Dilaton Charge Research Articles

PERFECT FLUID AND TEST PARTICLE WITH SPIN AND DILATONIC CHARGE IN A WEYL–CARTAN SPACE

The equation of perfect dilaton-spin fluid motion in the form of generalized hydrodynamic Euler-type equation in a Weyl–Cartan space is derived. The isoentropic character of perfect dilaton-spin fluid motion is established. The equation of motion of a test particle with spin and dilatonic charge in the Weyl–Cartan geomtry background is obtained. The peculiarities of test particle motion in a Weyl–Cartan space are discussed.

The Variational Theory of the Perfect Dilaton-Spin Fluid in a Weyl–Cartan Space

The variational theory of the perfect fluid with intrinsic spin and dilatonic charge (dilaton-spin fluid) is developed. The spin tensor obeys the classical Frenkel condition. The Lagrangian density of such fluid is stated, and the equations of motion of the fluid, the Weyssenhoff-type evolution equation of the spin tensor and the conservation law of the dilatonic charge are derived. The expressions of the matter currents of the fluid (the canonical energy-momentum three-form, the metric stress-energy four-form and the dilaton-spin momentum three-form) are obtained.

Sp(4, R)/GL(2, R) Matrix Structure of Geodesic Solutions for Einstein–Maxwell–Dilaton–Axion Theory

The Sp (4, R)/ GL (2, R) matrix operator defining the family of isotropic geodesic lines in the target space of the stationary D = 4 Einstein–Maxwell–dilaton–axion theory is constructed. This operator is used to derive a class of solutions describing a system of point centers with nontrivial values of mass, parameter NUT, as well as electric, magnetic, dilaton and axion charges. It is shown that this class contains the Majumdar–Papapetrou-like solutions and also the solutions for massless naked singularities.

The Post-Newtonian Limit of Dilaton Gravity

We study the post-Newtonian limit of a generalized dilaton gravity in which gravity is coupled to dilaton and eletromagnetic fields. The field equations are derived using the post-Newtonian scheme, and the approximate solution is presented for a point mass with electric and dilaton charges. The result indicates that the dilaton effect can be detected, in post-Newtonian level, using a charged test particle but not a neutral one. We have also checked that the approximate solution is indeed consistent with the weak field expansion of charged dilaton black hole solution in the harmonic coordinate. E-mail address: rrhsu@mail.ncku.edu.tw E-mail address: phycrl@ccunix.ccu.edu.tw 1

Stationary BPS solutions to dilaton-axion gravity.

Stationary four-dimensional BPS solutions to gravity coupled bosonic theories admitting a three-dimensional sigma-model representation on coset spaces are interpreted as null geodesics of the target manifold equipped with a certain number of harmonic maps. For asymptotically flat (or Taub-NUT) space-times such geodesics can be directly parametrized in terms of charges saturating the Bogomol'nyi-Gibbons-Hull bound, and classified according to the structure of related coset matrices. We investigate in detail the ``dilaton-axion gravity'' with one vector field, and show that in the space of BPS solutions an $SO(1,2) \times SO(2)$ classical symmetry is acting. Within the present formalism the most general multicenter (IWP/Taub-NUT dyon) solutions are derived in a simple way. We also discover a large new class of asymptotically flat solutions for which the dilaton and axion charges are constrained only by the BPS bound. The string metrics for these solutions are generically regular. Both the IWP class and the new class contain massless solutions.

New vacua for type II string theory

Lorentz-invariant expectation values for antisymmetric tensor field strengths in Calabi-Yau compactification of IIA string theory are considered. These are found to impart magnetic and/or electric charges to the dilation hypermultiplet. This results in a potential which can have supersymmetric minima at zero coupling or at conifold points in the moduli space. The latter occurs whenever the dilaton charge is aligned with that of the light black hole at the conifold. It is shown that there is a flat direction extending from the conifold along which there is a black hole condensate whose strength is of order the string coupling g s . It is speculated that these new vacua correspond to string compactification on generalized Calabi-Yau spaces which have c 1 = 0 but are not Kahler.

Dilatonic black holes in higher curvature string gravity.

We give analytical arguments and demonstrate numerically the existence of black hole solutions of the $4D$ Effective Superstring Action in the presence of Gauss-Bonnet quadratic curvature terms. The solutions possess non-trivial dilaton hair. The hair, however, is of ``secondary" type", in the sense that the dilaton charge is expressed in terms of the black hole mass. Our solutions are not covered by the assumptions of existing proofs of the ``no-hair" theorem. We also find some alternative solutions with singular metric behaviour, but finite energy. The absence of naked singularities in this system is pointed out.

Sequences of Einstein-Yang-Mills-dilaton black holes.

Einstein-Yang-Mills-dilaton theory possesses sequences of neutral static spherically symmetric black hole solutions. The solutions depend on the dilaton coupling constant $\gamma$ and on the horizon. The SU(2) solutions are labelled by the number of nodes $n$ of the single gauge field function, whereas the SO(3) solutions are labelled by the nodes $(n_1,n_2)$ of both gauge field functions. The SO(3) solutions form sequences characterized by the node structure $(j,j+n)$, where $j$ is fixed. The sequences of magnetically neutral solutions tend to magnetically charged limiting solutions. For finite $j$ the SO(3) sequences tend to magnetically charged Einstein-Yang-Mills-dilaton solutions with $j$ nodes and charge $P=\sqrt{3}$. For $j=0$ and $j \rightarrow \infty$ the SO(3) sequences tend to Einstein-Maxwell-dilaton solutions with magnetic charges $P=\sqrt{3}$ and $P=2$, respectively. The latter also represent the scaled limiting solutions of the SU(2) sequence. The convergence of the global properties of the black hole solutions, such as mass, dilaton charge and Hawking temperature, is exponential. The degree of convergence of the matter and metric functions of the black hole solutions is related to the relative location of the horizon to the nodes of the corresponding regular solutions.

Black holes with regular horizons in Maxwell-scalar gravity

A class of exact static spherically symmetric solutions of the Einstein–Maxwell gravity coupled to a massless scalar field is obtained in the harmonic coordinates of Minkowski space-time. For each value of the coupling constant a, these solutions are characterized by a set of three parameters, the physical mass μ0, the electric charge Q0 and the scalar-field parameter k. We find that the solutions for both gravitational and electromagnetic fields are not only affected by the scalar field, but also the nontrivial coupling with matter constrains the scalar field itself. In particular, we find that the constant k differs generically from ±1/2, falling into the interval [Formula: see text]. It takes these values only for black holes or in the case when a scalar field [Formula: see text] is totally decoupled from the matter. Our results differ from those previously obtained in that the presence of an arbitrary coupling constant a gives an opportunity to rule out the nonphysical horizons. In one of the special cases, the obtained solution corresponds to a charged dilatonic black hole with only one horizon μ+ and hence to the Kaluza–Klein case. The most remarkable property of this result is that the metric, the scalar curvature, and both the electromagnetic and scalar fields are all regular on this surface. Moreover, while studying the dilaton charge, we found that the inclusion of the scalar field in the theory resulted in a contraction of the horizon. The behavior of the scalar curvature was analysed.

Stringy sphalerons and Gauss-Bonnet term

The effect of the Gauss-Bonnet term on the SU(2) non-Abelian regular stringy sphaleron solutions is studied within the non-perturbative treatment. It is found that the existence of regular solutions depends crucially on the value of the numerical factor β in front of the Gauss-Bonnet term in the four-dimensional effective action. Numerical solutions are constructed in the N = 1, 2, 3 cases for different β below certain critical values β N which decrease with growing N ( N being the number of nodes of the Yang-Mills function). It is proved that for any static spherically symmetric asymptotically flat regular solution the ADM mass is exactly equal to the dilaton charge. No solutions were found for β above critical values, in particular, for β = 1.

Duality and four-dimensional black holes

Abstract We consider the effects of abelian duality transformations on static, spherically symmetric, asymptotically flat string spacetimes in four dimensions, where the dilaton, axion, metric, and gauge fields are allowed to be nonzero. Independent of the α ′ expansion, there is a six-parameter family of such configurations, labelled by the charges characterizing the asymptotic behaviour of the various fields: i.e. their mass, dilaton charge, axion charge, electric charge, magnetic charge, and Taub-NUT parameter. We show that duality, based on time-translation invariance, maps these solutions amongst themselves, with the effect of interchanging two pairs of these six labels, namely: (1) the mass and dilaton charge, and (2) the axion charge and the Taub-NUT parameter. We consider in detail the special case of the purely Schwarzschild black hole, for which the mass of the dual configuration vanishes to leading order in α ′. Working to next-to-leading order in α ′ for the bosonic and heterotic strings, we find that duality takes a black hole of mass M to a (singular) solution having mass ∼ −1/ α ′ M . Finally, we argue that two solutions which are related by duality based on a noncompact symmetry are not always physically equivalent.

On spherically symmetric string solutions in four dimensions

We reconsider here the problem of finding the general 4D spherically symmetric, asymptotically flat and time-independent solutions to the lowest-order string equations in the $\ap$ expansion. Our construction includes earlier work, but differs from it in three ways. (1) We work with general background metric, dilaton, axion and $U(1)$ gauge fields. (2) Much of the original solutions were required to be nonsingular at the apparent horizon, motivated by an interest in finding string corrections to black hole spacetimes. We relax this condition throughout, motivated by the realization that string theory has a less restrictive notion of what constitutes a singular field configuration than do point particle theories. (3) We can construct the general solution from a particularly simple one, by generating it from successive applications of the {\it noncommuting} \sltwor\ and \ooneone\ symmetries of the low-energy string equations containing $S$ and target--space dualities respectively. This allows its construction using relatively simple, purely algebraic, techniques. The general solution is determined by the asymptotic behaviour of the various fields: \ie\ by the mass, dilaton charge, axion charge, electric charge, magnetic charge, and Taub-NUT parameter.

Shock wave mixing in Einstein and dilaton gravity

We consider possible mixing of electromagnetic and gravitational shock waves, in the Planckian energy scattering of point particles in Minkowski space. By boosting a Reissner-Nordström black hole solution to the velocity of light, it is shown that no mixing of shock waves takes place for arbitrary finite charge carried by the black hole. However, a similar boosting procedure for a charged black hole solution in dilation gravity yields some mixing the wave function of even a neutral test particle, acquires a small additional phase factor depending on the dilatonic black hole charge. Possible implications for poles in the amplitudes for the dilaton gravity case are discussed.

Class of stationary axisymmetric solutions of the Einstein-Maxwell-dilaton-axion field equations.

A wide class of solutions, endowed with stationary and axial symmetries, of the Einstein-Maxwell-dilaton-axion equations are explicitly given. The chosen coordinate system is such that the structural functions are expressible as a ratio of polynomials of, at most, second degree. It is equipped with six continuous free parameters and two discrete constants. In particular, it contains the generalized Sen black hole with mass, Newman-Unti-Tamburino parameter, charge, angular momentum, dilaton and axion limiting parameters, and related magnetic, dilaton, and axion charges.

Dilaton black holes with electric charge.

New static spherically symmetric solutions of the Einstein-Maxwell gravity with the dilaton field are found. The solutions correspond to black holes and naked singularities. In addition to mass and electric charge these solutions are labeled by a new parameter, the dilaton charge of the black hole. Depending on the values of electric and dilaton charges there are different types of solutions. The solutions exhibit a new type of a symmetry. Namely one solution transforms into another when the mass and the dilaton charge are interchanged. We also found that there is a finite interval of values of electric charge for which no black hole can exist. This gap separates two different types of solutions. Inside the gap the solution can exist only if the dilaton charge is exactly equal to the negative of the mass. The behavior of the solution in the extremal regime is also analyzed.

Motion of test particles around a charged dilatonic black hole

We examine motion of test particles with various masses, electric charges and dilatonic charges in a background metric and fields of a charged dilatonic black hole.

Stringy sphalerons and non-abelian black holes

Static spherically symmetric asymptotically flat particle-like and black hole solutions are constructed within the SU(2) sector of 4-dimensional heterotic string effective action. They separate topologically distinct Yang-Mills vacua and are qualitatively similar to the Einstein-Yang-Mills spha- lerons and non-abelian black holes discussed recently. New solutions possess quantized values of the dilaton charge.

Fifth force from Kaluza-Klein unification

We discuss the possible modification of Einstein's theory of gravitation due to the fifth force generated by the Kaluza-Klein dilaton. In particular we discuss the gravitational redshift, the deflection of light, the precession of perihelia, and the time-delay of radar echo around a spherically symmetric black hole in a 7-dimensional Kaluza-Klein unification which hasE2 as the internal isometry. It is shown that the long-range effect of the higher-dimensional fifth force is characterized by the dilatonic charge carried by the black hole even when it is neutral.

Higher-dimensional unification and fifth force

We discuss the possible modification of Einstein’s theory of gravitation due to the fifth force generated by the Kaluza-Klein dilaton. In particular we discuss the gravitational red-shift, the deflection of light, the precession of perihelia, and the time-delay of radar echo around a spherically symmetric black hole in a 7-dimensional Kaluza-Klein unification which hasE2 as the internal isometry. It is shown that the long-range effect of the higherdimensional fifth force is characterized by the dilatonic charge carried by the black hole even when it is neutral.

Spontaneous generation of massive multiplets and central charges in extended supersymmetric theories

Massless gauge theories invariant under extended supersymmetry algebras with N = 2 or N = 4 spinorial generators have U(2) or SU(4) as the global internal symmetry group. The translation of scalar fields in these theories generate massive, gauge or matter, multiplets of various types. The existence of most of these multiplets requires an (apparent) modification of the structure of the algebra: in the anticommutators of spinorial generators we now find “central charges”, which commute with all symmetries of the theory. Such central charges are not new symmetries, but only some of the (Abelian or non-Abelian) generators of the gauge group, which are preserved by the translation. In the non-Abelian case, the promotion of some of the Yang-Mills generators to the role of central charges implies of course a spontaneous breaking of the Yang-Mills group. In addition the appearance of central charges in the algebra requires a breaking of the global internal symmetry group U(2) or SU(4) to a smaller subgroup. The generation of masses in an originally massless theory results in a massless gauge or matter multiplet containing the following noteworthy fields: the dilaton, one or several Goldstone bosons, and N pseudo-Goldstone spinors, associated with the breaking of dilatation, global internal symmetry and the N extra spinorial generators appearing in the conformal superalgebra (while the N ordinary supersymmetry generators remain conserved). The connection between the dilaton and central charges leads to a relation between the (mass) 2 operator and the sum of the squares of the central charges (and to the possibility of mass quantization). This can be interpreted by comparing the central charges with the translation operators in a two- or six-dimensional compact internal symmetry space.