We study an electric field created by a static electric charge near the higher dimensional Reissner-Nordstrom black hole. The relation between the static Green functions on the D-dimensional Reissner-Nordstrom background and on the (D+2)-dimensional homogeneous Bertotti-Robinson spacetime is found. Using the biconformal symmetry we obtained a simple integral representation for the static Maxwell Green functions in arbitrary dimensions. We show that in a four-dimensional spacetime the static Green function obtained by the biconformal method correctly reproduces known results. We also found a closed form for the exact static Green functions and vector potentials in the five-dimensional Reissner-Nordstrom spacetime.
We study the full Maxwell-Dirac equations: Dirac field with minimally coupled electromagnetic field and Maxwell field with Dirac current as source. Our particular interest is the static case in which the Dirac current is purely time-like -- the "electron" is at rest in some Lorentz frame. In this case we prove two theorems under rather general assumptions. Firstly, that if the system is also stationary (time independent in some gauge) then the system as a whole must have vanishing total charge, i.e. it must be electrically neutral. In fact, the theorem only requires that the system be {\em asy…
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.
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.
General static solutions of effectively 2-dimensional Einstein-Dilaton-Maxwell-Scalar theories are obtained. Our model action includes a class of 2-d dilaton gravity theories coupled with a $U(1)$ gauge field and a massless scalar field. Therefore it also describes the spherically symmetric reduction of $d$-dimensional Einstein-Scalar-Maxwell theories. The properties of the analytic solutions are briefly discussed.
The soliton technique is applied to the 5D static Einstein-Maxwell equations, and an infinite number of solutions are explicitly obtained. We study the rod structure of 2-soliton solutions and we show that the 5D Reissner-Nordstrom solution and the 5D Majumdar-Papapetrou solution are included as the 2-soliton solutions.
We classify the spherically symmetric solutions of the Einstein-Maxwell Dilaton field equations in D dimensions and find some exact solutions of the string theory at all orders of the string tension parameter. We also show the uniqueness of the black hole solutions of this theory in static axially symmetric spacetimes.
We study the 5D static Einstein-Maxwell equations with a dilaton field. We construct an infinte number of solutions by using a soliton technique. We study the rod structure of 2-soliton solution and show the 5D dilatonic black ring and black hole solutions are included.
We obtain the general static solutions of the axially symmetric (2+1)-dimensional Einstein-Maxwell-Dilaton theory by dimensionally reducing it to a 2-dimensional dilaton gravity theory. The solutions consist of the magnetically charged sector and the electrically charged sector. We illuminate the relationship between the two sectors by pointing out the transformations between them.
We present a new approach for generation of solutions in the four-dimensional heterotic string theory with one vector field and in the five-dimensional bosonic string theory starting from the static Einstein-Maxwell fields. Our approach allows one to construct the solution classes invariant with respect to the total subgroup of the three-dimensional charging symmetries of these string theories. The new generation procedure leads to the extremal Israel-Wilson-Perjes subclass of string theory solutions in a special case and provides its natural continuous extension to the realm of non-extremal s…
The Kerr solution is generated from the Schwarzschild solution by a simple combination of real global coordinate transformations and of invariance transformations acting on the space of stationary solutions of the Einstein-Maxwell equations. The same transformation can be used to generate a spinning field configuration from any static axisymmetric configuration. We illustrate this by generating from the continuous family of Voorhees--Zipoy vacuum solutions a family of solutions endowed with mass, angular momentum, dipole magnetic moment and quadrupole electric moment.
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…
In this manuscript, we present an alternative method for calculating null geodesics in General Static Isotropic Metrics in General Relativity and Extended Theories of Gravity. By applying a conformal transformation, we are able to consider an analogue gravity model, where curvature is encoded in the dielectric and magnetic properties of a medium. In other words, we pass from curved to flat space-times, where instead of the Einstein field equations, the Maxwell equations are solved. Within this geometrical background, the photon geodesics are calculated. Then, given different black hole and wor…
Previous work has shown that static multi-black hole solutions of higher-dimensional Einstein-Maxwell theory do not possess smooth horizons. We show that the lack of smoothness is worse than previously demonstrated. We consider solutions describing multiple black holes on a common axis. In five dimensions, the metric is generically twice, but not three times, continuously differentiable at the horizon. The Maxwell field is generically continuous, but not differentiable, at the horizon. In more than five dimensions, the metric is once, but not twice, continuously differentiable, and there is a …
We prove a uniqueness theorem for traversable wormhole solutions in the Einstein-Maxwell-dilaton gravity with a phantom scalar field and a possible phantom electromagnetic field. In a certain region of the parameter space, determined by the asymptotic values of the scalar field and the lapse function, the regular wormholes are completely specified by their mass, scalar charge and electric charge. The argument is based on the positive energy theorem applied on an appropriate conformally transformed Riemannian space.
We explicitly construct static black hole solutions to the fully non-linear, D=4, Einstein-Maxwell-AdS equations that have no continuous spatial symmetries. These black holes have a smooth, topologically spherical horizon (section), but without isometries, and approach, asymptotically, global AdS spacetime. They are interpreted as bound states of a horizon with the Einstein-Maxwell-AdS solitons recently discovered, for appropriate boundary data. In sharp contrast with the uniqueness results for Minkowski electrovacuum, the existence of these black holes shows that single, equilibrium, BH solut…
Using the ADM formulation of the Einstein-Maxwell axion-dilaton gravity we derived the formulas for the variation of mass and other asymptotic conserved quantities in the theory under consideration. Generalizing this kind of reasoning to the initial dota for the manifold with an interior boundary we got the generalized first law of black hole mechanics. We consider an asymptotically flat solution to the Einstein-Maxwell axion-dilaton gravity describing a black hole with a Killing vector field timelike at infinity, the horizon of which comprises a bifurcate Killing horizon with a bifurcate surf…
We construct a new class of Einstein-Maxwell static solutions with a magnetic field in $D$-dimensions (with $D\geq 5$ an odd number), approaching at infinity a globally Anti-de Sitter (AdS) spacetime. In addition to the mass, the new solutions possess an extra-parameter associated with a non-zero magnitude of the magnetic potential at infinity. Some of the black holes possess a non-trivial zero-horizon size limit, which corresponds to a solitonic deformation of the AdS background.
We derive formulas for variations of mass, angular momentum and canonical energy in Einstein (n-2)-gauge form field theory by means of the ADM formalism. Considering the initial data for the manifold with an interior boundary which has the topology of (n-2)-sphere we obtained the generalized first law of black hole thermodynamics. Supposing that a black hole evevt horizon comprisesw a bifurcation Killing horizon with a bifurcate surface we find that the solution is static in the exterior world, when the Killing timelike vector field is normal to the horizon and has vanishing electric or magnet…
An effective potential is created for the dynamics of a test particle, which preserves dilatation symmetry for nonlinear static dilaton-Maxwell background. It is found that the central interaction in this theory is regular everywhere, and that the theory is asymptotically free at short distances and that it has a Coulomb properties at great distances from the source. It is shown that static and spherically symmetric source, behaves like a soliton: it has the finite energy characteristics that are inversely proportional to the dilaton-Maxwell coupling constant.
We explain how static multi-vortex solutions arise in non-linear field theories, by taking the non-linear Schrödinger equation coupled to Chern-Simons field (Jackiw-Pi model) and a fermion Chern-Simons theory as simple examples. We then construct a fermion Maxwell-Chern-Simons theory which has consistent static field equations, and show that it has the same vortex solutions as the Jackiw-Pi model, but gives rise to quite different vortex dynamics.
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.
We study Robinson-Trautman spacetimes in the presence of an aligned p-form Maxwell field and an arbitrary cosmological constant in n>=4 dimensions. As it turns out, the character of these exact solutions depends significantly on the (relative) value of n and p. In odd dimensions the solutions reduce to static black holes dressed by an electric and a magnetic field and whose horizon is an Einstein space (further constrained by the Einstein-Maxwell equations) -- both the Weyl and Maxwell type are D. Even dimensions, however, open up more possibilities. In particular, when 2p=n there exist non-st…
Three non-existence results are established for self-gravitating solitons in Einstein-Maxwell-scalar models, wherein the scalar field is, generically, non-minimally coupled to the Maxwell field via a scalar function $f(Φ)$. Firstly, a trivial Maxwell field is considered, which yields a consistent truncation of the full model. In this case, using a scaling (Derrick-type) argument, it is established that no stationary and axisymmetric self-gravitating scalar solitons exist, unless the scalar potential energy is somewhere negative in spacetime. This generalises previous results for the static and…
In this work a static spherically symmetric black hole's solution within the Einstein-Maxwell-Yang-Mills-dilaton theory is derived. The obtained solution is examined, in particular, we have calculated the Kretschmann scalar which allowed us to characterize singularity points. Using the obtained black hole's solution we have studied its thermodynamics. Namely, the temperature was calculated, the first law was written, and the heat capacity was studied. The extended thermodynamics approach is utilized to obtain the equation of state. Within the extended thermodynamics the Gibbs free energy is de…
We investigate rotating Einstein-Maxwell-Dilaton (EMd) black holes in odd dimensions. Focusing on black holes with equal-magnitude angular momenta, we determine the domain of existence of these black holes. Non-extremal black holes reside with the boundaries determined by the static and the extremal rotating black holes. The extremal EMd black holes show proportionality of their horizon area and their angular momenta. Thus the charge does not enter. We also address the Einstein-Maxwell case, where the extremal rotating black holes exhibit two branches. On the branch emerging from the Myers-Per…
The cosmological black hole solution on the Gibbons-Hawking space has been constructed. We also investigate the properties of this solution in the case of a single black hole. Unlike the Kastor-Traschen solution, which becomes static Reissner-Nortström de Sitter solution in a single black hole, this solution is not static even in a single black hole case.
The full ``classical" Dirac-Maxwell equations are considered under various simplifying assumptions. A reduction of the equations is performed in the case when the Dirac field is {\em static} and a further reduction is performed in the case of {\em spherical symmetry}. These static spherically symmetric equations are examined in some detail and a numerical solution presented. Some surprising results emerge: * Spherical symmetry necessitates the existence of a magnetic monopole. * There exists a uniquely defined solution, determined only by the demand that the solution be analytic at infinity. *…
The Arnowitt-Deser-Misner formalism is used to derive variations of mass, angular momentum and canonical energy for Einstein-Maxwell {\it dark matter} gravity in which the auxiliary gauge field coupled via kinetic mixing term to the ordinary Maxwell one, which mimics properties of {\it hidden sector}. Inspection of the initial data for the manifold with an interior boundary, having topology of $S^2$, enables us to find the generalised first law of black hole thermodynamics in the aforementioned theory. It has been revealed that the stationary black hole solution being subject to the condition …
Static spherically symmetric black hole solution is obtained in the framework of Einstein-dilaton theory with nonlinear Maxwell and Yang-Mills fields of power-law type. It is observed that black hole might have two horizons similarly as it takes place for linear gauge fields case. Thermodynamics of the black hole is studied, namely the behaviour of temperature is examined and the first law is written. The concept of extended phase space is also utilized, namely we have written and analyzed the equation of state for the black hole and examined the Gibbs free energy. The Gibbs free energy shows …
In this paper we propose a very special relativity (VSR)-inspired generalization of the Maxwell-Chern-Simons (MCS) electrodynamics. This proposal is based upon the construction of a proper study of the SIM$(1)$--VSR gauge-symmetry. It is shown that the VSR nonlocal effects present a significant and health departure from the usual MCS theory. The classical dynamics is analysed in full detail, by studying the solution for the electric field and static energy for this configuration. Afterwards, the interaction energy between opposite charges are derived and we show that the VSR effects play an im…
Recently, a no inner (Cauchy) horizon theorem for static black holes with non-trivial scalar hairs has been proved in Einstein-Maxwell-scalar theories. In this paper, we extend the theorem to the static black holes in Einstein-Maxwell-Horndeski theories. We study the black hole interior geometry for some exact solutions and find that the spacetime has a (space-like) curvature singularity where the black hole mass gets an extremum and the Hawking temperature vanishes. We discuss further extensions of the theorem, including general Horndeski theories from disformal transformations.
We consider a class of Einstein-Maxwell-dilaton theories in general dimensions and construct both static and dynamic charged black holes. We adopt the reverse engineering procedure and make a specific ansatz for the scalar field and then derive the necessary scalar potential and the non-minimal coupling function between the scalar and the Maxwell field. The resulting static black holes contain mass and electric charge as integration constants. We find that some of the static solutions can be promoted to become dynamical ones in the Eddington-Finkelstein-like coordinates. The collapse solutions…
We present a simple and complete classification of static solutions in the Einstein-Maxwell system with a massless scalar field in arbitrary $n(\ge 3)$ dimensions. We consider spacetimes which correspond to a warped product $M^2 \times K^{n-2}$, where $K^{n-2}$ is a $(n-2)$-dimensional Einstein space. The scalar field is assumed to depend only on the radial coordinate and the electromagnetic field is purely electric. Suitable Ansätze enable us to integrate the field equations in a general form and express the solutions in terms of elementary functions. The classification with a non-constant re…
In this study we apply two different methods in the context of $AdS/CFT$ correspondence and calculate the diffusion coefficient and $DC$ conductivity of a four-dimensional spatially anisotropic static black hole. First, the \emph{modified} transport coefficients is obtained by stretched horizon method and Fick's law in the context of the membrane paradigm. In order to do such calculation, we use the Maxwell equations with electromagnetic gauge field propagating in two dimensions. Two dimensional propagating gauge field leads to the complex transport coefficients which is proved by present pape…
We present higher-dimensional generalizations of the Buchdahl and Janis-Robinson-Winicour transformations which generate static solutions in the Einstein-Maxwell system with a massless scalar field. While the former adds a nontrivial scalar field to a vacuum solution, the latter generates a charged solution from a neutral one with the same scalar field. Applying these transformations to (i) a static solution with an Einstein base manifold, (ii) a multi-center solution, and (iii) a four-dimensional cylindrically symmetric solution, we construct several new exact solutions.
We have constructed nonrelativistic fermion and scalar field theories coupled to a Maxwell-Chern-Simons gauge field which admit static multi-vortex solutions. This is achieved by introducing a magnetic coupling term in addition to the usual minimal coupling.
We consider the new version of the gedanken experiments proposed recently by Sorce and Wald to overcharge a static charged dilaton black hole. First of all, we derive the first-order and second-order perturbation inequalities in the Einstein-Maxwell-dilaton gravitational theory based on the Iyer-Wald formalism. As a result, we find that the weak cosmic censorship conjecture associated with this black hole can be protected after taking into account the second-order perturbation inequality, although violated by the scene without considering this inequality. Therefore, there is no violation of th…
We report the discovered class of exact static solutions of several 4D Einstein-Maxwell-dilaton systems: string-induced, Liouville, trigonometric, polynomial, etc., for three basic topologies (spherical, hyperbolical and flat) being uniformly treated. In addition to the usual electric-magnetic duality this class obeys a certain extended duality between Maxwell-dilaton coupling and dilaton mass. Though major solutions we obtain are dyonic, the class also comprises interesting neutral models. As a by-product, we significantly succeded in resolving of the two important problems, one of which has …
Using the solution phase space method, we investigate the thermodynamics of black holes in Einstein-aether-Maxwell theory, for which the traditional Wald method (covariant phase space method) fails. We show the first laws of thermodynamics and definitive entropy expressions at both Killing and universal horizons for some examples of exact black hole solutions, including 3-dimensional static charged quasi-BTZ black hole, two 4-dimensional static charged black holes and 3-dimensional rotating solution. At Killing horizons the entropies are exactly one quarter of the horizon area, but at universa…
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.
A non-relativistic version of the 2+1 dimensional gauged Chern-Simons O(3) sigma model, augmented by a Maxwell term, is presented and shown to support topologically stable static self-dual vortices. Exactly like their counterparts of the ungauged model, these vortices are shown to exhibit Hall behaviour in their dynamics.
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.
In the large coupling regime of the 5-dimensional Einstein--Maxwell--Chern--Simons theory, charged and rotating cohomogeneity-1 black holes form sequences of extremal and non-extremal radially excited configurations. These asymptotically global Anti-de Sitter (AdS$_5$) black holes form a discrete set of solutions, characterised by the vanishing of the total angular momenta, or the horizon angular velocity. However, the solutions are not static. In this paper, we study the branch structure that contains these excited states, and its relation with the static Reissner-Nordström-AdS black hole. Th…
We get the general static, spherically symmetric solutions of the d-dimensional Einstein-Maxwell-Dilaton theories by dimensionally reducing them to a class of 2-dimensional dilaton gravity theories. By studying the symmetries of the actions for the static equations of motion, we find field redefinitions that nearly reduce these theories to the d-dimensional Einstein-Maxwell-Scalar theories, and therefore enable us to get the exact solutions. We do not make any assumption about the asymptotic space-time structure. As a result, our 4-dimensional solutions contain the asymptotically flat Garfinkl…
We obtain the general static, spherically symmetric solution for the Einstein-Maxwell-dilaton system in four dimensions with a phantom coupling for the dilaton and/or the Maxwell field. This leads to new classes of black hole solutions, with single or multiple horizons. Using the geodesic equations, we analyse the corresponding Penrose diagrams revealing, in some cases, new causal structures.
Based on the conformal energy theorem we prove the uniqueness theorem for static higher dimensional electrically and magnetically charged black holes being the solution of Einstein (n-2)-gauge forms equations of motion. Black hole spacetime contains an asymptotically flat spacelike hypersurface with compact interior and non-degenerate components of the event horizon.
This paper investigates a particular type of wormhole. The wormhole solutions studied are obtained by sewing together two static, spherically symmetric, charged black-hole metrics at their horizons. The charged wormholes are in a background Kalb-Ramond field, which is the source of the necessary tension in the gravitational field. The metric-tensor elements are studied by numerically solving Einstein's equations with stress-energy-tensor elements given by the combination of static electric and Kalb-Ramond fields. For a certain range of electric charge the tension is positive away from the worm…
We propose a general method for solving exactly the static field equations of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field. Our method starts from an ansatz for the scalar field profile, and determines, together with the metric functions, the corresponding form of the scalar self-interaction potential. Using this method we prove a new no-hair theorem about the existence of hairy black-hole and black-brane solutions and derive broad classes of static solutions with radial symmetry of the theory, which may play an important role in applications of the AdS/CFT corresp…
We compute the graviton induced corrections to Maxwell's equations in the one-loop and weak field approximations. The corrected equations are analogous to the classical equations in anisotropic and inhomogeneous media. We analyze in particular the corrections to the dispersion relations. When the wavelength of the electromagnetic field is much smaller than a typical length scale of the graviton two-point function, the speed of light depends on the direction of propagation and on the polarisation of the radiation. In the opposite case, the speed of light may also depend on the energy of the ele…
We find the static vortex solutions of the model of Maxwell-Chern-Simons gauge field coupled to a (2+1)-dimensional four-fermion theory. Especially, we introduce two matter currents coupled to the gauge field minimally: the electromagnetic current and a topological current associated with the electromagnetic current. Unlike other Chern-Simons solitons the N-soliton solution of this theory has binding energy and the stability of the solutions is maintained by the charge conservation laws.
