Scalar Field Source Research Articles

Analytical approximate solutions of AdS black holes in Einstein-Weyl-scalar gravity* *M. Z. is supported by the Natural Science Basic Research Program of Shaanxi, China (2023-JC-QN-0053). D. C. Z is supported by the Natural Science Foundation of China (12365009) and the Natural Science Foundation of Jiangxi Province, China (20232BAB201039)

We consider Einstein-Weyl gravity with a minimally coupled scalar field in four dimensional spacetime. Using the minimal geometric deformation (MGD) approach, we split the highly nonlinear coupled field equations into two subsystems that describe the background geometry and scalar field source, respectively. By considering the Schwarzschild-AdS metric as background geometry, we derive analytical approximate solutions of the scalar field and deformation metric functions using the homotopy analysis method (HAM), providing their analytical approximations to fourth order. Moreover, we discuss the accuracy of the analytical approximations, showing they are sufficiently accurate throughout the exterior spacetime.

New time-dependent solutions of viable Horndeski gravity

We generate new spherical and time-dependent solutions of viable Horndeski gravity by disforming a solution of the Einstein equations with scalar field source and positive cosmological constant. They describe dynamical objects embedded in asymptotically FLRW spacetimes and contain apparent horizons and a finite radius singularity that evolve in time in peculiar ways apparently not encountered before in Einstein and “old” scalar-tensor gravity.

Linearized propagation equations for metric fluctuations in a general (non-vacuum) background geometry

The linearized dynamical equation for metric perturbations in a fully general, non-vacuum, background geometry is obtained from the Hamilton variational principle applied to the action up to second order. We specialize our results to the case of traceless and transverse metric fluctuations, and we discuss how the intrinsic properties of the matter stress tensor can affect (and modify) the process of gravity wave propagation even in most conventional geometric scenarios, like (for instance) those described by a FLRW metric background. We provide explicit examples for fluid, scalar field and electromagnetic field sources.

Late-time acceleration with a scalar field source: Observational constraints and statefinder diagnostics

This article discusses a dark energy cosmological model in the standard theory of gravity - general relativity with a broad scalar field as a source. Exact solutions of Einstein's field equations are derived by considering a particular form of deceleration parameter $q$, which shows a smooth transition from decelerated to accelerated phase in the evolution of the universe. The external datasets such as Hubble ($H(z)$) datasets, Supernovae (SN) datasets, and Baryonic Acoustic Oscillation (BAO) datasets are used for constraining the model par parameters appearing in the functional form of $q$. The transition redshift is obtained at $% z_{t}=0.67_{-0.36}^{+0.26}$ for the combined data set ($H(z)+SN+BAO$), where the model shows signature-flipping and is consistent with recent observations. Moreover, the present value of the deceleration parameter comes out to be $q_{0}=-0.50_{-0.11}^{+0.12}$ and the jerk parameter $% j_{0}=-0.98_{-0.02}^{+0.06}$ (close to 1) for the combined datasets, which is compatible as per Planck2018 results. The analysis also constrains the omega value i.e., $\Omega _{m_{0}}\leq 0.269$ for the smooth evolution of the scalar field EoS parameter. It is seen that energy density is higher for the effective energy density of the matter field than energy density in the presence of a scalar field. The evolution of the physical and geometrical parameters is discussed in some details with the model parameters' numerical constrained values. Moreover, we have performed the state-finder analysis to investigate the nature of dark energy.

Inflation without a trace of lambda

We generalise Einstein’s formulation of the traceless Einstein equations to f(R) gravity theories. In the case of the vacuum traceless Einstein equations, we show that a non-constant Weyl tensor leads via a conformal transformation to a dimensionally homogeneous (‘no-scale’) theory in the conformal frame with a scalar field source that has an exponential potential. We then formulate the traceless version of f(R) gravity, and we find that a conformal transformation leads to a no-scale theory conformally equivalent to general relativity and a scalar field phi with a potential given by the scale-invariant form: V(phi )=frac{D-2}{4D}Re^{-phi }, where phi =[2/(D-2)]ln f^{prime }(R). In this theory, the cosmological constant is a mere integration constant, statistically distributed in a multiverse of independent causal domains, the vacuum energy is another unrelated arbitrary constant, and the same is true of the height of the inflationary plateau present in a huge variety of potentials. Unlike in the conformal equivalent of full general relativity, flat potentials are found to be possible in all spacetime dimensions for polynomial lagrangians of all orders. Hence, we are led to a novel interpretation of the cosmological constant vacuum energy problem and have accelerated inflationary expansion in the very early universe with a very small cosmological constant at late times for a wide range of no-scale theories. Fine-tunings required in traceless general relativity or standard non-traceless f(R) theories of gravity are avoided. We show that the predictions of the scale-invariant conformal potential are completely consistent with microwave background observational data concerning the primordial tilt and the tensor-to-scalar ratio.

Leader–follower formation source seeking control of multiple ships using sliding mode active disturbance rejection observer

In this paper, the control of multiple ships for unknown scalar field source seeking problem with unknown external disturbances is considered. The sliding mode active disturbance rejection observers are designed first to converge to fixed multiple of the unknown external disturbances in finite time, respectively, and a least square method is adopted to estimate the gradient of the unknown scalar field at the position of the leading ship. Second, the surge, sway and angle velocity of the leading ship can converge to the virtual kinematic controllers through the input control of the dynamic controllers using force and torque in finite time. Third, the virtual controllers and dynamic controllers of the following ships are developed to urge the following ships to accomplish the source seeking problem from the perspective of dynamics. Finally, theoretical proofs and simulations are provided to prove the effectiveness of the strategy proposed.

Evolving metric perturbations in dynamical Chern-Simons gravity

We present a well-posed constraint-preserving scheme for evolving first-order metric perturbations on an arbitrary background with arbitrary source. We use this scheme to evolve the leading-order metric perturbation in order-reduced dynamical Chern-Simons gravity (dCS) on a Kerr background. In particular we test the stability of stationary dCS data on a Kerr background with stationary first-order dCS scalar field source. We find that the leading-order metric perturbation numerically exhibits linear growth, but that the level of this growth converges to zero with numerical resolution. This analysis shows that spinning black holes in dCS gravity are numerically stable to leading-order perturbations in the metric.

Five-Dimensional Warped Product Space-Time with Time-Dependent Warping and a Scalar Field in the Bulk

We have considered gravity in a five-dimensional warped product space-time, with a time-dependent warp factor and a time-dependent extra dimension. The five-dimensional field equations are derived for a spatially flat FRW brane and the energy conditions and the nature of bulk geometry have been examined. It is found that the expansion of the four-dimensional universe depends on its location along the extra dimension and will be different at different locations in the bulk spacetime. At low energies, the trapping of fields within the brane implies a specific correlation between the warp factor and the extra-dimensional scale factor. Generally, the bulk is not conformally flat. At high energies, the bulk is assumed to be sourced by a scalar field with self-interaction. The analysis shows that the potential of the scalar field source of gravity at a given position along the fifth dimension, is related to the Hubble parameter on the brane at that position in the bulk.

Canonical and phantom scalar fields as an interaction of two perfect fluids

In this article we investigate and develop specific aspects of Friedmann-Robertson-Walker (FRW) scalar field cosmologies related to the interpretation that canonical and phantom scalar field sources may be interpreted as cosmological configurations with a mixture of two interacting barotropic perfect fluids: a matter component $\rho_1(t)$ with a stiff equation of state ($p_1=\rho_1$), and an "effective vacuum energy" $\rho_2(t)$ with a cosmological constant equation of state ($p_2=-\rho_2$). An important characteristic of this alternative equivalent formulation in the framework of interacting cosmologies is that it gives, by choosing a suitable form of the interacting term $Q$, an approach for obtaining exact and numerical solutions. The choice of $Q$ merely determines a specific scalar field with its potential, thus allowing to generate closed, open and flat FRW scalar field cosmologies.

Cooperative Control of Multiple UAVs for Source Seeking

This paper considers the problem of unknown scalar field source seeking using multiple UAVs subject to input constraints. In this problem, each UAV can only measure the scalar field value at its current location. In order to seek the scalar field source, cooperation of multiple UAVs is carried out by adopting a leader-follower formation strategy. A least squares method is introduced to estimate the gradient of the scalar field at the leader UAV location based on the measurements of all UAVs. By using the estimated gradient, this paper proposes a guidance law for the heading of the leader UAV, and a sliding mode based heading rate controller is designed for the leader UAV to follow the desired heading angle. Furthermore, a heading rate controller is developed for each follower UAV to achieve circular formation around the leader UAV. Finally, simulation results are provided to demonstrate the effectiveness of the proposed approach.

A comment on positive mass for scalar field sources

We use a transformation due to Bekenstein to relate the ADM and Bondi masses of asymptotically-flat solutions of the Einstein equations with, respectively, scalar sources and conformal-scalar sources. Although the conformal-scalar energy-momentum tensor does not satisfy the Dominant Energy Condition one may, by this means, still conclude that the ADM mass is positive.

On asymptotically flat solutions of Einstein's equations periodic in time: II. Spacetimes with scalar-field sources

We extend the work in our earlier paper (Bičák J et al 2010 Class. Quantum Grav. 27 055007) to show that time-periodic, asymptotically flat solutions of the Einstein equations analytic at , whose source is one of a range of scalar-field models, are necessarily stationary. We also show that, for some of these scalar-field sources, in stationary, asymptotically flat solutions analytic at , the scalar field necessarily inherits the symmetry. To prove these results we investigate miscellaneous properties of massless and conformal scalar fields coupled to gravity, in particular Bondi mass and its loss.

The dynamical behavior of homogeneous scalar-field spacetimes with general self-interaction potentials

The dynamics of homogeneous Robertson–Walker cosmological models with a self-interacting scalar field source is examined here in full generality, requiring only the scalar field potential to be bounded from below and divergent when the field diverges. In this way we are able to give a unified treatment of all the already studied cases—such as positive potentials which exhibit asymptotically polynomial or exponential behaviors—together with its extension to a much wider set of physically sensible potentials. Since the set includes potentials with negative inferior bound, we are able to give, in particular, the analysis of the asymptotically anti De Sitter states for such cosmologies.

Slowly rotating wormholes: the first-order approximation

We discuss a solution describing a rotating wormhole in general relativity with a scalar field source having negative kinetic energy. To solve the problem, we use the assumption of slow rotation. The role of a small dimensionless parameter is played the ratio of the linear velocity of rotation of the wormhole throat and the velocity of light. The rotating wormhole solution is constructed in the first-order approximation with respect to the small parameter. We analyze the solution obtained and study test particle motion and light propagation in the spacetime of a rotating wormhole.

Scalar fields coupled to gravity in (3+1) dimensions: Static spherically symmetric stiff matter solutions

Einstein’s field equations for a spherically symmetric metric and a massless scalar field source are reduced to a system effectively of second order in time for the metric function μ. The solutions of this system split into two classes that we called the positive and negative branches, corresponding to scalar fields with spacelike and timelike gradients. Static solutions for the positive branch are well known, but the proof that μ=0 is a global attractor for the region μs+μ>0, μ<1∕2 is given for completeness. The negative branch of static solutions have the interpretation of a perfect fluid with pressure equal to mass density, called “stiff matter.” The main result of the paper is the characterization of static solutions of the negative branch by phase plane analysis. We prove that the solution μ=1∕4 is a global attractor for the region where μs+μ>0 and μ<1∕2. Two first integrals, one of which reducing to the solution μ=1∕4 in the static case, are also presented.

Applications of theorems of Jean Leray to the Einstein-scalar field equations

The Einstein-scalar field theory can be used to model gravitational physics with scalar field sources. We discuss the initial value formulation of this field theory, and show that the ideas of Leray can be used to show that the Einstein-scalar field system of partial differential equations is well-posed as an evolutionary system. We also show that one can generate solutions of the Einstein-scalar field constraint equations using conformal methods.

Variational approach to Robertson–Walker spacetimes with homogeneous scalar fields

Existence of solutions between prescribed configurations is proved for spatially flat Robertson–Walker spacetimes coupled with homogeneous scalar field sources, using a modified version of the Euler–Maupertuis least action variational principle. The solutions are obtained as limits of approximating variational problems, solved using the techniques originally introduced by Rabinowitz.

Correspondence between kinematical backreaction and scalar field cosmologies—the ‘morphon field’

Spatially averaged inhomogeneous cosmologies in classical general relativity can be written in the form of effective Friedmann equations with sources that include backreaction terms. In this paper, we propose to describe these backreaction terms with the help of a homogeneous scalar field evolving in a potential; we call it the ‘morphon field’. This new field links classical inhomogeneous cosmologies to scalar field cosmologies, allowing to reinterpret, e.g., quintessence scenarios by routing the physical origin of the scalar field source to inhomogeneities in the universe. We investigate a one-parameter family of scaling solutions to the backreaction problem. Subcases of these solutions (all without an assumed cosmological constant) include scale-dependent models with Friedmannian kinematics that can mimic the presence of a cosmological constant or a time-dependent cosmological term. We explicitly reconstruct the scalar field potential for the scaling solutions and discuss those cases that provide a solution to the dark energy and coincidence problems. In this approach, dark energy emerges from morphon fields, a mechanism that can be understood through the proposed correspondence: the averaged cosmology is characterized by a weak decay (quintessence) or growth (phantom quintessence) of kinematical fluctuations, fed by ‘curvature energy’ that is stored in the averaged 3-Ricci curvature. We find that the late-time trajectories of those models approach attractors that lie in the future of a state that is predicted by observational constraints.

Field strength computation at edges in nonlinear magnetostatics

Magnetostatic problems including iron components can be solved by a nonlinear indirect volume integral equation. Its unknowns are scalar field sources. They are evaluated iteratively. In doing so the integral representation of fields has to be calculated. At edges singularities occur. Following a method to calculate the field strength on charged surfaces a way out is presented.

Isotropic singularity in inhomogeneous brane cosmological models

We discuss the asymptotic dynamical evolution of spatially inhomogeneous brane-world cosmological models close to the initial singularity. By introducing suitable scale-invariant dependent variables and a suitable gauge, we write the evolution equations of the spatially inhomogeneous G2 brane cosmological models with one spatial degree of freedom as a system of autonomous first-order partial differential equations. We study the system numerically, and we find that there always exists an initial singularity, which is characterized by the fact that spatial derivatives are dynamically negligible. More importantly, from the numerical analysis we conclude that there is an initial isotropic singularity in all these spatially inhomogeneous brane cosmologies for a range of parameter values which include the physically important cases of radiation and a scalar field source. The numerical results are supported by a qualitative dynamical analysis and a calculation of the past asymptotic decay rates. Although the analysis is local in nature, the numerics indicate that the singularity is isotropic for all relevant initial conditions. Therefore this analysis, and a preliminary investigation of general inhomogeneous (G0) models, indicates that it is plausible that the initial singularity is isotropic in spatially inhomogeneous brane-world cosmological models and consequently that brane cosmology naturally gives rise to a set of initial data that provide the conditions for inflation to subsequently take place.