Takahiro Azuma, Takao Koikawa
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.
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We derive a set of complex potentials which linearize the action of charging symmetries of the stationary Einstein-Maxwell dilaton-axion 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.
Two-dimensional dilaton gravity coupled to a Klein-Gordon matter field with a quartic interaction term is considered. The theory has a classical solution which exhibits black hole formation by a soliton. The geometry of black hole induced by a soliton is investigated.
Two-dimensional Maxwell-dilaton quantum gravity, which covers a large family of the actions for two-dimensional gravity (in particular, string-inspired models) is investigated. Charged black holes which appear in the theory are briefly discussed. The one-loop divergences in the linear covariant gauges are calculated. It is shown that for some choices of the dilaton potential and dilaton-Maxwell coupling, the theory is one-loop multiplicatively renormalizable (or even finite). A comparison with the divergences structure of four-dimensional Einstein-Maxwell gravity is given.
The CGHS model of two-dimensional dilaton gravity coupled to a sine-Gordon matter field is considered. The theory is exactly solvable classically, and the solutions of a kink and two-kink type solitons are studied in connection with black hole formation.
The Kramer--Neugebauer--like transformation is constructed for the stationary axisymmetric D=4 Einstein--Maxwell--dilaton--axion system. This transformation directly maps the dualized sigma--model equations of the theory into the nondualized ones. Also the new chiral $4 \times 4$ matrix representation of the problem is presented.
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 present a new class of slowly rotating black hole solutions in $(n+1)$-dimensional $(n\geq3)$ Einstein-Maxwell-dilaton gravity in the presence of Liouville-type potential for the dilaton field and an arbitrary value of the dilaton coupling constant. Because of the presence of the dilaton field, the asymptotic behaviour of these solutions are neither flat nor (A)dS. In the absence of a dilaton field, our solution reduces to the $(n+1)$-dimensional Kerr-Newman modification thereof for small rotation parameter \cite{Aliev2}. We also compute the angular momentum and the gyromagnetic ratio of th…
Dilaton coupled electromagnetic field is essential element of low-energy string effective action or it may be considered as result of spherical compactification of Maxwell theory in higher dimensions. The large $N$ and large curvature effective action for $N$ dilaton coupled vectors is calculated. Adding such quantum correction to classical dilaton gravity action we show that effective dilaton-Maxwell gravity under consideration may generate Schwarzschild-de Sitter black holes (SdS BHs) with constant dilaton as solutions of the theory. That suggests a mechanism (alternative to BHs production) …
Within the metric structure endowed with two orthogonal space-like Killing vectors a class of solutions of the Einstein-Maxwell-Dilaton field equations is presented. Two explicitly given sub-classes of solutions bear an interpretation as colliding plane waves in the low-energy limit of the heterotic string theory.
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 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 electrically charged, dilaton black holes, which possess infinitesimal angular momentum in the presence of one or two Liouville type potentials. These solutions are neither asymptotically flat nor (anti)-de Sitter. Some properties of the solutions are discussed.
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 …
The action of the isometry subgroup which preserves the trivial values of the fields is studied for the stationary D=4 Einstein--Maxwell--Dilaton--Axion theory. The technique for generation of charges and the corresponding procedure for construction of new solutions is formulated. A solution describing the double rotating dyon with independent values of all physical charges is presented.
We investigate the critical behavior of an $(n+1)$-dimensional topological dilaton black holes, in an extended phase space in both canonical and grand-canonical ensembles, when the gauge field is in the form of power-Maxwell field. In order to do this we introduce for the first time the counterterms that remove the divergences of the action in dilaton gravity for the solutions with curved boundary. Using the counterterm method, we calculate the conserved quantities and the action and therefore Gibbs free energy in both the canonical and grand-canonical ensembles. We treat the cosmological cons…
A general model of dialton-Maxwell gravity in two dimensions is investigated. The corresponding one-loop effective action and the generalized $β$-functions are obtained. A set of models that are fixed points of the renormalization group equations are presented.
We present an interesting reformulation of a collection of dilaton gravity models in two space-time dimensions into a field theory of two decoupled Liouville fields in flat space, in the presence of a Maxwell gauge field. An effective action is also obtained, encoding the dynamics of the dilaton field and the single gravitational degree of freedom in a decoupled regime. This effective action represents an interesting starting point for future work, including the canonical quantization of these classes of non trivial models of gravity coupled matter systems.
We study Einstein-Maxwell-dilaton theories with a cosmological constant and U(1)^N gauge symmetry, considering metrics asymptotically approaching the Lifshiftz metric. We study the dependence of the phase diagram on the value of the dynamical exponent. Along the way, we apply holographic renormalization and propose a counterterm valid for arbitrary dimension and dynamical exponent in our setup.
The renormalization structure of two-dimensional quantum gravity is investigated, in a covariant gauge. One-loop divergences of the effective action are calculated. All the surface divergent terms are taken into account, thus completing previous one-loop calculations of the theory. It is shown that the on-shell effective action contains only surface divergences. The off-shell renormalizability of the theory is discussed and classes of renormalizable dilaton and Maxwell potentials are found.
We construct exact charged rotating black holes in Einstein-Maxwell-dilaton theory in $D$ spacetime dimensions, $D \ge 5$, by embedding the $D$ dimensional Myers-Perry solutions in $D+1$ dimensions, and performing a boost with a subsequent Kaluza-Klein reduction. Like the Myers-Perry solutions, these black holes generically possess $N=[(D-1)/2]$ independent angular momenta. We present the global and horizon properties of these black holes, and discuss their domains of existence.
It is shown that electro (magneto) static sector of Maxwell's electrodynamics coupled to the dilaton field in a string theory form possesses the symmetry group of the stationary General Relativity in vacuum. Performing the Ernst formalism, we develope a technique for generation of exact solutions in this modified electrodynamics on the base of the normalized Ehlers symmetry transformation. In the electrostatic case, we construct and study a general class of spherically symmetric solutions that describes a point-like sourse of the Coulomb type. It is shown that this source is characterized by a…
The constructed $Sp(4,R)/GL(2,R)$ matrix operator defines the family of isotropic geodesic containing vacuum point lines in the target space of the stationary D=4 Einstein--Maxwell--dilaton--axion theory. This operator is used to derive a class of solutions which describes a point center system with nontrivial values of mass, parameter NUT, as well as electric, magnetic, dilaton and axion charges. It is shown that this class contains both particular solutions Majumdar--Papapetrou--like black holes and massless asymptotically nonflat naked singularities.
We use soliton techniques of the two-dimensional reduced beta-function equations to obtain non-trivial string backgrounds from flat space. These solutions are characterized by two integers (n, m) referring to the soliton numbers of the metric and axion-dilaton sectors respectively. We show that the Nappi-Witten universe associated with the SL(2) x SU(2) / SO(1, 1) x U(1) CFT coset arises as an (1, 1) soliton in this fashion for certain values of the moduli parameters, while for other values of the soliton moduli we arrive at the SL(2)/SO(1, 1) x SO(1, 1)^2 background. Ordinary 4-dim black-hole…
Recent progress in the holographic approach makes it more transparent that each conductivity can be decomposed into the coherent contribution due to momentum relaxation and the incoherent contribution due to intrinsic current relaxation. In this paper we investigate this decomposition in the framework of Einstein-Maxwell-dilaton theory. We derive the perturbation equations, which are decoupled for a large class of background solutions, and then obtain the analytic results of conductivity with the slow momentum relaxation in low frequency approximation, which is consistent with the known result…
The structure of one-loop divergences of two-dimensional dilaton-Maxwell quantum gravity is investigated in two formalisms: one using a convenient effective action and the other a unique effective action. The one-loop divergences (including surface divergences) of the convenient effective action are calculated in three different covariant gauges: (i) De Witt, (ii) $Ω$-degenerate De Witt, and (iii) simplest covariant. The on-shell effective action is given by surface divergences only (finiteness of the $S$-matrix), which yet depend upon the gauge condition choice. Off-shell renormalizability is…
Unlike Einstein gravity, dilaton-Maxwell gravity with matter is renormalizable in $2+ε$ dimensions and has a smooth $ε\to 0$ limit.By performing a renormalization- group study of this last theory we show that the gravitational coupling constant $G$ has a non-trivial,ultraviolet stable fixed point (asymptotic freedom) and that the dilatonic coupling functions (including the dilatonic potential) exhibit also a real, non-trivial fixed point. At such point the theory represents a standard charged string-inspired model.Stability and the gauge dependence of the fixed-point solution is discussed.It i…
We consider near horizon fall-off conditions of stationary black holes in Einstein-Maxwell-Dilaton theory and find conserved charge conjugate to symmetry generator that preserves near horizon fall-off conditions. Subsequently, we find supertranslation, superrotation and multiple-charge modes. We apply the obtained results on a typical static dilaton black hole and on a charged rotating black string, as examples. In this case, supertranslation double-zero-mode charge $\mathcal{T}_{(0,0)}$ is not equal to black hole entropy times Hawking temperature. This may be seen as a problem but it is not, …
We extend earlier work by introducing an Einstein-Maxwell-dilaton (EMD) action with two quark flavours. We solve the corresponding equations of motion in the quenched approximation (probe quark flavours) via the potential reconstruction method in presence of a background magnetic field in search for a self-consistent dual magnetic AdS/QCD model. As an application we discuss the deconfinement transition temperature confirming inverse magnetic catalysis, whilst for moderate values of the magnetic field also the entropy density compares relatively well with corresponding lattice data in the vicin…
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 present qualitative evidence that closed string tachyon solitons describe backgrounds of lower-dimensional sub-critical string theory. We show that a co-dimension one soliton in the low energy effective gravity-dilaton-tachyon theory in general has a flat string-frame metric, and a dilaton that grows in both directions away from the core, and is linear in the soliton worldvolume coordinates. Spacetime, as seen in the Einstein frame, is therefore effectively localized in (D-1)-dimensions, in which the dilaton is linear, in agreement with the linear dilaton background of the (D-1)-dimensional…
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.
Einstein-dilaton-four-Maxwell Holographic Anisotropic Models
本文推广了五维Einstein-dilaton-Maxwell全息模型，引入四个Maxwell场描述空间与磁场诱导的各向异性，证明了完全各向异性对角度规下七个方程仅六个独立，并提供了求解该系统的程序。
We construct analytical Lifshitz massive black brane solutions in massive Einstein-Maxwell-dilaton gravity theory. We also study the thermodynamics of these black brane solutions and obtain the thermodynamical stability conditions. On the dual nonrelativistic boundary field theory with Lifshitz symmetry, we analytically compute the DC transport coefficients, including the electric conductivity, thermoelectric conductivity, and thermal conductivity. The novel property of our model is that the massive term supports the Lifshitz black brane solutions with $z\neq 1$ in such a way that the DC trans…
We consider the D-dimensional massive dilaton gravity coupled to Maxwell and antisymmetric tensor fields (EMATD). We derive the full separability of this theory in static case. This discloses the core structure of the theory and yields the simple procedure of how to generate integrability classes. As an example we take a certain new class, obtain the two-parametric families of dyonic solutions. It turns out that at some conditions they tend to the D-dimensional dyonic Reissner-Nordström-deSitter solutions but with ``renormalized'' dyonic charge plus a small logarithmic correction. The latter h…
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 show that a class of Einstein-Maxwell-Dilaton (EMD) theories are related to higher dimensional AdS-Maxwell gravity via a dimensional reduction over compact Einstein spaces combined with continuation in the dimension of the compact space to non-integral values (`generalized dimensional reduction'). This relates (fairly complicated) black hole solutions of EMD theories to simple black hole/brane solutions of AdS-Maxwell gravity and explains their properties. The generalized dimensional reduction is used to infer the holographic dictionary and the hydrodynamic behavior for this class of theori…
We presented the proof of the positive mass theorem for black holes in Einstein-Maxwell axion-dilaton gravity being the low-energy limit of the heterotic string theory. We show that the total mass of a spacetime containing a black hole is greater or equal to the square root of the sum of squares of the adequate dilaton-electric and dilaton-axion charges.
We discuss the application of the solitonic techniques to the 5D Einstein-Maxwell gravity. As an illustration we construct an exact solution describing two concentric rotating dipole black rings. The properties of the solution are investigated.
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.
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 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.
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.
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.
In the context of holography applied to condensed matter physics, we study Einstein-Maxwell-dilaton theory with curvature squared corrections. This theory has three couplings eta_i for the three R^2 invariants and two theory functions: a dilaton potential V(phi) and a dilaton-dependent gauge coupling f(phi). We find hyperscaling violating solutions of this theory, parametrized by dynamical critical exponent z and HSV parameter theta. We obtain restrictions on the form of the theory functions required to support HSV-type solutions using three physical inputs: the null energy condition, causalit…
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 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.
In this paper, we study the four dimensional Einstein-Maxwell-dilaton (EMD) theories in the Newman-Penrose (NP) formalism. We adapt the equations of motion into the NP formalism, and obtain the solution space that is asymptotic to the flat space-time. We then investigate the gravitational and electromagnetic memory effects. We find that the dilaton does not contribute to the displacement nor the kick memory effects, but it does contribute to the time-delayed memory effect.
Thermodynamics of charged black holes in Maxwell-dilaton-massive gravity
本文在Maxwell-标量-大质量引力中获得带电黑洞解析解，验证热力学第一定律，并发现具有三临界点的反向重入相变，表现为“小-大-小黑洞”过程。
By use of the potential reconstruction approach we obtain a series of asymptotically AdS (aAdS) black hole solutions in an Einstein-Maxwell-Dilaton (EMD) system. Basing on the solutions of the system, we reconstruct a semi-analytical holographic QCD (hQCD) model with a quadratic term in warped factor. We discuss some aspects of the hQCD model, in particular we calculate the free energy of two static color sources (a heavy quark-antiquark pair) which is an important order parameter to describe confinement/deconfinement phase transition. The behavior of the free energy with respect to temperatur…
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.
We derive inequalities between the area, the angular momentum and the charges for axisymmetric closed outermost stably marginally outer trapped surfaces, embedded in dynamical and, in general, non-axisymmetric spacetimes satisfying the Einstein-Maxwell-dilaton-matter equations. In proving the inequalities we assume that the dilaton potential is nonnegative and that the matter energy-momentum tensor satisfies the dominant energy condition.
We construct holographic superconductors from Einstein-Maxwell-dilaton gravity in 3+1 dimensions with two adjustable couplings $α$ and the charge $q$ carried by the scalar field. For the values of $α$ and $q$ we consider, there is always a critical temperature at which a second order phase transition occurs between a hairy black hole and the AdS RN black hole in the canonical ensemble, which can be identified with the superconducting phase transition of the dual field theory. We calculate the electric conductivity of the dual superconductor and find that for the values of $α$ and $q$ where $α/…
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 construct a class of charged, rotating solutions of (n+1)-dimensional Einstein-Maxwell-dilaton gravity with Liouville-type potentials and investigate their properties. These solutions are neither asymptotically flat nor (anti)-de Sitter. We find that these solutions can represent black brane, with two inner and outer event horizons, an extreme black brane or a naked singularity provided the parameters of the solutions are chosen suitably. We also compute temperature, entropy, charge, electric potential, mass and angular momentum of the black brane solutions, and find that these quantities s…
Without assuming rotational invariance, we derive Bogomol'nyi equations for the solitons in the abelian Chern-Simons gauge theories with the anomalous magnetic moment interaction. We also evaluate the number of zero modes around a static soliton configuration.
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 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.
We explore the cosmic censorship in the Einstein-Maxwell-dilaton theory following Wald's thought experiment to destroy a black hole by throwing in a test particle. We discover that at probe limit the extremal charged dilaton black hole could be destroyed by a test particle with specific energy. Nevertheless the censorship is well protected if backreaction or self-force is included. At the end, we discuss an interesting connection between Hoop Conjecture and Weak Gravity Conjecture.
In the present paper we prove a classification (uniqueness) theorem for stationary, asymptotically flat black hole spacetimes with connected and non-degenerate horizon in 4D Einstein-Maxwell-dilaton theory with an arbitrary dilaton coupling parameter $α$. We show that such black holes are uniquely specified by the length of the horizon interval, angular momentum, electric and magnetic charge and the value of the dilaton field at infinity when the dilaton coupling parameter satisfies $0\le α^2\le3$. The proof is based on the nonpositivity of the Riemann curvature operator on the space of the po…
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