Dilaton Field Equations Research Articles

The hierarchy problem and [formula omitted] supergravity

We introduce a new scenario to solve the hierarchy problem based on N=2, five-dimensional supergravity compactified on Calabi–Yau threefold down from D=11 supergravity. When modeling the universe as a 3-brane embedded in a five-dimensional bulk, the background metric is proportional to one of the hypermultiplets fields, namely the dilaton, the volume modulus of the Calabi–Yau space. When solving the dilaton field equation, we find that it is dependent on the extra dimension. We solve the modified Friedmann equations and find the implications of the model on the relation between the effective four-dimensional gravity scale in the brane and the Planck scale of the fifth extra dimension (M). A couple of different scales are considered for the extra dimension, the first where the extra dimension is in range of the solar system and M is of order of the electroweak scale, and the second where the scale of the extra dimension is of order μm and the higher dimensional Planck scale M∼1013GeV. In both cases, the signatures of Kaluza–Klein excitations are quite distinct from the signatures of any previous extra dimensions model.

Quantum Black Holes in Conformal Dilaton–Higgs Gravity on Warped Spacetimes

A promising method for understanding the geometric properties of a spacetime in the vicinity of the horizon of a Kerr-like black hole can be developed by applying the antipodal boundary condition on the two opposite regions in the extended Penrose diagram. By considering a conformally invariant Lagrangian on a Randall–Sundrum warped five-dimensional spacetime, an exact vacuum solution is found, which can be interpreted as an instanton solution on the Riemannian counterpart spacetime, R+2×R1×S1, where R+2 is conformally flat. The antipodal identification, which comes with a CPT inversion, is par excellence, suitable when quantum mechanical effects, such as the evaporation of a black hole by Hawking radiation, are studied. Moreover, the black hole paradoxes could be solved. By applying the non-orientable Klein surface, embedded in R4, there is no need for instantaneous transport of information. Further, the gravitons become “hard” in the bulk, which means that the gravitational backreaction on the brane can be treated without the need for a firewall. By splitting the metric in a product ω2g˜μν, where ω represents a dilaton field and g˜μν the conformally flat “un-physical” spacetime, one can better construct an effective Lagrangian in a quantum mechanical setting when one approaches the small-scale area. When a scalar field is included in the Lagrangian, a numerical solution is presented, where the interaction between ω and Φ is manifest. An estimate of the extra dimension could be obtained by measuring the elapsed traversal time of the Hawking particles on the Klein surface in the extra dimension. Close to the Planck scale, both ω and Φ can be treated as ordinary quantum fields. From the dilaton field equation, we obtain a mass term for the potential term in the Lagrangian, dependent on the size of the extra dimension.

Confined chiral dynamo action in torsional dilatonic DWs from CME discontinuities

In this paper, spin polarized domain walls in Einstein–Cartan (EC) gravity have been recently investigated [L. C. Garcia de Andrade, Einstein–Cartan non-supersymmetric dynamo walls, Ann. Phys. 432 (2021).], where the spin polarizes along the direction orthogonal to planar domain wall. In this case, dynamo effects may appear on the wall. Moreover, dilatonic domain walls (DDWs) have shown to be responsible for inflating DWs in EC gravity, where DWs were non-magnetized [L. Garcia de Andrade, Axial and chiral anomalies in Riemann–Cartan spacetime black holes and electrodynamics, Class. Quantum Grav. 16 (1999) 2097–2103.]. In this paper, our goal is to show that when we consider a magnetized DW in the EC–Maxwell cosmology, the dilaton potential in the form of a DDW potential expressed in terms of torsion and the magnetic energy density may drive dynamo effects. Analytical solution of the dynamo equation shows that depending on the handness of DDW metric, the magnetic fields are amplified by dynamo action. From the coupled system of ECM and dilaton field equations, we find a relation between the magnetic energy density of [Formula: see text] and the DDW torsion of [Formula: see text] which leads to a thin DDW thickness of [Formula: see text]. For a galactic magnetic field, energy density of [Formula: see text] leads to a thickness of [Formula: see text], a much thinner DDW. For galactic dynamo amplification, the ratio r between the magnetic energy density and photon energy density is around [Formula: see text]. From this ratio, a relation between photon mass density and torsion is obtained. Chiral Magnetic effect (CME), torsion and magnetic discontinuities along the wall are investigated. Magnetic field discontinuity across the wall allows us to understand why the magnetic fields at DDW must be located along the wall since the orthogonal magnetic field may vanish.

Dilatonic black holes in superstring gravity

We solve the dilaton field equation in the background of a spherically symmetric black hole in type II superstring theory with $\alpha'^3$ corrections in arbitrary $d$ spacetime dimensions. We then apply this result to obtain a spherically symmetric black hole solution with $\alpha'^3$ corrections in superstring theory compactified on a torus, coupled to such dilaton. For this black hole we obtain its mass, entropy, temperature, specific heat, and free energy.

Uniqueness of higher-dimensional Einstein-Maxwell-phantom dilaton field wormholes

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.

Elliptic Function Solutions in Jackiw-Teitelboim Dilaton Gravity

We present a new family of solutions for the Jackiw-Teitelboim model of two-dimensional gravity with a negative cosmological constant. Here, a metric of constant Ricci scalar curvature is constructed, and explicit linearly independent solutions of the corresponding dilaton field equations are determined. The metric is transformed to a black hole metric, and the dilaton solutions are expressed in terms of Jacobi elliptic functions. Using these solutions, we compute, for example, Killing vectors for the metric.

General class of anisotropic cosmological models with dilaton and magnetic fields

The Einstein–Maxwell dilaton field equations are considered for four-dimensional anisotropic Bianchi models. The general solutions have been obtained and their properties have been discussed. The exact solutions to the corresponding field equations are obtained for two different physical viable cosmologies. The cosmological parameters have been discussed in detail and it is also shown that the solutions tend asymptotically to isotropic Friedmann–Robertson–Walker cosmological model.

Waves, particles and fields: an explicitly covariant approach

The idea of associating particle trajectories with wave propagation rays exploited in a previous paper in the context of general relativity with a synchronous gauge, here is examined with no assumptions on co-ordinate choice (no synchronous gauge condition on the metric). Identification of particle Hamilton–Jacobi equation with wave-sheet equation in a space–time with more than 4 dimensions, is performed in an explicitly covariant formulation, leading to a Kaluza–Klein type theory involving Klein–Gordon equation arising from dilaton field equations. De Broglie and Einstein-Planck quantum relations are also deduced in a natural way. Adding suitable Yang–Mills fields provides unification of gravitational, electromagnetic, weak and strong interactions into a \(16\) dimensional space–time geometry. The electron mass gap is also avoided compactifying extra dimensional co-ordinates on fractalized closed paths.

On the Bogomol'nyi bound in Einstein–Maxwell-dilaton gravity

It has been shown that the four-dimensional Einstein–Maxwell-dilaton theory allows a Bogomol'nyi-type inequality for an arbitrary dilaton coupling constant α, and that the bound is saturated if and only if the (asymptotically flat) spacetime admits a nontrivial spinor satisfying the gravitino and the dilatino Killing spinor equations. This paper revisits this issue and argues that the dilatino equation fails to ensure the dilaton field equation unless the solution is purely electric/magnetic, or the dilaton coupling constant is given by , corresponding to the Brans–Dicke–Maxwell theory and the Kaluza–Klein reduction of five-dimensional vacuum gravity, respectively. A systematic classification of the supersymmetric solutions reveals that the solution can be rotating if and only if the solution is dyonic or the coupling constant is given by . This implies that the theory with cannot be embedded into supergravity except for the static truncation. Physical properties of supersymmetric solutions are explored from various points of view.

String-corrected dilatonic black holes inddimensions

We solve the dilaton field equation in the background of a spherically symmetric black hole in bosonic or heterotic string theory with curvature-squared corrections in arbitrary d spacetime dimensions. We then apply this result to obtain a spherically symmetric black hole solution with dilatonic charge and curvature-squared corrections in bosonic or heterotic string theory compactified on a torus. For this black hole we obtain its free energy, entropy, temperature, specific heat and mass.

Holographic description of glueball and baryon in noncommutative dipole gauge theory

We study the glueball spectrum in the supersymmetric and non-supersymmetric 4D non-commutative dipole gauge theory from the holographic description. We adopt the semiclassical WKB approximation to solve the dilaton and antisymmetric tensor field equations on the dual supergravity backgrounds to find the analytic formula of the spectrum of $0^{++}$ and $1^{--}$ glueballs, respectively. In the supersymmetric theory we see that the dipole length plays the intrinsic scale which reflects the discrete spectrum therein. In the non-supersymmetric theory, the temperature (or the radius of compactification) in there will now play the intrinsic scale and we see that the dipole has an effect to produce attractive force between the gluons within the glueball. We also study the confining force between the quarks within the baryon via strings that hang into the dipole deformed AdS geometry and see that the dipole could also produce an attractive force between the quarks. In particular, we find that the baryon has two phases in which a big baryon is dual to the static string while a small baryon is described by a moving dual string .

Symmetric space σ-model dynamics: Internal metric formalism

For the symmetric space sigma model in the internal metric formalism we explicitly construct the Lagrangian in terms of the axions and the dilatons of the solvable Lie algebra gauge and then we exactly derive the axion–dilaton field equations.

BIANCHI TYPE I UNIVERSES WITH DILATON AND MAGNETIC FIELDS

We consider the dynamics of a Bianchi type I spacetime in the presence of dilaton and magnetic fields. The general solution of the Einstein–Maxwell dilaton field equations can be obtained in an exact parametric form. Depending on the numerical values of the parameters of the model there are three distinct classes of solutions. The time evolution of the mean anisotropy, shear and deceleration parameters is considered in detail and it is shown that a magnetic-dilaton anisotropic Bianchi type I geometry does not isotropize, the initial anisotropy being present in the universe for all times.

FOUR- AND HIGHER-DIMENSIONAL MODELS WITH DILATON–ELECTROMAGNETIC FIELDS

The Einstein–Maxwell dilaton field equations are constructed for four-dimensional Bianchi III and five-dimensional FRW models. The general solutions have been obtained and their asymptotic behavior have been studied.

Dilaton electromagnetic Bianchi-I cosmologies

The Einstein-Maxwell dilaton field equations for a Bianchi-I geometry are written as an autonomous system of differential equations. The general solution for this system is obtained and its main properties are discussed.

Solitons and black holes

We explore the relationship between black holes in Jackiw-Teitelboim(JT) dilaton gravity and solitons in sine-Gordon field theory. Our analysis expands on the well known connection between solutions of the sine-Gordon equation and constant curvature metrics. In particular, we show that solutions to the dilaton field equations for a given metric in JT theory also solve the sine-Gordon equation linearized about the corresponding soliton. Since the dilaton generates Killing vectors of the constant curvature metric, it is interesting that it has an analoguous interpretation in terms of symmetries of the soliton solution. We also show that from the B${\ddot a}$cklund transformations relating different soliton solutions, it is possible to construct a flat SL(2,R) connection which forms the basis for the gauge theory formulation of JT dilaton gravity.

Static spherically symmetric solutions to Einstein-Maxwell dilaton field equations in D dimensions

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.

Background field equations for the heterotic string at finite temperature

The breaking of supersymmetry at T ≠ 0 leads to non-vanishing massless particle tadpoles and therefore to BRST anomalies in the degeneration limit of one-loop amplitudes. Cancellation of those anomalies gives the loop-corrected background field equations where the thermal energy-momentum tensor appears as source term for the graviton and dilaton field equations.

σ-MODELS AND STRING THEORIES

The propagation of closed bosonic strings interacting with background gravitational and dilaton fields is reviewed. The string is treated as a quantum field theory on a compact 2-dimensional manifold. The question is posed as to how the conditions for the vanishing trace anomaly and the ensuing background field equations may depend on global features of the manifold. It is shown that to the leading order in σ-model perturbation theory the string loop effects do not modify the gravitational and the dilaton field equations. However for the purely bosonic strings new terms involving the modular parameter of the world sheet are induced by quantum effects which can be absorbed into a re-definition of the background fields. We also discuss some aspects of several regularization schemes such as dimensional, Pauli-Villars and the proper-time cut off in an appendix.