories. The basic properties of these solutions are discussed, looking for generic features. For example, we notice that the horizon has an oblate spheroidal shape for solutions with a scalar field and a prolate one for black holes with Yang-Mills fields. The deviation from sphericity of the horizon geometry manifests itself in the holographic stress tensor. Finally, based on the results obtained in the probe limit, we conjecture the existence in Einstein-Maxwell theory of static black holes with axial symmetry only.

Matter around Kerr black holes in scalar-tensor theories: Scalarization and superradiant instability

In a stationary electrovacuum, asymptotically flat black holes in scalar-tensor theories of gravity are described by the Kerr-Newman family of solutions, just as in general relativity. We show that there exist two mechanisms which can render Kerr black holes unstable when matter is present in the vicinity of the black hxole, as this induces an effective mass for the scalar. The first mechanism is a tachyonic instability that appears when the effective mass squared is negative, triggering the development of scalar hair---a black-hole version of ``spontaneous scalarization.'' The second instability is associated with superradiance and is present when the effective mass squared is positive and when the black-hole spin exceeds a certain threshold. The second mechanism is also responsible for a resonant effect in the superradiant scattering of scalar waves, with amplification factors as large as ${10}^{5}$ or more.

A local characterization for static charged black holes

We obtain a purely local characterization that singles out the Majumdar–Papapetrou class, the near-horizon Bertotti–Robinson geometry and the Reissner–Nordström exterior solution, together with its plane and hyperbolic counterparts, among the static electrovacuum spacetimes. These five classes are found to form the whole set of static Einstein–Maxwell fields without sources and conformally flat space of orbits, that is, the conformastat electrovacuum spacetimes. The main part of the proof consists in showing that a functional relationship between the gravitational and electromagnetic potentials must always exist. The classification procedure also provides an improved characterization of Majumdar–Papapetrou, by only requiring a conformally flat space of orbits with a vanishing Ricci scalar of the usual conveniently rescaled 3-metric. A simple global consideration allows us to state that the asymptotically flat subset of the Majumdar–Papapetrou class and the Reissner–Nordström exterior solution are the only asymptotically flat conformastat electrovacuum spacetimes.

On the classification of stationary electro-vacuum black holes

We obtain a classification of stationary, I+-regular, non-degenerate and analytic electro-vacuum spacetimes in terms of Weinstein solutions. In particular, for connected horizons, we prove uniqueness of the Kerr–Newman black holes.

Newman-Penrose constants of stationary electrovacuum space-times

A theorem related to the Newman-Penrose constants is proven. The theorem states that all the Newman-Penrose constants of asymptotically flat, stationary, asymptotically algebraically special electrovacuum space-times are zero. Straightforward application of this theorem shows that all the Newman-Penrose constants of the Kerr-Newman space-time must vanish.

Rotating and counterrotating relativistic thin disks as sources of stationary electrovacuum spacetimes

A detailed study is presented of the counterrotating model (CRM) for electrovacuum stationary axially symmetric relativistic thin disks of infinite extension without radial stress, in the case when the eigenvalues of the energy-momentum tensor of the disk are real quantities, so that there is not heat flow. We find a general constraint over the counterrotating tangential velocities needed to cast the surface energy-momentum tensor of the disk as the superposition of two counterrotating charged dust fluids. We then show that, in some cases, this constraint can be satisfied if we take the two counterrotating tangential velocities as equal and opposite or by taking the two counterrotating streams as circulating along electro-geodesics. However, we show that, in general, it is not possible to take the two counterrotating fluids as circulating along electro-geodesics nor take the two counterrotating tangential velocities as equal and opposite. A simple family of models of counterrotating charged disks based on the Kerr-Newman solution are considered where we obtain some disks with a CRM well behaved. We also show that the disks constructed from the Kerr-Newman solution can be interpreted, for all the values of parameters, as a matter distribution with currents and purely azimuthal pressure without heat flow. The models are constructed using the well-known "displace, cut and reflect" method extended to solutions of vacuum Einstein-Maxwell equations. We obtain, in all the cases, counterrotating Kerr-Newman disks that are in agreement with all the energy conditions.

Why does gravitational radiation produce vorticity?

We calculate the vorticity of worldlines of observers at rest in a Bondi–Sachs frame, produced by gravitational radiation, in a general Sachs metric. We claim that such an effect is related to the super-Poynting vector, in a similar way as the existence of the electromagnetic Poynting vector is related to the vorticity in stationary electrovacuum spacetimes.

The Classification of Static Electro–Vacuum Space–Times Containing an Asymptotically Flat Spacelike Hypersurface with Compact Interior

We show that static electro–vacuum black hole space–times containing an asymptotically flat spacelike hypersurface with compact interior and with both degenerate and non–degenerate components of the event horizon do not exist. This is done by a careful study of the near-horizon geometry of degenerate horizons, which allows us to eliminate the last restriction of the static electro-vacuum no-hair theory.

The asymptotics of stationary electro-vacuum metrics in odd spacetime dimensions

We show that for stationary, asymptotically flat solutions of the electro-vacuum Einstein equations, the Riemannian metric on the quotient space of the timelike Killing vector is analytic at i0, for a large family of gauges, in odd spacetime dimensions larger than 7. The same is true in spacetime dimension 5 for static vacuum solutions with non-vanishing mass.

Frame dragging, vorticity and electromagnetic fields in axially symmetric stationary spacetimes

We present a general study about the relation between the vorticity tensor and the Poynting vector of the electromagnetic field for axially symmetric stationary electrovacuum metrics. The obtained expressions allow us to understand the role of the Poynting vector in the dragging of inertial frames. The particular case of the rotating massive charged magnetic dipole is analysed in detail. In addition, the electric and magnetic parts of the Weyl tensor are calculated and the link between the latter and the vorticity is established. Then we show that, in the vacuum case, the necessary and sufficient condition for the vanishing of the magnetic part is that the spacetime be static.

On the uniqueness of harmonic coordinates

Harmonic coordinate conditions in stationary asymptotically flat spacetimes with matter sources have more than one solution. The solutions depend on the degree of smoothness of the metric and its first derivatives, which we wish to impose across the material boundary, and on the conditions at infinity and at a suitable point inside the matter. This is illustrated in detail by simple fully solvable examples of static spherically symmetric spacetimes in global harmonic coordinates. Examples of stationary electrovacuum spacetimes described simply in harmonic coordinates are also given. They can represent the exterior fields of material discs.The use of an appropriate background metric considerably simplifies the calculations.

String theory extensions of Einstein–Maxwell fields: The stationary case

We present a new approach for generating solutions in heterotic string theory compactified down to three dimensions on a torus with d+n>2, where d and n stand for the number of compactified space–time dimensions and Abelian gauge fields, respectively. It is shown that in the case when d=2k+1, and n is arbitrary, one can apply a solution-generating procedure which consists of mapping seed solutions of the stationary Einstein theory with k Maxwell fields to the heterotic string realm by using pure field redefinitions. A novel feature of this method is that it is precisely the electromagnetic sector of the stationary electrovacuum that mainly gives rise to a nontrivial multidimensional metric. This approach leads to classes of solutions which are invariant with respect to the total group of three-dimensional charging symmetries of the heterotic string theory, i.e., to all finite transformations which generate charged solutions from neutral ones and preserve the asymptotics of the starting field configurations. As an application of the presented approach we generate a particular extension of the stationary Einstein–multi-Maxwell theory obtained on the basis of the Kerr–multi-Newman–NUT special class of solutions and establish the conditions under which the resulting multi-dimensional metric of the heterotic string theory is asymptotically flat.

On the equilibrium of charged masses in general relativity: II. The stationary electrovacuum case

The equilibrium states in the axisymmetric systems of charged, magnetized, aligned, spinning masses are investigated. We show that in the stationary binary systems consisting of a black hole and a hyperextreme object, or of two hyperextreme objects, the equilibrium can exist for the constituents possessing positive Komar masses; at the same time, Smarr's mass formula does not generally hold for the former systems due to a specific behaviour of the magnetic field.

Towards a classification of static electrovacuum spacetimes containing an asymptotically flat spacelike hypersurface with compact interior

We show that static electrovacuum black hole spacetimes containing an asymptotically flat spacelike hypersurface with compact interior and with both degenerate and non-degenerate components of the event horizon do not exist, under the supplementary hypothesis that all degenerate components of the event horizon have charges of the same sign. This extends previous uniqueness theorems of Simon and Masood-ul-Alam (where only non-degenerate horizons were allowed) and Heusler (where only degenerate horizons were allowed).

Factor structure of rational electrovacuum metrics

We consider axisymmetric stationary electrovacuum solutions of Einstein's equations for which the metric functions and the electromagnetic potential are rational in certain coordinate systems. The present case offers a much richer structure than the vacuum case studied previously. It is shown that many, but not all, of the factorizability properties discovered for the vacuum case hold here as well.

New axially symmetric solutions of the Einstein-Maxwell equations

New exact solutions of the algebraic form for the static Einstein-Maxwell equations representing the exterior gravitational field of a massive magnetic dipole are derived. They are then used for construction of the stationary electrovacuum solutions reducing to the Schwarzschild metric in a pure vacuum limit.