Einstein-Maxwell Solutions Research Articles

Non-spinning tops are stable

We consider coupled gravitational and electromagnetic perturbations of a family of five-dimensional Einstein-Maxwell solutions that describes both magnetized black strings and horizonless topological stars. We find that the odd perturbations of this background lead to a master equation with five Fuchsian singularities and compute its quasinormal mode spectrum using three independent methods: Leaver, WKB and numerical integration. Our analysis confirms that odd perturbations always decay in time, while spherically symmetric even perturbations may exhibit for certain ranges of the magnetic fluxes instabilities of Gregory-Laflamme type for black strings and of Gross-Perry-Yaffe type for topological stars. This constitutes evidence that topological stars and black strings are classically stable in a finite domain of their parameter space.

Non-minimally coupled Einstein-Yang-Mills field equations and Wu-Yang monopoles in Bertotti-Robinson spacetimes

Bertotti-Robinson spacetimes are topologically and described by a conformally flat metric. Together with the Coulomb electric potential, they provide a class of static, geodetically complete Einstein-Maxwell solutions. We show here that the Bertotti-Robinson metric together with Wu-Yang magnetic pole potentials give a class of static solutions of a system of non-minimally coupled Einstein-Yang-Mills equations that may be relevant for investigating vacuum polarization effects in a first-order perturbative approach to quantum fields.

Cosmological solutions, a new wick-rotation, and the first law of thermodynamics

We present a modified implementation of the Euclidean action formalism suitable for studying the thermodynamics of a class of cosmological solutions containing Killing horizons. To obtain a real metric of definite signature, we perform a “triple Wick-rotation” by analytically continuing all spacelike directions. The resulting Euclidean geometry is used to calculate the Euclidean on-shell action, which defines a thermodynamic potential. We show that for the vacuum de Sitter solution, planar solutions of Einstein-Maxwell theory and a previously found class of cosmological solutions of mathcal{N} = 2 supergravity, this thermodynamic potential can be used to define an internal energy which obeys the first law of thermodynamics. Our approach is complementary to, but consistent with the isolated horizon formalism. For planar Einstein-Maxwell solutions, we find dual solutions in Einstein-anti-Maxwell theory where the sign of the Maxwell term is reversed. These solutions are planar black holes, rather than cosmological solutions, but give rise, upon a standard Wick-rotation to the same Euclidean action and thermodynamic relations.

Scalar hairy black holes in the presence of nonlinear electrodynamics

We study influence of scalar fields on Nonlinear Electrodynamics spacetimes. The investigation is carried out using both test and gravitating scalar fields. After revisiting Einstein-Maxwell scalar field solutions we focus on analytic investigation of Nonlinear Electrodynamics scalar field spacetimes, especially Square Root Lagrangian model. The main motivation being to understand whether certain specific signatures of scalar fields are preserved when Nonlinear Electrodynamics as an additional source is considered. We show that the regularity of horizon which is spoiled by scalar field in spherically symmetric static scalar-vacuum spacetimes is not improved by including Nonlinear Electrodynamics or other sources satisfying certain condition. We confirm these findings using test scalar field that enables us to go beyond spherical symmetry.

Intermediate scalings for solv, nil, and SL2(R) black branes

In this work we will study black brane solutions that are not translationally invariant in the spatial directions along which it extends. Instead, we require homogeneity, which still allows points along the spatial directions to be related to each other by symmetries. We find Einstein-Maxwell black hole solutions whose near horizon geometry correspond to Solv (Bianchi $V1_{-1}$), Nil (Bianchi $II$) or $SL_2({\cal R})$ (Bianchi $VIII$). Interestingly we observe that at intermediate temperatures our solutions have an scaling regime where different spacetime directions scale differently. We also compute the DC conductivities for these charged solutions and study how they scale in this intermediate regime.

A new class of non-aligned Einstein–Maxwell solutions with a geodesic, shearfree and non-expanding multiple Debever–Penrose vector

In a recent study of algebraically special Einstein–Maxwell fields (Van den Bergh 2017 Gen. Relativ. Gravit. 49 1) it was shown that, for non-zero cosmological constant, non-aligned solutions cannot have a geodesic and shearfree multiple Debever–Penrose vector . When such solutions do exist and can be classified, after fixing the null-tetrad such that and , according to whether the Newman–Penrose coefficient π is 0 or not. The family contains the Griffiths solutions (Griffiths 1986 Gen. Relativ. Gravit. 18 4), with as sub-families the Cahen–Spelkens, Cahen–Leroy and Szekeres metrics. It was claimed in Griffiths (1986 Gen. Relativ. Gravit. 18 4) and repeated in Van den Bergh (2017 Gen. Relativ. Gravit. 49 1) that for both null-rays and are non-twisting (): while it is certainly true that , the case appears to have been overlooked. A family of solutions is presented in which is twisting but non-expanding.

Ultrarelativistic boost of a black hole in the magnetic universe of Levi-Civita–Bertotti–Robinson

We consider an exact Einstein-Maxwell solution constructed by Alekseev and Garcia which describes a Schwarzschild black hole immersed in the magnetic universe of Levi-Civita, Bertotti and Robinson (LCBR). After reviewing the basic properties of this spacetime, we study the ultrarelativistic limit in which the black hole is boosted to the speed of light, while sending its mass to zero. This results in a non-expanding impulsive wave traveling in the LCBR universe. The wave front is a 2-sphere carrying two null point particles at its poles -- a remnant of the structure of the original static spacetime. It is also shown that the obtained line-element belongs to the Kundt class of spacetimes, and the relation with a known family of exact gravitational waves of finite duration propagating in the LCBR background is clarified. In the limit of a vanishing electromagnetic field, one point particle is pushed away to infinity and the single-particle Aichelburg-Sexl pp-wave propagating in Minkowski space is recovered.

The classical double copy in maximally symmetric spacetimes

The classical double copy procedure relates classical asymptotically-flat gravitational field solutions to Yang-Mills and scalar field solutions living in Minkowski space. In this paper we extend this correspondence to maximally symmetric curved spacetimes. We consider asymptotically (A)dS spacetimes in Kerr-Schild form and construct the corresponding single and zeroth copies. In order to clarify the interpretation of these copies, we study several examples including (A)dS-Schwarzschild, (A)dS-Kerr, black strings, black branes, and waves, paying particular attention to the source terms. We find that the single and zeroth copies of stationary solutions satisfy different equations than those of wave solutions. We also consider how to obtain Einstein-Maxwell solutions using this procedure. Finally, we derive the classical single and zeroth copy of the BTZ black hole.

Non-static spherically symmetric exact solution of the Einstein-Maxwell field equations

We present a class of exact spherically symmetric and non-static solutions of Einstein-Maxwell’s field equations. We have assumed isotropic pressure distribution and have taken ansatz on two of the gravitational potentials. The solutions admit negative pressure. We show that the solutions satisfy physical boundary conditions associated with the Einstein-Maxwell exact solutions. Therefore, these solutions can model physical systems such as moving dark energy stars.

Euclidean supergravity and multi-centered solutions

In ungauged supergravity theories, the no-force condition for BPS states implies the existence of stable static multi-centered solutions. The first solutions to Einstein-Maxwell theory with a positive cosmological constant describing an arbitrary number of charged black holes were found by Kastor and Traschen. Generalisations to five and higher dimensional theories were obtained by London. Multi-centered solutions in gauged supergravity, even with time-dependence allowed, have yet to be constructed. In this letter we construct supersymmetry-preserving multi-centered solutions for the case of D=5, N=2 Euclidean gauged supergravity coupled to an arbitrary number of vector multiplets. Higher dimensional Einstein-Maxwell multi-centered solutions are also presented.

Labeling spherically symmetric spacetimes with the Ricci tensor

We complete the intrinsic characterization of spherically symmetric solutions partially accomplished in a previous paper (Ferrando and Sáez 2010 Class. Quantum Grav. 27 205024). In this approach we consider every compatible algebraic type of the Ricci tensor, and we analyze specifically the conformally flat case for perfect fluid and Einstein–Maxwell solutions. As a direct application we obtain the ideal labeling (exclusively involving explicit concomitants of the metric tensor) of the Schwarzschild interior metric and the Vaidya solution. The Stephani universes and some significative subfamilies are also characterized.

Strongly Hermitian Einstein–Maxwell solutions on ruled surfaces

This paper produces explicit strongly Hermitian Einstein–Maxwell solutions on the smooth compact 4-manifolds that are $$S^2$$ -bundles over compact Riemann surfaces of any genus. This generalizes the existence results by LeBrun (J Geom Phys 91:163–171, 2015, The Einstein–Maxwell equations and conformally Kaehler geometry. arXiv:1504.06669 , 2016). Moreover, by calculating the (normalized) Einstein–Hilbert functional of our examples, we generalize Theorem E of LeBrun (The Einstein–Maxwell equations and conformally Kaehler geometry. arXiv:1504.06669 , 2016), which speaks to the abundance of Hermitian Einstein–Maxwell solutions on such manifolds. As a bonus, we exhibit certain pairs of strongly Hermitian Einstein–Maxwell solutions, first found in LeBrun (The Einstein–Maxwell equations and conformally Kaehler geometry. arXiv:1504.06669 , 2016), on the first Hirzebruch surface in a form which clearly shows that they are conformal to a common Kahler metric. In particular, this yields a non-trivial example of non-uniqueness of positive constant scalar curvature metrics in a given conformal class.

The nuts and bolts of Einstein-Maxwell solutions

We find new non-supersymmetric solutions of five-dimensional ungauged supergravity coupled to two vector multiplets. The solutions are regular, horizonless and have the same asymptotic charges as non-extremal charged black holes. An essential ingredient in our construction is a four-dimensional Euclidean base which is a solution to Einstein-Maxwell equations. We construct stationary solutions based on the Euclidean dyonic Reissner-Nordstrom black hole as well as a six-parameter family with a dyonic Kerr-Newman-NUT base. These solutions can be viewed as compactifications of eleven-dimensional supergravity on a six-torus and we discuss their brane interpretation.

Energy contents of some non-vacuum spacetimes in teleparallel gravity

This paper elaborates the problem of energy-momentum in the framework of teleparallel equivalent of General Relativity. For this purpose, we consider energy-momentum prescription derived from the integral form of the constraint equations developed in the Hamiltonian formulation of the teleparallel equivalent of General Relativity. We use this technique to investigate energy-momentum of stationary axisymmetric Einstein-Maxwell solutions and cosmic string spacetimes. The angular momentum, gravitational and matter energy-momentum fluxes of these spacetimes are also evaluated. It is concluded that the results of teleparallel theory are relatively analogous to the results of General Relativity.

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.

Rainich theory for type D aligned Einstein–Maxwell solutions

The original Rainich theory for the non-null Einstein–Maxwell solutions consists of a set of algebraic conditions and the Rainich (differential) equation. We show here that the subclass of type D aligned solutions can be characterized just by algebraic restrictions.

Classes of exact Einstein–Maxwell solutions

We find new classes of exact solutions to the Einstein–Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein–Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.

Analyticity of strictly static and strictly stationary, inheriting and non-inheriting Einstein–Maxwell solutions

Following the technique of Müller zum Hagen (Proc. Camb. Phil. Soc. 67: 415–421, 1970) we show that strictly static and strictly stationary solutions of the Einstein–Maxwell equations are analytic in harmonic coordinates. This holds whether or not the Maxwell field inherits the symmetry.

Magnetovac cylinder to magnetovac torus

A method for mapping known cylindrical magnetovac solutions to solutions in torus coordinates is developed. Identification of the cylinder ends changes topology from R1 × S1 to S1 × S1. An analytic Einstein–Maxwell solution for a toroidal magnetic field in tori is presented. The toroidal interior is matched to an asymptotically flat vacuum exterior, connected by an Israel boundary layer.

Completely integrable sector in 5D Einstein-Maxwell gravity and derivation of the dipole black ring solutions

We consider 5D Einstein-Maxwell (EM) gravity in spacetimes with three commuting Killing vectors: one timelike and two spacelike Killing vectors one of them being hypersurface orthogonal. Assuming a special ansatz for the Maxwell field we show that the 2-dimensional reduced EM equations are completely integrable by deriving a Lax-pair presentation. We also develop a solution generating method for explicit construction of exact EM solutions with considered symmetries. We also derive explicitly a new rotating six parametric 5D EM solution which includes the dipole black ring solution as a particular case.