Electrovacuum Spacetimes Research Articles

On the stability of electrovacuum space-times in scalar–tensor gravity

We study the behavior of static, spherically symmetric solutions to the field equations of scalar–tensor theories (STT) of gravity belonging to the Bergmann–Wagoner–Nordtvedt class, in the presence of an electric and/or magnetic charge. This class of theories includes the Brans–Dicke, Barker and Schwinger STT as well as nonminimally coupled scalar fields with an arbitrary parameter ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document}. The study is restricted to canonical (nonphantom) versions of the theories and scalar fields without a self-interaction potential. Only radial (monopole) perturbations are considered as the most likely ones to cause an instability. The static background solutions contain naked singularities, but we formulate the boundary conditions in such a way that would preserve their meaning if a singularity is smoothed, for example, due to quantum gravity effects. These boundary conditions look more physical than those used by other authors. Since the solutions of all STT under study are related by conformal transformations, the stability problem for all of them reduces to the same wave equation, but the boundary conditions for perturbations (and sometimes the boundaries themselves) are different in different STT, which affects the stability results. The stability or instability conclusions are obtained for different branches of solutions in the theories under consideration and are presented in a table form.

Scalar fields in Bonnor-Melvin-Lambda universe with potential: a study of dynamics of spin-zero particles-antiparticles

In this study, our primary focus is on exploring the relativistic quantum dynamics of spin-zero scalar particles in a magnetic space-time background. Our investigation revolves around solving the Klein–Gordon (KG) equation within the framework of an electrovacuum space-time, while incorporating an external scalar potential. Specifically, we consider a cylindrical symmetric Bonnor-Melvin magnetic universe featuring a cosmological constant, where the magnetic field aligns parallel to the symmetry axis. Our approach involves deriving the radial equation of the wave equation, initially considering a linear confining potential and subsequently incorporating a Cornell-type scalar potential. We successfully obtain an approximate analytical solution for the eigenvalues of the quantum system under examination. Worth noting is our observation that the energy spectrum and the corresponding radial wave function experience notable modifications due to the presence of various factors including the cosmological constant, the topological parameter characterizing the space-time geometry, and the potential parameters.

Bach equation and the matching of spacetimes in conformal cyclic cosmology models

We consider the problem of matching two spacetimes, the previous and present aeons, in the Conformal Cyclic Cosmology model. The common boundary between them inherits two sets of constraints -- one for each solution of the Einstein field equations extended to the conformal boundaries. The previous aeon is assumed to be an asymptotically de Sitter spacetime, so the standard conformal formulation of the Einstein field equations suffice to derive the constraints on the future null infinity. For the future aeon, which is supposed to evolve from an initial singularity, they are obtained with the use of the Bach equation. This equation is regular at the past conformal infinity for conformally flat and conformally Einstein spacetimes, so we will mostly focus on them here. An example of the electrovacuum spacetime which does not fall into this class and has regular conformal Bach tensor will be discussed in the appendix.

The relations between the multipole moments in axistationary electrovacuum spacetimes and the N-soliton solution

A general formulation of the relativistic multipole moments in axistationary electrovac spacetimes is introduced in a closed analytical form. We give a complete description of how the Ernst potentials on the symmetry axis can be completely characterized by these arbitrary multipole moments. Some concrete applications are also developed.

Calculation of multipole moments of axistationary electrovacuum spacetimes

The multipole moments of stationary axially symmetric vacuum or electrovacuum spacetimes can be expressed in terms of the power series expansion coefficients of the Ernst potential on the axis. In this paper we present a simpler, more efficient calculation of the multipole moments, applying methods introduced by B\"ackdahl and Herberthson. For the nonvacuum electromagnetic case, our results for the octupole and higher moments differ from the results already published in the literature. The reason for this difference is that we correct an earlier unnoticed mistake in the power series solution of the Ernst equations. We also apply the presented method to directly calculate the multipole moments of a five-parameter charged magnetized generalization of the Kerr and Tomimatsu-Sato exact solutions.

Double shadows of reflection-asymmetric wormholes supported by positive energy thin-shells

We consider reflection-asymmetric thin-shell wormholes within Palatini f(R) gravity using a matching procedure of two patches of electrovacuum space-times at a hypersurface (the shell) via suitable junction conditions. The conditions for having (linearly) stable wormholes supported by positive-energy matter sources are determined. We also identify some subsets of parameters able to locate the shell radius above the event horizon (when present) but below the photon sphere (on both sides). We illustrate with an specific example that such two photon spheres allow an observer on one of the sides of the wormhole to see another (circular) shadow in addition to the one generated by its own photon sphere, which is due to the photons passing above the maximum of the effective potential on its side and bouncing back across the throat due to a higher effective potential on the other side. We finally comment on the capability of these double shadows to seek for traces of new gravitational physics beyond that described by General Relativity.

Deconstructing Frame-Dragging

The vorticity of world-lines of observers associated with the rotation of a massive body was reported by Lense and Thirring more than a century ago. In their example, the frame-dragging effect induced by the vorticity is directly (explicitly) related to the rotation of the source. However, in many other cases, it is not so, and the origin of vorticity remains obscure and difficult to identify. Accordingly, in order to unravel this issue, and looking for the ultimate origin of vorticity associated to frame-dragging, we analyze in this manuscript very different scenarios where the frame-dragging effect is present. Specifically, we consider general vacuum stationary spacetimes, general electro-vacuum spacetimes, radiating electro-vacuum spacetimes, and Bondi–Sachs radiating spacetimes. We identify the physical quantities present in all these cases, which determine the vorticity and may legitimately be considered as responsible for the frame-dragging. Doing so, we provide a comprehensive, physical picture of frame-dragging. Some observational consequences of our results are discussed.

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.

Enhanced Ehlers transformation and the Majumdar-Papapetrou-NUT spacetime

The transformation which adds (or removes) NUT charge when it is applied to electrovacuum, axisymmetric and stationary space-times is studied. After analysing the Ehlers and the Reina-Treves transformations we propose a new one, more precise in the presence of the Maxwell electromagnetic field. The enhanced Ehlers transformation proposed turns out to act as a gravitomagnetic duality, analogously to the electromagnetic duality, but for gravity: it rotates the mass charge into the gravomagnetic (or NUT) charge. As an example the Kerr-Newman-NUT black hole is obtained with the help of this enhanced transformation. Moreover a new analytical exact solution is built adding the NUT charge to a double charged black hole, at equilibrium. It describes the non-extremal generalisation of the Majumdar-Papapetrou-NUT solution. From the near-horizon analysis, its microscopic entropy, according to the Kerr/CFT correspondence, is found and the second law of black hole thermodynamics is discussed.

Photon sphere uniqueness in higher-dimensional electrovacuum spacetimes

We show a uniqueness result for the n-dimensional spatial Reissner–Nordström manifold: a static, electrovacuum, asymptotically flat system which is asymptotically Reissner–Nordström is a subextremal Reissner–Nordström manifold with positive mass, provided that its inner boundary is a (possibly disconnected) photon sphere that fulfils a suitably defined quasilocal subextremality condition.Our result implies a number of earlier uniqueness results for the Schwarzschild and the Reissner–Nordström manifolds in the static, (electro-)vacuum, asymptotically flat context, both for photon sphere and black hole inner boundaries, in the tradition of Bunting–Masood-ul Alaam (1987 Gen. Relativ. Gravit. 19 147–54) and Ruback (1988 Class. Quantum Grav. 5 L155–9). The proof relies on the ideas from those works, combined with newer techniques developed by Cederbaum and Galloway (2017 Commun. Anal. Geom. 25 303–20) and Cederbaum (in progress). The author kindly made a draft available to us.

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.

Stable photon orbits in stationary axisymmetric electrovacuum spacetimes

We investigate the existence and phenomenology of stable photon orbits (SPOs) in stationary axisymmetric electrovacuum spacetimes in four dimensions. First, we review the classification of equatorial circular photon orbits on Kerr-Newman spacetimes in the charge-spin plane. Second, using a Hamiltonian formulation, we show that Reissner-Nordstr\"om di-holes (a family encompassing the Majumdar-Papapetrou and Weyl-Bach special cases) admit SPOs, in a certain parameter regime that we investigate. Third, we explore the transition from order to chaos for typical SPOs bounded within a toroidal region around a di-hole, via a selection of Poincar\'e sections. Finally, for general axisymmetric stationary spacetimes, we show that the Einstein-Maxwell field equations allow for the existence of SPOs in electrovacuum; but not in pure vacuum.

Asymptotical null structure of an electro-vacuum spacetime with a cosmological constant

Bondi–Sachs (BS) framework is a powerful tool to analyze the asymptotical null structure of a spacetime. Based on Bondi’s outgoing boundary condition, the asymptotical null structure of an electro-vacuum spacetime without a cosmological constant has been constructed clearly. Recently more and more observations imply that the Einstein equation should be modified with an nonzero cosmological constant. It is interesting to investigate the asymptotical null structure of a spacetime with a cosmological constant. In this paper, we extend our previous result from vacuum case to electro-vacuum case. We find that the gravitational sector of the asymptotical null structure depends strongly on the boundary conditions, while the electrical sector is independent of the boundary condition.

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.

Spherically symmetric conformal gravity and ``gravitational bubbles''

The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson-Walker metrics. One of them we called the ``gravitational bubbles'', which is compact and with zero Weyl tensor. Thus, we obtained the pure vacuum curved space-times (without any material sources, including the cosmological constant) what is absolutely impossible in General Relativity. Such a phenomenon makes it easier to create the universe from ``nothing''. The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family. It appears that it can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We also investigated the general structure of the energy-momentum tensor in the spherical conformal gravity and constructed the vectorial equation that reveals clearly some features of non-vacuum solutions. Two of them are explicitly written, namely, the metrics à la Vaidya, and the electrovacuum space-time metrics.

Stationary axially symmetric solutions in Brans-Dicke theory

Stationary, axially symmetric Brans-Dicke-Maxwell solutions are reexamined in the framework of the Brans-Dicke (BD) theory. We see that, employing a particular parametrization of the standard axially symmetric metric simplifies the procedure of obtaining the Ernst equations for axially symmetric electrovacuum space-times for this theory. This analysis also permits us to construct a two parameter extension in both Jordan and Einstein frames of an old solution generating technique frequently used to construct axially symmetric solutions for BD theory from a seed solution of general relativity. As applications of this technique, several known and new solutions are constructed including a general axially symmetric BD-Maxwell solution of Plebanski-Demianski with vanishing cosmological constant, i.e. the Kinnersley solution and general magnetized Kerr-Newman--type solutions. Some physical properties and the circular motion of test particles for a particular subclass of Kinnersley solution, i.e., a Kerr-Newman-NUT--type solution for BD theory, are also investigated in some detail.

On a zero-gravity limit of the Kerr–Newman spacetimes and their electromagnetic fields

We discuss the limit of vanishing G (Newton’s constant of universal gravitation) of the maximal analytically extended Kerr–Newman electrovacuum spacetimes represented in Boyer–Lindquist coordinates. We investigate the topologically nontrivial spacetime M0 emerging in this limit and show that it consists of two copies of flat Minkowski spacetime cross-linked at a timelike solid cylinder (spacelike 2-disk × timelike ℝ). As G → 0, the electromagnetic fields of the Kerr–Newman spacetimes converge to nontrivial solutions of Maxwell’s equations on this background spacetime M0. We show how to obtain these fields by solving Maxwell’s equations with singular sources supported only on a circle in a spacelike slice of M0. These sources do not suffer from any of the pathologies that plague the alternate sources found in previous attempts to interpret the Kerr–Newman fields on the topologically simple Minkowski spacetime. We characterize the singular behavior of these sources and prove that the Kerr–Newman electrostatic potential and magnetic scalar potential are the unique solutions of the Maxwell equations among all functions that have the same blow-up behavior at the ring singularity.

Black hole hair in Lovelock gravity

We present a method to analyse black hole hair in the spherical symmetric sector of the Lovelock theory in arbitrary dimensions that is an alternative to solving the equations of motion in their complete form. We explicitly show that the method matches with the known black hole solutions for the vacuum and electro-vacuum spacetimes in Lovelock gravity theories. We further apply the method to the case of minimally coupled non-self-interacting massless scalar field and prove that there is no (non-self-interacting) massless scalar hair for the spherically symmetric Lovelock black holes.

Stationary black holes as holographs II

Within the generic null characteristic initial value problem a reduced set of the evolution equations are deduced from the coupled Newman–Penrose and Maxwell equations for smooth four-dimensional electrovacuum spacetimes allowing a non-zero cosmological constant. It is shown that these reduced equations make up a first-order symmetric hyperbolic system of evolution equations, and also that the solutions to this reduced system are also solutions to the full set of the Newman–Penrose and Maxwell equations provided that the inner equations hold on the initial data surfaces. The derived generic results are applied in carrying out the investigation of electrovacuum spacetimes distinguished by the existence of a pair of null hypersurfaces, and , generated by expansion and shear-free geodesically complete null congruences such that they intersect on a two-dimensional spacelike surface, . Besides the existence of this pair of null hypersurfaces, no assumption concerning the asymptotic structure is made. It is shown that both the spacetime geometry and the electromagnetic field are uniquely determined, in the domain of dependence of once a complex vector field ξA (determining the metric induced on ), the τ spin coefficient and the ϕ1 electromagnetic potential are specified on . The existence of a Killing vector field—with respect to which the null hypersurfaces and comprise a bifurcate-type Killing horizon—is also justified in the domain of dependence of . Since, in general, the freely specifiable data on do not have any sort of symmetry, the corresponding spacetimes do not possess any symmetry in addition to the horizon Killing vector field. Thereby, they comprise the class of generic ‘stationary’ distorted electrovacuum black hole spacetimes which for the case of a positive cosmological constant may also (or, in certain cases, only) contain a distorted de Sitter-type cosmological horizon to which our results equally apply. It is also shown that there are stationary distorted electrovacuum black hole configurations such that parallelly propagated curvature blow-up occurs both to the future and to the past ends of some of the null generators of their bifurcate Killing horizon, and also that this behavior is universal. In particular, it is shown that in the space of vacuum solutions to Einstein’s equations, in an arbitrarily small neighborhood of the Schwarzschild solution this type of distorted vacuum black hole configurations always exist. A short discussion on the relation of these results and some of the recent claims on the instability of extremal black holes is also given.