Scalar Field In General Relativity Research Articles

Scalar field as a perfect fluid: thermodynamics of minimally coupled scalars and Einstein frame scalar-tensor gravity

We revisit the analogy between a minimally coupled scalar field in general relativity and a perfect fluid, correcting previous identifications of effective temperature and chemical potential. This provides a useful complementary picture for the first-order thermodynamics of scalar-tensor gravity, paving the way for the Einstein frame formulation (which eluded previous attempts) and raises interesting questions to further develop the analogy.

ϕ-modes of neutron stars in a massless scalar–tensor theory

Scalar–tensor theories allow for a rich spectrum of quasinormal modes of neutron stars. The presence of the scalar field allows for polar monopole and dipole radiation, as well as for additional higher multipole modes led by the scalar field. Herein, we present one family of the modes which are dominated by the scalar fields, the scalar-led ϕ-modes computed numerically with a shooting method, for the lowest multipoles, that is, l = 0, 1, and 2 for a massless scalar–tensor theory of the Brans–Dicke type, motivated by the R2 theory, and compare with those of a minimally coupled scalar field in general relativity. We consider a set of six realistic equations of state and extract universal relations for the modes.

Black bounces, wormholes, and partly phantom scalar fields

Simpson and Visser recently proposed a phenomenological way to avoid some kinds of space-time singularities by replacing a parameter whose zero value corresponds to a singularity (say, $r$) with the manifestly nonzero expression $r(u) = \sqrt{u^2 + b^2}$, where $u$ is a new coordinate, and $b =$ \const $>0$. This trick, generically leading to a regular minimum of $r$ beyond a black hole horizon (called a "black bounce"), may hopefully mimic some expected results of quantum gravity, and was previously applied to regularize the Schwarzschild, Reissner-Nordstr\"om, Kerr and some other metrics. In this paper it is applied to regularize the Fisher solution with a massless canonical scalar field in general relativity (resulting in a traversable wormhole) and a family of static, spherically symmetric dilatonic black holes (resulting in regular black holes and wormholes). These new regular metrics represent exact solutions of general relativity with a sum of stress-energy tensors of a scalar field with a nonzero self-interaction potential and a magnetic field in the framework of nonlinear electrodynamics with a Lagrangian function $L(F)$, $F = F_{\mu\nu} F^{\mu\nu}$. A novel feature in the present study is that the scalar fields involved have "trapped ghost" properties, that is, are phantom in a strong-field region and canonical outside it, with a smooth transition between the regions. It is also shown that any static, spherically symmetric metric can be obtained as an exact solution to the Einstein equations with the stress-energy tensor of the above field combination.

The simplest wormhole in Rastall and k-essence theories

The geometry of the Ellis–Bronnikov wormhole is implemented in the Rastall and k-essence theories of gravity with a self-interacting scalar field. The form of the scalar field potential is determined in both cases. A stability analysis with respect to spherically symmetric time-dependent perturbations is carried out, and it shows that in k-essence theory the wormhole is unstable, like the original version of this geometry supported by a massless phantom scalar field in general relativity. In Rastall’s theory, it turns out that a perturbative approach reveals the same inconsistency that was found previously for black hole solutions: time-dependent perturbations of the static configuration prove to be excluded by the equations of motion, and the wormhole is, in this sense, stable under spherical perturbations.

Static spacetimes haunted by a phantom scalar field. I. Classification and global structure in the massless case

We discuss various novel features of $n(\ge 4)$-dimensional spacetimes sourced by a massless (non-)phantom scalar field in general relativity. Assuming that the metric is a warped product of static two-dimensional Lorentzian spacetime and an $(n-2)$-dimensional Einstein space $K^{n-2}$ with curvature $k=0, \pm 1$, and that the scalar field depends only on the radial variable, we present a complete classification of static solutions for both signs of kinetic term. Contrary to the case with a non-phantom scalar field, the Fisher solution is not unique, and there exist two additional metrics corresponding to the generalizations of the Ellis-Gibbons solution and the Ellis-Bronnikov solution. We explore the maximal extension of these solutions in detail by the analysis of null/spacelike geodesics and singularity. For the phantom Fisher and Ellis-Gibbons solutions, we find that there inevitably appear parallelly propagated (p.p) curvature singularities in the parameter region where there are no scalar curvature singularities. Interestingly, the areal radius blows up at these p.p curvature singularities, which are nevertheless accessible within a finite affine time along the radial null geodesics. It follows that only the Ellis-Bronnikov solution describes a regular wormhole in the two-sided asymptotically flat spacetime. Using the general transformation relating the Einstein and Jordan frames, we also present a complete classification of solutions with the same symmetry coupled to a conformal scalar field. Additionally, by solving the field equations in the Jordan frame, we prove that this classification is genuinely complete.

Energy balance of a Bose gas in a curved space-time

We derive a general energy balance equation for a self-interacting boson gas at vanishing temperature in a curved spacetime. This represents a first step towards a formulation of the first law of thermodynamics for a scalar field in general relativity. By using a $3+1$ foliation of the spacetime and performing a Madelung transformation, we rewrite the Klein-Gordon-Maxwell equations in a general curved spacetime into its hydrodynamic version where we can identify the different energy contributions of the system and separate them into kinetic, quantum, electromagnetic, and gravitational.

Bianchi type-V dark energy cosmological model in general relativity in the presence of massive scalar field

In this paper, we discuss spatially homogeneous and anisotropic Bianchi type-V dark energy cosmological model in the presence of an attractive massive scalar field in general relativity. We have solved the field equations using (i) the shear scalar of the metric is proportional to the expansion scalar which results a relationship between metric potentials and (ii) a power law between the massive scalar field and the average scale factor. We have computed the cosmological parameters like dark energy density, equation of state parameter, skewness parameters, deceleration parameter and statefinder parameters of our dark energy model with massive strings and discussed their physical significance in the light of the recent scenario of accelerated expansion of the universe and cosmological observations.

Jeans-type instability of a complex self-interacting scalar field in general relativity

We study the gravitational instability of a general relativistic complex scalar field with a quartic self-interaction in an infinite homogeneous static background. This quantum relativistic Jeans problem provides a simplified framework to study the formation of the large-scale structures of the Universe in the case where dark matter is made of a scalar field. The scalar field may represent the wave function of a relativistic self-gravitating Bose-Einstein condensate. Exact analytical expressions for the dispersion relation and Jeans length $\lambda_J$ are obtained from a hydrodynamical representation of the Klein-Gordon-Einstein equations. When relativistic effects are fully accounted for, we find that the perturbations are stabilized at very large scales of the order of the Hubble length $\lambda_H$. Numerical applications are made for ultralight bosons without self-interaction (fuzzy dark matter), for bosons with a repulsive self-interaction, and for bosons with an attractive self-interaction (QCD axions and ultralight axions). We show that the Jeans instability is inhibited in the ultrarelativistic regime (early Universe and radiationlike era) because the Jeans length is of the order of the Hubble length ($\lambda_J\sim\lambda_H$), except when the self-interaction of the bosons is attractive. By contrast, structure formation can take place in the nonrelativistic regime (matterlike era) for $\lambda_J\le \lambda\le \lambda_H$. Since the scalar field has a nonzero Jeans length due to its quantum nature (Heisenberg uncertainty principle or quantum pressure due to the self-interaction of the bosons), it appears that the wave properties of the scalar field can stabilize gravitational collapse at small scales, providing halo cores and suppressing small-scale linear power. This may solve the CDM crisis such as the cusp problem and the missing satellite problem.

Einstein’s gravity from a polynomial affine model

We show that the effective field equations for a recently formulated polynomial affine model of gravity, in the sector of a torsion-free connection, accept general Einstein manifolds—with or without cosmological constant—as solutions. Moreover, the effective field equations are partially those obtained from a gravitational Yang–Mills theory known as Stephenson–Kilmister–Yang theory. Additionally, we find a generalization of a minimally coupled massless scalar field in General Relativity within a ‘minimally’ coupled scalar field in this affine model. Finally, we present a brief (perturbative) analysis of the propagators of the gravitational theory, and count the degrees of freedom. For completeness, we prove that a Birkhoff-like theorem is valid for the analyzed sector.

Geometric flows and Perelman’s thermodynamics for black ellipsoids in [formula omitted] and Einstein gravity theories

We study geometric relativistic flow and Ricci soliton equations which (for respective nonholonomic constraints and self-similarity conditions) are equivalent to the gravitational field equations of R2 gravity and/or to the Einstein equations with scalar field in general relativity, GR. Perelman’s functionals are generalized for modified gravity theories, MGTs, which allows to formulate an analogous statistical thermodynamics for geometric flows and Ricci solitons. There are constructed and analyzed generic off-diagonal black ellipsoid, black hole and solitonic exact solutions in MGTs and GR encoding geometric flow evolution scenarios and nonlinear parametric interactions. Such new classes of solutions in MGTs can be with polarized and/or running constants, nonholonomically deformed horizons and/or embedded self-consistently into solitonic backgrounds. They exist also in GR as generic off-diagonal vacuum configurations with effective cosmological constant and/or mimicking effective scalar field interactions. Finally, we compute Perelman’s energy and entropy for black ellipsoids and evolution solitons in R2 gravity.

The body motion in gravitational field of a spherically symmetrical configuration with scalar field in General relativity

The body motion in gravitational field of a spherically symmetrical configuration with scalar field in General relativity

Islands of stability and recurrence times in AdS

We study the stability of anti-de Sitter (AdS) spacetime to spherically symmetric perturbations of a real scalar field in general relativity. Further, we work within the context of the "two time framework" (TTF) approximation, which describes the leading nonlinear effects for small amplitude perturbations, and is therefore suitable for studying the weakly turbulent instability of AdS---including both collapsing and non-collapsing solutions. We have previously identified a class of quasi-periodic (QP) solutions to the TTF equations, and in this work we analyze their stability. We show that there exist several families of QP solutions that are stable to linear order, and we argue that these solutions represent islands of stability in TTF. We extract the eigenmodes of small oscillations about QP solutions, and we use them to predict approximate recurrence times for generic non-collapsing initial data in the full (non-TTF) system. Alternatively, when sufficient energy is driven to high-frequency modes, as occurs for initial data far from a QP solution, the TTF description breaks down as an approximation to the full system. Depending on the higher order dynamics of the full system, this often signals an imminent collapse to a black hole.

Interior Dynamics of Neutral and Charged Black Holes in f(R) Gravity

In this paper, we explore the interior dynamics of neutral and charged black holes in f(R) gravity. We transform f(R) gravity from the Jordan frame into the Einstein frame and simulate scalar collapses in flat, Schwarzschild, and Reissner-Nordström geometries. In simulating scalar collapses in Schwarzschild and Reissner-Nordström geometries, Kruskal and Kruskal-like coordinates are used, respectively, with the presence of f′ and a physical scalar field being taken into account. The dynamics in the vicinities of the central singularity of a Schwarzschild black hole and of the inner horizon of a Reissner-Nordström black hole is examined. Approximate analytic solutions for different types of collapses are partially obtained. The scalar degree of freedom Φ, transformed from f′, plays a similar role as a physical scalar field in general relativity. Regarding the physical scalar field in f(R) case, when dΦ/dt is negative (positive), the physical scalar field is suppressed (magnified) by Φ, where t is the coordinate time. For dark energy f(R) gravity, inside black holes, gravity can easily push f′ to 1. Consequently, the Ricci scalar R becomes singular, and the numerical simulation breaks down. This singularity problem can be avoided by adding an R2 term to the original f(R) function, in which case an infinite Ricci scalar is pushed to regions where f′ is also infinite. On the other hand, in collapse for this combined model, a black hole, including a central singularity, can be formed. Moreover, under certain initial conditions, f′ and R can be pushed to infinity as the central singularity is approached. Therefore, the classical singularity problem, which is present in general relativity, remains in collapse for this combined model.

Holographic thermalization, stability of anti-de sitter space, and the Fermi-Pasta-Ulam paradox.

For a real massless scalar field in general relativity with a negative cosmological constant, we uncover a large class of spherically symmetric initial conditions that are close to anti-de Sitter space (AdS) but whose numerical evolution does not result in black hole formation. According to the AdS/conformal field theory (CFT) dictionary, these bulk solutions are dual to states of a strongly interacting boundary CFT that fail to thermalize at late times. Furthermore, as these states are not stationary, they define dynamical CFT configurations that do not equilibrate. We develop a two-time-scale perturbative formalism that captures both direct and inverse cascades of energy and agrees with our fully nonlinear evolutions in the appropriate regime. We also show that this formalism admits a large class of quasiperiodic solutions. Finally, we demonstrate a striking parallel between the dynamics of AdS and the classic Fermi-Pasta-Ulam-Tsingou problem.

Reconstruction of [formula omitted] models with scale-invariant power spectrum

Following our previous work in [T. Qiu, JCAP 1206 (2012) 041 [1]], in this Letter, we continue our study of reconstructing f(R) modified gravity models that can be connected to a single scalar field in general relativity via conformal transformation, which lead to scale-invariant power spectrum in the early universe. With f(R) modified gravity, one does not need to introduce extra scalar, the nature of which are to be explained. Different from general nonminimal coupling theory, the behavior of the f(R) theory has been fixed by its counterpart in Einstein frame, and thus have one-to-one correspondence. Numerical plots of the functional form of f(R) as well as the evolution of R in terms of cosmic time t are also presented.

Scale-dependent growth from a transition in dark energy dynamics

We investigate the observational consequences of the quintessence field rolling to and oscillating near a minimum in its potential, if it happens close to the present epoch ($z\ensuremath{\lesssim}0.2$). We show that in a class of models, the oscillations lead to a rapid growth of the field fluctuations and the gravitational potential on subhorizon scales. The growth in the gravitational potential occurs on time scales $\ensuremath{\ll}{H}^{\ensuremath{-}1}$. This effect is present even when the quintessence parameters are chosen to reproduce an expansion history consistent with observations. For linearized fluctuations, we find that although the gravitational potential power spectrum is enhanced in a scale-dependent manner, the shape of the dark matter/galaxy power spectrum is not significantly affected. We find that the best constraints on such a transition in the quintessence field is provided via the integrated Sachs-Wolfe effect in the CMB-temperature power spectrum. Going beyond the linearized regime, the quintessence field can fragment into large, localized, long-lived excitations (oscillons) with sizes comparable to galaxy clusters; this fragmentation could provide additional observational constraints. Two quoted signatures of modified gravity are a scale-dependent growth of the gravitational potential and a difference between the matter power spectrum inferred from measurements of lensing and galaxy clustering. Here, both effects are achieved by a minimally coupled scalar field in general relativity with a canonical kinetic term. In other words we show that, with some tuning of parameters, scale-dependent growth does not necessarily imply a violation of General Relativity.

Class of Einstein–Maxwell phantom fields: rotating and magnetized wormholes

Using a new ansatz for solving the Einstein equations with a scalar field with the sign of the kinetic term inverted, I find a series of formulae to derive axial symmetric stationary exact solutions of the Phantom scalar field in general relativity. We focus on the solutions which represent wormholes. The procedure presented in this work allows to derive new exact solutions up to very simple integrations. Among other results, I find exact rotating solutions containing magnetic monopoles, dipoles, etc., coupled to Phantom scalar and to gravitational multipole fields.

Spherical systems in models of nonlocally corrected gravity

The properties of static, spherically symmetric configurations are considered in the framework of two models of nonlocally corrected gravity, suggested in S. Deser and R. Woodard., Phys. Rev. Lett. 663, 111301 (2007), and S. Capozziello et al., Phys. Lett. B 671, 193 (2009). For the first case, where the Lagrangian of nonlocal origin represents a scalar-tensor theory with two massless scalars, an explicit condition is found under which both scalars are canonical (non-phantom). If this condition does not hold, one of the fields exhibits a phantom behavior. Scalar-vacuum configurations then behave in a manner known for scalar-tensor theories. In the second case, the Lagrangian of nonlocal origin exhibits a scalar field interacting with the Gauss-Bonnet (GB) invariant and contains an arbitrary scalar field potential. It is found that the GB term, in general, leads to violation of the well-known no-go theorems valid for minimally coupled scalar fields in general relativity. It is shown, however, that some configurations of interest are still forbidden, whatever be the scalar field potential and the GB-scalar coupling function, namely, "force-free" wormholes (such that g_{tt}= const) and black holes with higher-order horizons.

Unimodular metagravity vs. general relativity with a scalar field

The unimodular metagravity, with the graviscalar as a dark matter, is compared with General Relativity (GR) in the presence of a scalar field. The effect of the graviscalar on the static spherically symmetric metric is studied. An exact limit solution representing a new cosmic object, the (harmonic) graviscalar black hole, is given. The relation with the black hole in the environment of a scalar field in GR is discussed.

Scalar field confinement as a model for accreting systems

We investigate the possibility of localizing scalar field configurations as a model for black hole accretion. We analyse and resolve difficulties encountered when localizing scalar fields in general relativity. We illustrate this ability with a simple spherically symmetric model which can be used to study features of accreting shells around a black hole. This is accomplished by prescribing a scalar field with a coordinate-dependent potential. Numerical solutions to the Einstein–Klein–Gordon equations are shown, where a scalar field is indeed confined within a region surrounding a black hole. The resulting spacetime can be described in terms of simple harmonic time dependence.