Nahomi Kan, Kiyoshi Shiraishi
We discuss the role of a particular combination of higher derivative terms in higher dimensional theories, especially in the background of spontaneous compactification. We find that the special extension of Einstein-Maxwell theory with higher order terms admits interesting cosmological solutions.
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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.
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.
We study solutions of the Wheeler-DeWitt equation obtained when considering homogeneous and isotropic (up to a gauge transformation) field configurations of the Einstein-Yang-Mills system in $D=4+d$ dimensions with an $R \times S^3 \times S^d$ topology and assuming the Hartle-Hawking boundary conditions.
Euclidean Maxwell-Einstein Theory
在回顾了欧几里德传播是有用的背景下，我们比较和对比欧几里德和洛伦兹麦克斯韦-爱因斯坦理论，并给出了一些欧几里德解决方案的例子。
The first law of black hole mechanics is derived from the Einstein-Maxwell (EM) Lagrangian by comparing two infinitesimally nearby stationary black holes. With similar arguments, the first law of black hole mechanics in Einstein-Yang-Mills (EYM) theory is also derived.
We consider a particular example of dynamical compactification of an anisotropic 7+1 dimensional Universe in Einstein - Gauss - Bonnet gravity. Starting from rather general totally anisotropic initial conditions a Universe in question evolves towards a product of two isotropic subspaces. The first subspace expands isotropically, the second represents an "inner" isotropic subspace with stabilized size. The dynamical evolution does not require fine-tuning of initial conditions, though it is possible for a particular range of coupling constants. The corresponding condition have been found analyti…
Using an estimate, we prove that if solution of the spherically symmetric Einstein-Vlasov-Maxwell system develops a singularity at all time, then the first one has to appear at the center of symmetry.
A simple method is presented which enables us to construct scalar field solutions from any given Einstein-Maxwell solution in colliding plane waves. As an application we give scalar field extensions of the solution found by Hogan, Barrabes and Bressange.
Compactification to Non-symmetric Homogeneous Space in Multidimensional Einstein-Yang-Mills Theory
研究了额外维空间为非对称齐性空间且不变度量由两个尺度参数化的10维Einstein-Yang-Mills模型。对模型进行了降维，计算了降维理论的标势。在宇宙学的设置在辐射占主导地位的时期，随后的通货膨胀的潜力极小值被发现，并分析其稳定性。紧化的解决方案被证明是稳定的适当的参数值。
Following the technique of Müller-zum-Hagen, refs [1,2], 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.
We report on a new two-parameter class of cosmological solutions to the Einstein-Maxwell equations. The solutions have everywhere regular curvature invariants. We prove that the solutions are geodesically complete and globally hyperbolic.
Using the iterative Scheme we prove the local existence and uniqueness of solutions of the spherically symmetric Einstein-Vlasov-Maxwell system with small initial data. We prove a continuation criterion to global in-time solutions.
It is shown how to generate three-dimensional Einstein-Maxwell fields from known ones in the presence of a hypersurface-orthogonal non-null Killing vector field. The continuous symmetry group is isomorphic to the Heisenberg group including the Harrison-type transformation. The symmetry of the Einstein-Maxwell-dilaton system is also studied and it is shown that there is the $SL(2,{\bf R})$ transformation between the Maxwell and the dilaton fields. This $SL(2,{\bf R})$ transformation is identified with the Geroch transformation of the four-dimensional vacuum Einstein equation in terms of the Kał…
We obtain a class of rotating charged stationary circularly symmetric solutions of Einstein-Maxwell theory coupled to a topological mass term for the Maxwell field. These solutions are regular, have finite mass and angular momentum, and are asymptotic to the uncharged extreme BTZ black hole.
We present solution generating methods which allow to construct exact static solutions to the equations of four-dimensional Einstein-Maxwell-Dilaton gravity starting with arbitrary static solutions to the pure vacuum Einstein equations, Einstein-dilaton or Einstein-Maxwell equations.
It is shown in the first part of this paper that a combined model comprising ordinary and quintessential matter can support a traversable wormhole in Einstein-Maxwell gravity. Since the solution allows zero tidal forces, the wormhole is suitable for a humanoid traveler. The second part of the paper shows that the electric field can be eliminated (Einstein gravity), but only by tolerating enormous tidal forces. Such a wormhole would still be capable of transmitting signals.
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.
A simple derivation is given of the Einstein-Maxwell field equations from the 2nd ordinary exterior differential of a precursor to the soldering form for n-dimensional differentiable manifolds having a general linear connection and in 5-dimensional general relativity in particular.
We study a solution of the Einstein-Gauus-Bonnet theory in 5 dimensions coupled to a Maxwell field, whose euclidean continuation gives rise to an instanton describing black hole pair production. We also discuss the dual theory with a 3-form field coupled to gravity.
Adopting a simple ansatz, we find exact solutions to the Einstein-Maxwell-dilaton equations, which stand for the multi-black hole configuration with maximal charge in a cosmological metric and dilaton field background driven by a cosmological term.
An example of application of the specialized computer algebra system Grg-EC to the searching for solutions to the source-free Maxwell and Einstein--Maxwell equations is demonstrated. The solution involving five arbitrary functions of two variables is presented in explicit form (up to quadratures). An emphasis is made on the characterizing of the software utilized.
We investigate the flux compactification mechanism in simple toy models of Einstein-Born-Infeld theories. These are the direct generalizations of the Einstein-Maxwell flux compactifications that recently gained fame as a toy model for tunneling in the landscape. Our investigation reveals that the Born-Infeld form does not significantly modify the qualitative result of the Einstein-Maxwell theory. for the case of Einstein-Higgs theory, however, we found that the effect of Born-Infeld nonlinearity is to render all q>1 extradimensional compactification unstable against semiclassical tunneling to …
The recent birth of gravitational wave astronomy invites a new generation of precision tests of general relativity. Signatures of black hole (BH) mergers must be systematically explored in a wide spectrum of modified gravity theories. Here, we turn to one such theory in which the initial value problem for BH mergers is well posed, the Einstein-Maxwell-dilaton system. We present conservative estimates for the merger parameters (final spins, quasinormal modes) based on techniques that have worked well for ordinary gravity mergers and utilize information extracted from test particle motion in the…
The first results of Einstein-Maxwell equations established by Raincih in 1925 are therefore called the Raincih conditions. Later the result was rediscovered by Misner and Wheeler in 1957 and made the basis of their geometrodynamics. The present survey will consider didactically the curvature of spacetime attributed to an electromagnetic field with conceptual and calculational details.
Using ODE techniques we prove the existence of large classes of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system. These include data for which the ratio of total charge to total mass is arbitrarily large.
I derive an exact, static, axially symmetric solution of the Einstein-Maxwell equations representing two massless magnetic dipoles, and compare it with the corresponding solution of Einstein's equations for two massless spinning particles (see gr-qc/0201094). I then obtain an exact stationary solution of the Einstein-Maxwell equations representing two massless spinning magnets in balance. The conclusion is that the spin-spin force is analogous to the force between two magnetic dipoles, but of opposite sign, and that the latter agrees with the classical value in the first approximation.
Classes of exact static solutions in four-dimensional Einstein-Maxwell-Dilaton gravity are found. Besides of the well-known solutions previously found in the literature, new solutions are presented.It's shown that spherically symmetric solutions, except the case of charged dilaton black hole, represent globally naked strong curvature singularities.
In this paper the macroscopic Einstein and Maxwell equations for system, in which the electromagnetic interactions are dominating (for instance, the cosmological plasma before the moment of recombination), are derived. Ensemble averaging of the microscopic Einstein - Maxwell equations and the iouville equations for the random functions leads to a closed system of macroscopic Einstein - Maxwell equations and kinetic equations for one-particle distribution functions. The macroscopic Einstein equations for a relativistic plasma differ from the classical Einstein equations in that their left-hand …
Stealth black hole solutions in higher-order Maxwell-Einstein theories
本文研究高阶麦克斯韦-爱因斯坦理论中的静态球对称黑洞解，证明特定耦合下Reissner-Nordström-(反)德西特解及带非零电场的Schwarzschild-(反)德西特隐形黑洞解存在，并发现退化类理论中双子Reissner-Nordström-(反)德西特解可为解。
In this article, we analyze the weak gravitational lensing in the context of Einstein-non-linear Maxwell-Yukawa black hole. To this desire, we derive the deflection angle of light by Einstein-non-linear Maxwell-Yukawa black hole using the Gibbons and Werner method. For this purpose, we obtain the Gaussian curvature and apply the Gauss-Bonnet theorem to find the deflection angle of Einstein-non-linear Maxwell-Yukawa black hole in weak field limits. Moreover, we derive the deflection angle of light in the influence of plasma medium. We also analyze the graphical behavior of deflection angle by E…
This paper has been withdrawn.
A new formalism for construction of the stationary solutions is developed for the four-dimensional gravity coupled to the dilaton, Kalb-Ramond and two Maxwell fields in a low-energy heterotic string theory form. The result of generation is automatically invariant in respect to subgroup of the stationary charging symmetry transformations; the generation can be started from the stationary Einstein-Maxwell fields. The formalism is given both in real and new compact complex form, the result of maximal symmetry extension of the stationary Einstein-Maxwell theory to discussing string gravity model i…
Global existence to the coupled Einstein-Maxwell system which rules the dynamics of a kind of charged matter with a pseudo-tensor of pressure is proved, in Bianchi I-VIII spacetimes. We study the geodesics completeness, the asymptotic behavior, the positivity conditions, and we prove that the problem is well-posed in the sense of Hadamard.
For the plane symmetry we have found the electro-vacuum exact solutions of the Einstein-Maxwell equations and we have shown that one of them is equivalent to the McVittie solution of a charged infinite thin plane. The analytical extension has been accomplished and the Penrose conformal diagram has been obtained as well.
In this article, we construct explicit analytical exact solutions to the six and higher dimensional Einstein-Maxwell theory. In all solutions, a subspace of the metric is the Eguchi-Hanson space where the metric functions are completely determined in terms of known analytical functions. Moreover, we find the solutions can be extended to non-stationary exact solutions to Einstein-Maxwell theory with cosmological constant. We show that the solutions are asymptotically expanding patches of de-Sitter spacetime.
Recently a simple solution of the vacuum Einstein-Maxwell field equations was given describing a plane electromagnetic shock wave sharing its wave front with a plane gravitational impulse wave. We present here an exact solution of the vacuum Einstein-Maxwell field equations describing the head-on collision of such a wave with a plane gravitational impulse wave. The solution has the Penrose-Khan solution and a solution obtained by Griffiths as separate limiting cases.
Applications of the monodromy transform approach to construction of exact solutions of electrovacuum Einstein - Maxwell field equations are considered. Examples of new solutions are given.
We present the study of exact inhomogeneous cosmological solutions to a four-dimensional low energy limit of string theory containing non-minimal interacting electromagnetic, dilaton and axion fields. We analyze Einstein-Rosen solutions of Einstein-Maxwell-dilaton-axion equations and show, by explicitly taken the asymptotic limits, that they have asymptotically velocity-term dominated (AVTD) singularities.
We derive the energy fluxes radiated by compact binary systems, including "hairy" black holes, in Einstein-Maxwell-dilaton theories, for circular orbits and at quadrupolar order. This enables to include in their resummed effective-one-body (EOB) dynamics the effect of the radiation reaction force at the origin of their inspiral and merger. We also exhibit typical examples of the resulting tensor and scalar waveforms.
We present a new solution in 5D Einstein-Maxwell-dilaton gravity describing an equilibrium configuration of extremal rotating black holes with lens space horizon topologies. The basic properties of the solution are investigated and the basic physical quantities are calculated. It is shown that the black hole horizons are superconducting in the sense that they expel the magnetic flux lines.
We consider asymptotically-flat, static and stationary solutions of the Einstein equations representing Einstein-Maxwell space-times in which the Maxwell field is not constant along the Killing vector defining stationarity, so that the symmetry of the space-time is not inherited by the electromagnetic field. We find that static degenerate black hole solutions are not possible and, subject to stronger assumptions, nor are static, non-degenerate or stationary black holes. We describe the possibilities if the stronger assumptions are relaxed.
We construct thin shell Lorentzian wormholes in higher dimensional Einstein-Maxwell theory applying the ' Cut and Paste ' technique proposed by Visser. The linearized stability is analyzed under radial perturbations around some assumed higher dimensional spherically symmetric static solution of the Einstein field equations in presence of Electromagnetic field. We determine the total amount of exotic matter, which is concentrated at the wormhole throat.
We present a family of solutions for the axisymmetric Plebanski-Demianski metric and other corresponding reduced metrics. We also present the black hole characteristics using a new set of parameters for Kerr-Newman metric.
The Einstein-Maxwell equations in D-dimensions admitting (D-3) commuting Killing vector fields have been investigated. The existence of the electric, magnetic and twist potentials have been proved. The system is formulated as the harmonic map coupled to gravity on three-dimensional base space generalizing the Ernst system in the four-dimensional stationary Einstein-Maxwell theory. Some classes of the new exact solutions have been provided, which include the electro-magnetic generalization of the Myers-Perry solution, which describes the rotating black hole immersed in a magnetic universe, and …
For space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein and Einstein--Maxwell equations as represented by their Ernst potentials. This hierarchy contains three arbitrary rational functions of an auxiliary complex parameter. They are constructed using the so called `monodromy transform' approach and our new method for the solution of the linear singular integral equation form of the reduced Einstein equations. The solutions presented, which describe inhomogeneous cosmological models or gravitational and electromagnetic waves and their in…
We construct charged asymptotically flat black hole solutions in Einstein-Maxwell-Weyl(EMW) gravity. These solutions can be interpreted as generalizations of two different groups: Schwarzschild black hole (SBH) and non-Schwarzschild black hole (NSBH) solutions. In addition, we discuss the thermodynamic properties of two groups of numerical solutions in detail, and show that they obey the first law of thermodynamics.
The exact interior static solution of Einstein-Maxwell equations in Bondi's coordinates for the electrically charged fluid ball is obtained as a source of the Reissner-Nordström solution.
In this paper we characterize the source-free Einstein-Maxwell spacetimes which have a trace-free Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pure-radiation type and that it restricts the spacetimes to Petrov types \textbf{N} or \textbf{O}. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all Einstein-Maxwell spacetimes with a zero cosmological constant that have a vanishing Bach tensor. Among these spacetimes we then look for those which are conformal to Einstein spaces. We find that the electromagnetic f…
We consider $d$-dimensional solutions to the electrovacuum Einstein-Maxwell equations with the Weyl tensor of type N and a null Maxwell $(p+1)$-form field. We prove that such spacetimes are necessarily aligned, i.e. the Weyl tensor of the corresponding spacetime and the electromagnetic field share the same \textit{aligned null direction} (AND). Moreover, this AND is geodetic, shear-free, non-expanding and non-twisting and hence Einstein-Maxwell equations imply that Weyl type N spacetimes with a null Maxwell $(p+1)$-form field belong to the Kundt class. Moreover, these Kundt spacetimes are nece…
We investigate the spherical accretion process for general static spherically symmetric fluids. We analyze this process by using the general metric ansatz for spherically symmetric black holes. We specialize to the case of normal and phantom isothermal fluids and investigate their accretion process onto normal and phantom Einstein-Maxwell-dilaton black holes. Backreaction effects are discussed.
The Lambda-renormalized Einstein-Schrodinger theory is a modification of the original Einstein-Schrodinger theory in which a cosmological constant term is added to the Lagrangian, and it has been shown to closely approximate Einstein-Maxwell theory. Here we generalize this theory to non-Abelian fields by letting the fields be composed of dxd Hermitian matrices. The resulting theory incorporates the U(1) and SU(d) gauge terms of Einstein-Maxwell-Yang-Mills theory, and is invariant under U(1) and SU(d) gauge transformations. The special case where symmetric fields are multiples of the identity m…
We introduce a new class of inhomogeneous cosmological models as solutions to the Einstein-Maxwell equations in electrovacuum. The new models can be considered to be nonlinear perturbations, through an electromagnetic field, of the previously studied `smooth Gowdy-symmetric generalised Taub-NUT solutions' in vacuum. Utilising methods from soliton theory, we analyse the effects of the Maxwell field on global properties of the solutions. In particular, we show existence of regular Cauchy horizons, and we investigate special singular cases in which curvature singularities form.
What forms will have an equations of modern physics if the dimensions of our time and space are fractional? The generalized equations enumerated by title are presented by help the generalized fractional derivatives of Riemann-Liouville.
We consider Einstein-Maxwell-self-interacting scalar field theory described by a potential $V\left( ϕ\right) $ in $2+1-$dimensions. The self-interaction potential is chosen to be a highly non-linear double-Liouville type. Exact solutions, including chargeless black holes and singularity-free non-black hole solutions are obtained in this model.
The solutions of the Einstein-Maxwell-Chern-Simons theory are studied in (1+2) dimensions with the self-duality condition imposed on the Maxwell field. We give a closed form of the general solution which is determined by a single function having the physical meaning of the quasilocal angular momentum of the solution. This function completely determines the geometry of spacetime, also providing the direct computation of the conserved total mass and angular momentum of the configurations.
We construct new classes of exact cosmological solutions to five dimensional Einstein-Maxwell-dilaton theory with two coupling constants for the dilaton-Maxwell term and dilaton-cosmological constant term. All the solutions are non-stationary and the solutions that both coupling constants are non-zero are almost regular everywhere. The size of spatial section of the asymptotic metric shrinks to zero at early time and increases to infinitely large at very late time. The cosmological constant depends on the dilaton coupling constant and can take positive, zero or negative values.
Class of Einstein--Maxwell Dilatons
本文给出了三种不同类型的非极小耦合Einstein-麦克斯韦方程组的静态解。一般的解决方案中给出的两个任意谐波函数，并涉及其中一个任意的参数，它决定了其适用性的收费黑洞，黑洞或字符串。大多数已知的解决方案包含作为特殊情况，并可以通过不同的方式进行非平凡的推广。
We construct several examples of compactifications of Einstein metrics. We show that the Eguchi--Hanson instanton admits a projective compactification which is non--metric, and that a metric cone over any (pseudo)--Riemannian manifolds admits a metric projective compactification. We construct a para--$c$--projective compactification of neutral signature Einstein metrics canonically defined on certain rank--$n$ affine bundles $M$ over $n$-dimensional manifolds endowed with projective structures.
The method based on the Horsky-Mitskievitch conjecture is applied to the Levi-Civita vacuum metric. It is shown, that every Killing vector is connected with a particular class of Einstein-Maxwell fields and each of those classes is found explicitly. Some of obtained classes are quite new. Radial geodesic motion in constructed space-times is discussed and graphically illustrated in the Appendix.
We use Moeller's energy-momentum complex in order to explicitly evaluate the energy and momentum density distributions associated with the three-dimensional magnetic solution to the Einstein-Maxwell equations. The magnetic spacetime under consideration is a one-parametric solution describing the distribution of a radial magnetic field in a three-dimensional AdS background, and representing the superposition of the magnetic field with a 2+1 Einstein static gravitational field.
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