Merab Gogberashvili
New exact solution of the cylindrically symmetric Einstein-Maxwell equations is presented. The solution is singular on the axis of symmetry and at the radial infinity, where sources should be placed. The accepted source at the origin can be interpreted as a charged domain wall shell.
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We present static cylindrically symmetric electrovac solutions in the framework of the Brans-Dicke theory and show that our solution yields some of the well-known solutions for special values of the parameters of the resulting metric functions.
A reduction of the Dirac-Maxwell equations in the case of static cylindrical symmetry is performed. The behaviour of the resulting system of o.d.e.'s is examined analytically and numerical solutions presented. There are two classes of solutions. The first type of solution is a Dirac field surrounding a charged "wire". The Dirac field is highly localised, concentrated in cylindrical shells about the wire. A comparison with the usual linearized theory demonstrates that this localization is entirely due to the non-linearities in the equations which result from the inclusion of the "self-field". T…
We consider the existence of Einstein-Maxwell-dilaton plus fluid system for the case of stationary cylindrically symmetric spacetimes. An exact inhomogeneous $ ε$-order solution is found, where the parameter $ε$ parametrizes the non-minimally coupled electromagnetic field. Some its physical attributes are investigated and a connection with already known Gödel-type solution is given. It is shown that the found solution also survives in the string-inspired charged gravity framework. We find that a magnetic field has positive influence on the chronology violation unlike the dilaton influence.
This paper is an extended and more detailed version of arXiv:0812.0533. We tackle the problem of constructing explicit examples of topological cocycles of Roberts' net cohomology, as defined abstractly by Brunetti and Ruzzi. We consider the simple case of massive bosonic quantum field theory on the two dimensional Einstein cylinder. After deriving some crucial results of the algebraic framework of quantization, we address the problem of the construction of the topological cocycles. All constructed cocycles lead to unitarily equivalent representations of the fundamental group of the circle (see…
In this paper, Brans-Dicke-Maxwell type vacuum solutions are considered for a static cylindrically symmetric spacetime in arbitrary dimensions. Exact solutions are obtained by directly solving the field equations for the case where an azimuthal magnetic field is present. Other configurations such as axial magnetic field case can be obtained by suitably relabeling the coordinates. We have also considered conformally related "Einstein frame" to relate the solutions we have obtained with the dilaton-Maxwell type solutions that exist in the literature. We see that for a special case the general so…
We classify super-symmetric solutions of the minimal $N=2$ gauged Euclidean supergravity in four dimensions. The solutions with anti-self-dual Maxwell field give rise to anti-self-dual Einstein metrics given in terms of solutions to the $SU(\infty)$ Toda equation and more general three-dimensional Einstein--Weyl structures. Euclidean Kastor--Traschen metrics are also characterised by the existence of a certain super covariantly constant spinor.
A new solution to the Einstein-Maxwell field equations is presented describing a cylindrically symmetric homogeneous cosmology. The solution is conformally flat, it possesses seven Killing vectors of which the timelike one is rotating and one of the spacelike, pseudorotating. Our solution also admits a Kerr-Schild form. It is alternatively produced by different electromagnetic sources some of which represent constant null electromagnetic fields, while the others, a circularly polarized plane electromagnetic wave (seemingly, a unique situation in general relativity). The concrete electromagneti…
An exact plane-symmetric non-stationary solution to the Einstein-Maxwell equations for a magnetoactive plasma is obtained and studied.
In the framework of J-bundles a vielbein formulation of unified Einstein-Maxwell theory is proposed. In the resulting scheme, field equations matching the gravitational and electromagnetic fields are derived by constraining a five-dimensional variational principle. No dynamical scalar field is involved.
Here we describe a stationary cylindrically symmetric solution of Einstein's equation with matter consisting of a positive cosmological and rotating dust term. The solution approaches Einstein static universe solution.
We report a new family of solutions to Einstein-Maxwell-dilaton gravity in 2+1 dimensions and Einstein-Maxwell gravity with cylindrical symmetry in 3+1 dimensions. A set of static charged solutions in 2+1 dimensions are obtained by a compactification of charged solutions in 3+1 dimensions with cylindrical symmetry. These solutions contain naked singularities for certain values of the parameters considered. New rotating charged solutions in 2+1 dimensions and 3+1 dimensions are generated treating the static charged solutions as seed metrics and performing $SL(2;R)$ transformations.
In the present paper we investigate the general problem of uniqueness of the stationary black solutions in 5D Einstein-Maxwell-dilaton gravity with arbitrary dilaton coupling parameter containing the Einstein-Maxwell gravity as a particular case. We formulate and prove uniqueness theorems classifying the stationary black hole solutions in terms of their interval structure, electric and magnetic charges and the magnetic fluxes. The proofs are based on the nonpositivity of the Riemann curvature operator on the space of the potentials which imposes restrictions on the dilaton coupling parameter.
We investigated numerically dyon-like solutions of the SU(2) Einstein-Yang-Mills system on a cylindrically symmetric space time with a cosmological constant. We find a new kind of behaviour not found in the spherically symmetric models. For positive values of $Λ$ we have an oscillatory behaviour of the magnetic component of the YM field around the r-axis, so there is an arbitrary number of nodes. For increasing positive $Λ$, the frequency increases also and the solution breaks down at finite radius, indicating a singularity. The electric component, however, approaches a constant value. After f…
Global existence to the coupled Einstein-Maxwell-Massive Scalar Field system which rules the dynamics of a kind of charged pure matter in the presence of a massive scalar field is proved, in Bianchi I-VIII spacetimes; asymptotic behaviour, geodesic completeness, energy conditions are investigated in the case of a cosmological constant bounded from below by a strictly negative constant depending only on the massive scalar field.
I present a new method to generate rotating solutions of the Einstein--Maxwell equations from static solutions, and briefly discuss its general properties.
The uniqueness theorem for static, spherically symmetric, asymptotically flat, higher dimensional phantom black holes, with non-degenerate event horizon , being the solutions of Einstein phantom/dilaton Maxwell/anti-Maxwell gravity systems is considered. Conformal positive energy theorem and conformal transformations authorize the crucial tools for exploiting the boundary conditions and conformal flatness.
In this article a new stationary cylindrically symmetric solution of the Einstein's field equations with cosmological constant and Time machine is given. The garavitational field is created by ideal liquid with three massless scalar fields or by ideal liquid with electric-magnetic field and massless scalar field.
Cylindrically reduced Einstein gravity can be regarded as an $SL(2,R)/SO(2)$ sigma model coupled to 2D dilaton gravity. By using the corresponding 2D diffeomorphism algebra of constraints and the asymptotic behaviour of the Ernst equation we show that the theory can be mapped by a canonical transformation into a set of free fields with a Minkowskian target space. We briefly discuss the quantization in terms of these free-field variables, which is considerably simpler than in the other approaches.
In this summary article, we review and discuss the non-existence of stationary black hole solutions for the Einstein-Dirac-Maxwell equations.
We prove that in Einstein-Maxwell theory the inequality $(8πJ)^2+(4πQ^2)^2 < A^2$ holds for any sub-extremal axisymmetric and stationary black hole with arbitrary surrounding matter. Here $J, Q$, and $A$ are angular momentum, electric charge, and horizon area of the black hole, respectively.
We obtain charged rotating black hole solutions to the theory of Einstein-Maxwell gravity with cosmological constant in five dimensions. Some of the physical properties of these black holes are discussed.
We present a class of magnetically charged brane solutions for the theory of Einstein-Maxwell gravity with a negative cosmological constant in an arbitrary number of spacetime dimensions.
We study generalisations of the Einstein--Straus model in cylindrically symmetric settings by considering the matching of a static space-time to a non-static spatially homogeneous space-time, preserving the symmetry. We find that such models possess severe restrictions, such as constancy of one of the metric coefficients in the non-static part. A consequence of this is that it is impossible to embed static locally cylindrically symmetric objects in reasonable spatially homogeneous cosmologies.
It is shown that all homogeneous pure radiation solutions to the Einstein equations admit electromagnetic sources. This corrects an error in the literature.
We consider a static self-gravitating charged perfect fluid system in the Einstein-Maxwell theory. Assume Maxwell's equation and the Einstein constraint equation are satisfied, and the temperature of the fluid obeys Tolman's law. Then we prove that the total entropy of the fluid achieves an extremum implies other components of Einstein's equation for any variations of metric and electrical potential with fixed boundary values. Conversely, if Einstein's equation and Maxwell's equations hold, the total entropy achieves an extremum. Our work suggests that the maximum entropy principle is consiste…
A class of time dependent solutions to $(3+1)$ Einstein--Maxwell-dilaton theory with attractive electric force is found from Einstein--Weyl structures in (2+1) dimensions corresponding to dispersionless Kadomtsev--Petviashvili and $SU(\infty)$ Toda equations. These solutions are obtained from time--like Kaluza--Klein reductions of $(3+2)$ solitons.
We study Kerr-Schild-Kundt class of metrics in generic gravity theories with Maxwell's field. We prove that these metrics linearize and simplify the field equations of generic gravity theories with Maxwell's field.
Exact black hole solutions in the Einstein-Maxwell-scalar theory are constructed. They are the extensions of dilaton black holes in de Sitter or anti de Sitter universe. As a result, except for a scalar potential, a coupling function between the scalar field and the Maxwell invariant is present. Then the corresponding Smarr formula and the first law of thermodynamics are investigated.
We show that one-parameter family of Godel-type metrics are exact solutions in a wide class of Einstein-Maxwell-scalar field theories. In these solutions, the gauge field has a 1-form expectation value parallel to the timelike contact form that represents the rotation of the Godel universe.
Perfect-fluid, static, cylindrically symmetric solutions of Einstein's field equations are obtained for the equations of state $ρ+3p=0$ and $ρ=p$. In the former case, the density and the pressure turn out to be constant while in the later case, they depend on the radial parameter $r$. Evan's solution corresponding to the equation of state $ρ=p$ is included in the solutions discussed here.
In the present paper we consider 5D spacetimes satisfying the Einstein-Maxwell-dilaton gravity equations which are $U(1)^2$ axisymmetric but otherwise highly dynamical. We derive inequalities between the area, the angular momenta, the electric charge and the magnetic fluxes for any smooth stably outer marginally trapped surface.
We prove that any asymptotically flat static spacetime in higher dimensional Einstein-Maxwell theory must have no magnetic field. This implies that there are no static soliton spacetimes and completes the classification of static non-extremal black holes in this theory. In particular, these results establish that there are no asymptotically flat static spacetimes with non-trivial topology, with or without a black hole, in Einstein-Maxwell theory.
We compute the second Seely-DeWitt coefficient of the kinetic operator of the metric and gauge fields in Einstein-Maxwell theory in an arbitrary background field configuration. We then use this result to compute the logarithmic correction to the entropy of an extremal Kerr-Newmann black hole.
We prove the uniqueness theorem for stationary axisymmetric black hole solution in Einstein-Maxwell-axion-dilaton gravity being the low-energy limit of the heterotic string theory. We consider both non-degenerate and extremal Kerr-Sen black hole solutions.
Depending on five parameters, rotating counterparts of Einstein--Maxwell--dilaton black holes are derived. We discuss their physical and geometric properties and investigate their null and time-like geodesics including circular orbits. The Lense--Thirring effect is considered.
The scalarization of Reissner-Nordström black holes was recently proposed in the Einstein-Maxwell-scalar theory. Here, we show that the appearance of the scalarized Reissner-Nordström black hole is closely related to the Gregory-Laflamme instability of the Reissner-Nordström black hole without scalar hair.
In the present paper we prove a uniqueness theorem for stationary multi black hole configurations with Kaluza-Klein asymptotic in a certain sector of 5D Einstein-Maxwell gravity. We show that such multi black hole configurations are uniquely specified by the interval structure, angular momenta of the horizons, magnetic charges and the magnetic flux. A straightforward generalization of the uniqueness theorem for 5D Einstein-Maxwell-dilaton gravity is also given.
In this paper, under spherical symmetry we prove a trapped surface formation criterion for the Einstein-Maxwell-charged scalar field system. We generalize an approach introduced by Christodoulou for studying the Einstein-scalar field. In appendix, with double null foliation we also reprove Christodoulou's result and for Minkowskian incoming characteristic initial data, we improve Christodoulou's bound.
The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical solutions satisfying the dominant energy conditions. Furthermore, we show that the solutions can be matched at a finite radius to suitable $Λ$-vacuum exteriors given by the Linet-Tian spacetime.
We consider spherically symmetric and static charged black holes in Einstein-Gauss-Bonnet-Maxwell gravities in general $D\ge 5$ dimensions and study their photon spheres and black hole shadows. We show that they all satisfy the sequence of inequalities recently proposed relating a black hole's horizon, photon sphere, shadow and its mass.
We proved that strictly stationary Einstein-Maxwell-axion-dilaton spacetime with negative cosmological constant could not support a nontrivial configuration of complex scalar fields. We considered the general case of the arbitrary number of U(1) gauge fields in the theory under consideration.
Metrics depending on one variable in D-dimensional Einstein-Maxwell Theory
提出了D维Einstein-Maxwell理论中适用于所有时空符号且依赖单变量的新解族，可视为包含通量管、畴壁和宇宙学时空的广义Melvin解，并在四维和五维时空中给出了显式示例。
We report a new class of rotating charged solutions in 2+1 dimensions. These solutions are obtained for Einstein-Maxwell gravity coupled to a dilaton field with selfdual electromagnetic fields. The mass and the angular momentum of these solutions computed at spatial infinity are finite. The class of solutions considered here have naked singularities and are asymptotically flat.
The uniqueness of static asymptotically flat photon sphere for static black hole solution in Einstein-Maxwell-dilaton theory with arbitrary coupling constant was proposed. Using the conformal positive energy theorem we show that the dilaton sphere subject to the non-extremality condition authorizes a cylinder over a topological sphere.
The uniqueness of static spherically symmetric traversable wormholes with two asymptotically flat ends, subject to the higher-dimensional solutions of Einstein-Maxwell-phantom dilaton field equations was proved. We considered the case of an arbitrary dilaton coupling constant. Conformal positive energy theorem plays the key role in the considerations.
Avoiding the problem of the existence of asymptotically constant spinors satysfying certain differential equations on a non-compact hypersrface we presented the proof of positivity of the ADM and Bondi energy in Einstein-Maxwell axion-dilaton gravity. In our attitude spinor fields defining the enwergy need only be defined near infinity and there satysfying propagation equations.
We consider the problem for the classification of static and asymptotically flat Einstein-Maxwell-dilaton spacetimes with a photon sphere. It is first proven that the photon spheres in Einstein-Maxwell-dilaton gravity have constant mean and constant scalar curvature. Then we derive some relations between the mean curvature and the physical characteristics of the photon spheres. Using further the symmetries of the dimensionally reduced Einstein-Maxwell-dilaton field equations we show that the lapse function, the electrostatic potential and the dilaton field are functionally dependent in the pre…
We construct exact solutions to five-dimensional Einstein-Maxwell theory based on Atiyah-Hitchin space. The solutions cannot be written explicitly in a closed form, so their properties are investigated numerically. The five-dimensional metric is regular everywhere except on the location of original bolt in four-dimensional Atiyah-Hitchin base space. On each time-fixed slices, the metric, asymptotically approaches an Euclidean Taub-NUT space.
We construct exact solutions, which represent regular charged rotating Kaluza-Klein multi-black holes in the five-dimensional pure Einstein-Maxwell theory. Quantization conditions between the mass, the angular momentum, and charges appear from the regularity condition of horizon. We also obtain multi-black string solutions by taking some limits in the solutions. We extend the black hole solutions to the five-dimensional Einstein-Maxwell-Chern-Simons theory with an arbitrary Chern-Simons coupling constant.
We construct new supersymmetric solutions to the Euclidean Einstein-Maxwell theory with a non-vanishing cosmological constant, and for which the Maxwell field strength is neither self-dual or anti-self-dual. We find that there are three classes of solutions, depending on the sign of the Maxwell field strength and cosmological constant terms in the Einstein equations which arise from the integrability conditions of the Killing spinor equation. The first class is a Euclidean version of a Lorentzian supersymmetric solution found in arXiv:0804.0009, hep-th/0406238 . The second class is constructed…
We prove that there exists no aligned Einstein Maxwell generalization of the spherical class of Newman Tamburino solutions. The presence of an aligned Maxwell field automatically leads to the cylindrical class.
We examine cancellation of long-range forces in Einstein-Maxwell-Dilatonic system. Several conditions of the equilibrium of two charged masses in general relativity is found by many authors. These conditions are altered by taking account of dilatonic field. Under the new condition, we show cancellation of $1/r^2$ potential using Feynman diagrams.
We construct higher dimensional and exact black holes in Einstein-Maxwell-scalar-theory. The strategy we adopted is to extend the known, static and spherically symmetric black holes in the Einstein-Maxwell-dilaton gravity and Einstein-Maxwell-scalar theory. Then we investigate the black hole thermodynamics. Concretely, the generalized Smarr formula and the first law of thermodynamics are derived.
We present a proof of the positivity of the Bondi energy in Einstein-Maxwell axion-dilaton gravity, being the low-energy limit of the heterotic string theory. We consider the spacelike hypersurface which asymptotically approaches a null cone and on which the equations of the theory under consideration are given. Next, we generalize the proof allowing the hypersurface having inner boundaries.
For the cylindrically symmetric ''asymptotically flat'' Einstein equations in the case of electro-vacuum it is known that solutions exist globally and also that this class of spacetimes is causally geodesically complete. Hence strong cosmic censorship holds for this class. An interesting question is whether these results can be generalized to include spacetimes with phenomenological matter, e.g. collisionless matter described by the Vlasov equation. Spherically symmetric asymptotically flat solutions of the Einstein-Vlasov system with small initial data are known to be causally geodesically co…
We consider Einstein-Maxwell-dilaton theory in four dimensions including the Kaluza-Klein theory and obtain the general asymptotic solutions in Bondi gauge. We find that there are three different types of news functions representing gravitational, electromagnetic, and scalar radiations. The mass density at any angle of the system can only decrease whenever there is any type of news function. The solution space of the Kaluza-Klein theory is also lifted to five dimensions. We also compute the asymptotic symmetries in both four dimensional Einstein-Maxwell-dilaton theory and five dimensional pure…
We consider 5D Einstein-Maxwell-dilaton (EMd) gravity in spacetimes with three commuting Killing vectors: one timelike and two spacelike Killing vectors, one of which is hypersurface-orthogonal. Assuming a special ansatz for the Maxwell field we show that the 2-dimensional reduced EMd equations are completely integrable. We also develop a solution generating method for explicit construction of exact EMd solutions from known exact solutions of 5D vacuum Einstein equations with considered symmetries. We derive explicitly the rotating dipole black ring solutions as a particular application of the…
New similarity variables are introduced for the Einstein - Maxwell equations with one Killing vector that reduce the non-linear partial differential equations in three independent variables to ordinary differential equations. These similarity variables are the extensions of those previously found for the Einstein-Maxwell equations with two Killing vectors. The resulting equations are then solved, providing new solutions of the Einstein - Maxwell equations with one Killing Vector.
It was shown by Hiscock that the energy-momentum tensor commonly used to model local cosmic strings in linearized Einstein gravity can be extended and used in the full theory, obtaining a metric in the exterior of the source with the same deficit angle. Here we show that this tensor is an exception within a family for which a static solution does not exist in full Einstein nor in Brans-Dicke gravity.
We use a recently derived integral representation of the one-loop effective action in Einstein-Maxwell theory for an explicit calculation of the part of the effective action containing the information on the low energy limit of the five-point amplitudes involving one graviton, four photons and either a scalar or spinor loop. All available identities are used to get the result into a relatively compact form.
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