在本文中，我们研究了在具有非零时空挠率的 Brans-Dicke（BD）理论中，均匀且各向同性流体的坍缩过程。在该理论中，挠率可由 BD 标量场以及物质的内在角动量（自旋）产生。假设坍缩体的物质组成为 Weyssenhoff 流体（这是广义相对论（GR）中理想流体的推广，旨在包含自旋效应），我们发现，在带挠率的 BD 理论中，自旋效应的存在能够避免在该理论的原始版本中形成的时空奇点（Scheel 等人，Phys Rev D 51:4208, 1995; Phys Rev D 51:4236, 1995）。坍缩模型的数值模拟表明，时空奇点被非奇点反弹所取代，反弹是指坍缩过程在最小半径处停止并随后转变为膨胀阶段的时空事件。此外，通过设定模型参数，可使表观视界永远不会与坍缩体的边界相遇，从而使反弹事件能够被宇宙中的外部观察者观测到。
英文摘要：
In the present work we study collapse process of a homogeneous and isotropic fluid in Brans-Dicke ({BD}) theory with non-vanishing spacetime torsion. In this theory, torsion can be generated by the {BD} scalar field as well as the intrinsic angular momentum (spin) of matter. Assuming the matter content of the collapsing body to be a Weyssenhoff fluid, which is a generalization of perfect fluid in general relativity ({GR}) in order to include the spin effects, we find that in BD theory with torsion, the existence of spin effects could avoid the spacetime singularity that forms in the original version of this theory (Scheel et al. in Phys Rev D 51:4208, 1995, Scheel et al. in Phys Rev D 51:4236, 1995). Numerical simulations of collapse model show that the spacetime singularity is replaced by a non-singular bounce, the spacetime event at which the collapse process halts at a minimum radius and then turns into an expanding phase. Moreover, the model parameters can be set so that the apparent horizon will never meet the boundary of the collapsing body so that the bounce event can be detectable by external observers in the Universe.
Gravitational Collapse and Singularity Formation in Brans-Dicke Gravity
Sardar Vallabhbhai National Institute of Technology（萨达尔·瓦拉巴伊国家技术学院）；Beijing Institute of Mathematical Sciences and Applications（北京应用数学与物理研究所）；University of São Paulo, IAG（圣保罗大学天体物理学、地球物理学和大气科学研究所）
We consider a Brans-Dicke cosmology in five-dimensional space-time. Neglecting the quadratic and the mixed Brans-Dicke terms in the Einstein equation, we derive a modified wave equation of the Brans-Dicke field. We show that, at high energy limit, the 3-brane Brans-Dicke cosmology could be described as the standard one by changing the equation of state. Finally as an illustration of the purpose, we show that the dark energy component of the universe agrees with the observations data.
We present the new interpretation of scalar field for the Brans-Dicke theory. This interpretation is obtained by considering a fixed spacetime structure of manifold.
We study the Generalized Brans-Dicke cosmology in the presence of matter and dark energy. Of particular interest for a constant Brans-Dicke parameter, the de Sitter space has also been investigated.
In this short letter we present a some rigorous vacuum solutions of the D-dimensional Jordan-Brans-Dicke field equations. In contrast with the well known Brans-Dicke solutions, to the search of static and spherically symmetric space-time we choose the widespread Hilbert coordinates.
We present the static spherically symmetric vacuum solutions of the Jordan, Brans-Dicke field equations. The new solutions are obtained by considering a polar Gaussian, isothermal and radial hyperbolic metrics.
We consider Brans-Dicke theory with a self-interacting potential in Einstein conformal frame. We show that an accelerating expansion is possible in a spatially flat universe for large values of the Brans-Dicke parameter consistent with local gravity experiments.
We study spherically symmetric solutions to the Jordan-Brans-Dicke field equations under the assumption that the space-time may possess an arbitrary number of spatial dimensions. Assuming a perfect fluid with the equation of state, we show that there are static interior nontrivial solutions in three dimensional Jordan-Brans-Dicke gravity theory.
We discuss the physical equivalence between the Einstein and Jordan frames in Brans-Dicke theory. The inequivalence of conformal transformed theories is clarified with the help of an old equivalence theorem of Chrisholm's.
Einstein Frame Regularization of the JNW Spacetime: From Brans-Dicke Singularity to Ellis Wormhole
Kidderpore College（基德珀尔学院）；Bashkir State Pedagogical University（巴什基尔国立师范大学）；Institute of Molecule and Crystal Physics, Ufa Federal Research Centre, Russian Academy of Sciences（俄罗斯科学院乌法联邦研究中心分子与晶体物理研究所）
It is shown that the recently claimed two new Brans-Dicke wormhole solutions [F. He and S-W. Kim, Phys. Rev. D{\bf 65}, 084022 (2002)] are not really new solutions. They are just the well known Brans-Dicke solutions of Class I and II in a different conformal gauge.
We have studied the properties of the static, spherically symmetric solution of Jordan, Brans-Dicke theory. An exact interior solution for standard space-time line element in the Schwarzschild form is obtained.
A simple Lorentzian vacuum wormhole solution of Brans-Dicke gravitation is presented and analysed. It is shown that such solution holds for both, the Brans-Dicke theory endowed with torsion (for a value of the coupling parameter $ω> 1/2$) and for the vacuum -no torsion- case (for $ω< -2$).
A simple Heckmann's vacuum wormhole solution of Jordan-Brans-Dicke gravitation is presented and analysed. It is shown that in contrast with class I Brans solution where the throat radius becomes real when $ω< -4/3$ here it becomes positive when $ω< -1$.
We present static cylindrically symmetric electrovac solutions in the framework of the Brans-Dicke theory and show that our solution yields some of the well-known solutions for special values of the parameters of the resulting metric functions.
A two-way traversable wormhole solution in Brans-Dicke theory with torsion is obtained using the method of massive thin shells. The solution goes over general relativity for an infinite large value of the coupling parameter, however, the Brans-Dicke scalar could never be the ``carrier'' of exoticity that threads the wormhole throat.
We discuss the correspondence between metric $f(R)$ gravity and $ω=0$ Brans-Dicke theory with a potential, by working out an example that reconfirms this equivalence.
Spherically symmetric thin-shell wormholes are constructed within the framework of Brans-Dicke gravity. It is shown that, for appropriate values of the Brans-Dicke constant, these wormholes can be supported by matter satisfying the energy conditions.
Gravitational field of a nonstatic global string has been studied in the context of Brans-Dicke theory of gravity. Both the metric components and the BD scalar field are assumed to be nonseparable functions of time and space.The spacetime may or may not have any singularity at a finite distance from the string core but the singularity at a particular time always remains. It has been shown that the spacetime exhibits both outgoing and incoming gravitational radiation.
We construct a formal asymptotic series expansion for a general solution of the Brans-Dicke equations with a fluid source near a sudden singularity. This solution contains eleven independent arbitrary functions of the spatial coordinates as required by the Cauchy problem of the theory. We show that the solution is geodesically complete and has the character of a shock wave in the sudden asymptotic region. This solution is weak in the senses of Tipler and Krolak as in the corresponding case of general relativity.
The $ω\to\infty$ limit of Brans-Dicke theory is studied with the help of the conformal transformation approach without resorting, however, to the conformal invariance property of this formalism, that is shown to be spurious.
This paper is devoted to study the accelerated expansion of the universe by exploring the Brans-Dicke parameter in different eras. For this purpose, we take FRW universe model with viscous fluid (without potential) and Bianchi type I universe model with barotropic fluid (with and without potential). We evaluate deceleration parameter as well as Brans-Dicke parameter to explore cosmic acceleration. It is concluded that accelerated expansion of the universe can also be achieved for higher values of the Brans-Dicke parameter in some cases.
We analyse the fate of density perturbation in the Brans-Dicke Theory, giving a general classification of the solutions of the perturbed equations when the scale factor of the background evolves as a power law. We study with details the cases of vacuum, inflation, radiation and incoherent matter. We find, for the a negative Brans-Dicke parameter, a significant amplification of perturbations.
The definition of the Sparling-Thirring form is extended to the Brans-Dicke theory. By writing the Brans-Dicke field equations in a formally Maxwell-like form, a superpotential and a corresponding pseudo energy-momentum form are defined. The general energy expression provided by the superpotential in the Jordan frame is discussed in relation to the corresponding expression in the Einstein frame. In order to substantiate its formal definition, the generalized Sparling-Thirring form is used to calculate the energy for the spherically symmetric vacuum solution in the Brans-Dicke theory.
The Brans-Dicke Theory of Gravity is one of the most promising alternatives to the Einstein's Theory of General Relativity. We have examined an action term with wrong signs for both the kinetic and mass terms for the scalar field and have found solutions for both the scale factor of the universe and the Brans-Dicke scalar field which vary exponentially in time.
Analytical wormhole solutions in Brans-Dicke theory in the presence of matter are presented. It is shown that the wormhole throat must not be necessarily threaded with exotic matter.
The gravitational fields of vacuumless global and gauge strings have been studied in Brans-Dicke theory under the weak field assumption of the field equations. It has been shown that both global and gauge string can have repulsive as well as attractive gravitational effect in Brans-Dicke theory which is not so in General Relativity.
We consider the embedding of 3+1 dimensional cosmology in 4+1 dimensional Jordan-Brans-Dicke theory. We show that exponentially growing and power law scale factors are implied. Whereas the 4+1 dimensional scalar field is approximately constant for each, the effective 3+1 dimensional scalar field is constant for exponentially growing scale factor and time dependent for power law scale factor.
In order to investigate more features of the Brans-Dicke cosmology in the five-dimensional space-time, we explore the solutions of its dynamiacal systems. A behavior of the universe in its early and late time by means of the scale factor is considered. As a results, we show that it is possible to avoid the big rip singularity and to cross the phantom divide line. Furthermore, we review the dark energy component of the universe and its agreement with the observation data for this 3-brane Brans Dicke cosmology by means of the cosmological parameters.
It is known that Vilenkin's phenomenological equation of state for static straight cosmic strings is inconsistent with Brans-Dicke theory. We will prove that, in the presence of a cosmological constant, this equation of state is consistent with Brans-Dicke theory. The general solution of the full nonlinear field equations, representing the interior of a cosmic string with a cosmological constant is also presented.
A `no-hair' theorem for the Brans-Dicke field, in the domain of outer communications of a static black hole, is established, when the trace of the energy-momentum tensor, T, is a definite-sign scalar. This implies that Brans-Dicke theory of gravitation, for matter with T of definite sign, is equivalent to Einstein gravity with the constraint T=0.
The Geodesic Deviation Equation is being studied in Brans-Dicke-Rastall gravity. We briefly discuss the Brans-Dicke-Rastall gravity and then construct GDE for FLRW metric. In this way, the obtained geodesic deviation equation will correspond to the Brans-Dicke-Rastall gravity. Eventually, we solve numerically the null vector GDE to obtain from Mattig relation, the deviation vector $η(z)$ and observer area distance $r_0(z)$ and compare the results with $Λ$CDM model.
We present a new exact solution in Brans-Dicke theory. The solution describes inhomogeneous plane-symmetric perfect fluid cosmological model with an equation of state $p=γρ$. Some main properties of the solution are discussed.
The spectra of relic gravitational waves produced as a result of cosmological expansion of the inflationary models are derived in Brans-Dicke theory of gravity.The time dependence of the very early Hubble parameter and matter energy density are derived from frequency dependent spectrum of relic gravitational waves.Also it is found that Brans-Dicke scalar field contributes to the energy density of relic gravitons.
We have solved cosmological gravitational Wave(GW)equation in the frame work of Generalised Brans-Dicke(GBD) theory for all epochs of the Universe.The solutions are expressed in terms of the present value of the Brans-Dicke coupling parameter $ω(ϕ)$.It is seen that the solutions represent travelling growing modes for negative values of $ω_{0}$ for all epochs of the Universe.
A gravitating global monopole produces a repulsive grativational field outside the core in addition to a solid angular deficit in the Brans-Dicke theory. As a new feature, the angular deficit is dependent on the values of ϕ_{\infty} and ω, where ϕ_{\infty} is asymptotic value of scalar field in space-like infinity and ωis the Brans-Dicke parameter.
We derive the full projected Einstein-Brans-Dicke gravitational equations associated with a n-dimensional brane embedded in a (n+1)-dimensional bulk. By making use of general conditions, as the positivity of the Brans-Dicke parameter and the effective Newton gravitational constant as well, we are able to constrain the brane cosmological constant in terms of the brane tension, the Brans-Dicke scalar field, and the trace of the stress tensor on the brane, in order to achieve a $dS$ brane. Applying these constraints to a specific five-dimensional model, a lower bound for the scalar field on the b…
This article examines the claim that the Brans-Dicke scalar field ϕ\to ϕ_{0} + O(1/\sqrtω) for large $ω$ when the matter field is traceless. It is argued that such a claim can not be true in general.
We show that Gravitational Waves are exponetially amplified in the inflationary phase in Brans-Dicke theory, so that it would be possible to detect them and in this way verify several features of physical reality.
New classes composite vacuum wormhole solutions of Jordan-Brans-Dicke gravitation is presented and analysed. It is shown that such solution holds for both, a bridge between separated Schwarzschild and Brans Universes and for a bridge connecting two Schwarzschild asymptotically flat regions joined by Brans throat. We have also noticed that there are some new possible candidates for wormhole spacetimes.
The variational field equations of Brans-Dicke scalar-tensor theory of gravitation are presented in a Riemannian and non-Riemannian setting in the language of exterior differential forms over 4-dimensional spacetime. In Rosen coordinates, the equations of motion of non-spinning test masses are considered in a gravitational plane wave setup and detailed to interpret a scalar field $α$ as a candidate for dark energy for negative values of the Brans-Dicke parameter $-3/2 < ω< 0$ .
It is shown that in the weak field approximation solutions of Brans-Dicke equations are simply related to the solutions of General Relativity equations for the same matter distribution. A simple method is developed which permits to obtain Brans-Dicke solutions from Einstein solutions when both theories are considered in their linearized forms. To illustrate the method some examples found in the literature are discussed.
Gravitational collapse of the Brans-Dicke scalar field with non-zero potential in the presence of matter fluid obeying the barotropic equation of state, $p=wρ$ is studied. Utilizing the concept of expansion parameter, it is seen that the cosmic censorship conjecture may be violated for $w=-\frac{1}{3}$ and $ w=-\frac{2}{3}$ which correspond to cosmic string and domain wall, respectively. We show that physically, it is the rate of collapse and the presence of Brans-Dicke scalar field that govern the formation of a black hole or a naked singularity as the final fate of dynamical evolution and on…
It has been shown that Brans-Dicke (BD) theory in anisotropic cosmological model can alone solve the quintessence problem and we have accelerated expanding universe without any quintessence matter. Also the flatness problem has been discussed in this context.
The classification problem for conformally-flat space-times that admit a separation of variables in the Hamilton-Jacobi equation of the scalar-tensor Brans-Dicke theory of gravity is examined. The field equations of the scalar-tensor theory of Brans and Dicke for conformally-flat Stackel space-times of type (1.1) are solved. An explicit form of the metric tensor and scalar field is obtained.
The possibility that a charged particle propagating in a gravitational field described by Brans-Dicke theory of gravity could emit Cerenkov radiation is explored. This process is kinematically allowed depending on parameters occurring in the theory. The Cerenkov effect disappears as the BD parameter omega tends to inftinity, i.e. in the limit in which the Einstein theory is recovered, giving a signature to probe the validity of the Brans-Dicke theory.
In this article, a study of the scalar field shells in relativistic spherically symmetric configurations has been performed. We construct the composite solution of Jordan-Brans-Dicke field equation by matching the conformal Brans solutions at each junction surfaces. This approach allows us to associate rigorously with all solutions as a single glued "space", which is a unique differentiable manifold M^4.
We find a static solution for the scale-factor in a Brans-Dicke generalized theory where the scalar field and the coupling constant vary with time. We find also that in the early Universe there may be amplification of gravitational waves.
Using an energy-momentum complex we give a physical interpretation to the constants in the well-known static spherically symmetric asymptotically flat vacuum solution to the Brans-Dicke equations. The positivity of the tensor mass puts a bound on parameters in the solution.
We consider an approach to Brans-Dicke theory of gravity in which the scalar field has a geometrical nature. By postulating the Palatini variation, we find out that the role played by the scalar field consists in turning the space-time geometry into a Weyl integrable manifold. This procedure leads to a scalar-tensor theory that differs from the original Brans-Dicke theory in many aspects and presents some new features.
Using the Brans-Dicke theory of gravitation we put under investigation a hypothetical universe filled with a fermionic field (with a self interaction potential) and a matter constituent ruled by a barotropic equation of state. It is shown that the fermionic field (in combination with the Brans-Dicke scalar field) could be responsible for a final accelerated era, after an initial matter dominated period.
The gravitational field of a stationary circular cosmic string loop ,externally supported against collapse, is investigated in the context of Brans-Dicke theory in the weak field approximation of the field equations. The solution is quasi-conformally related to the corresponding solution in Einstein's General Relativity(GR) and goes over to the corresponding solution in GR when the Brans-Dicke parameter $ω$ becomes infinitely large.
In the present study, we comment on Brans-Dicke scalar field cosmological model in Lyra's geometry [Maurya \& Zia, Phys. Rev. D \textbf{100}, 023503 (2019)]. In this comment, we investigate that there is no acceleration in the model proposed by the authors of Phys. Rev. D \textbf{100}, 023503 (2019). Therefore, despite the claims to the contrary the Brans-Dicke Scalar Field Cosmological Model in Lyra's Geometry with high Brans-Dicke (BD) coupling parameter $ω$ and constant $β$ can not produce late time acceleration in the universe.
The loop quantization of Brans-Dicke theory (with coupling parameter $ω\neq-3/2$) is studied. In the geometry-dynamical formalism, the canonical structure and constraint algebra of this theory are similar to those of general relativity coupled with a scalar field. The connection dynamical formalism of the Brans-Dicke theory with real $su(2)$-connections as configuration variables is obtained by canonical transformations. The quantum kinematical Hilbert space of Brans-Dicke theory is constituted as of that loop quantum gravity coupled with a polymer-like scalar field. The Hamiltonian constraint…
Since the Brans-Dicke theory is conformal related to the dilaton gravity theory, by applying a conformal transformation to the dilaton gravity theory, we derived the cosmological constant term in the Brans-Dicke theory and the physical solution of black holes with the cosmological constant. It is found that, in four dimensions, the solution is just the Kerr-Newman-de Sitter solution with a constant scalar field. However, in $n>4$ dimensions, the solution is not yet the $n$ dimensional Kerr-Newman-de Sitter solution and the scalar field is not a constant in general. In Brans-Dicke-Ni theory, th…
We show that a recent letter claiming to present exact cosmological solutions in Brans-Dicke theory actually uses a flawed set of equations as the starting point for their analysis. The results presented in the letter are therefore not valid.
We studied the Einstein-Brans-Dicke cosmology in detail. The difference of the evolution of the universe is significant between Einstein-Brans-Dicke cosmology and standard big-bang model during the radiation-dominated era. The power-law evolution of the scale factor is fast enough to solve the cosmological puzzles and slow enough to avoid the graceful exit problem. However, the constraints from the satisfactory bubble distribution (beta^2>0.25) and the solar system observations (beta^2<0.002) are mutually exclusive. This suggests that this kind of inflationary model is ruled out. We also clari…
The collapse of a massless scalar field in the Brans-Dicke theory of gravitation is studied in the analysis of both analytical solution and numerical one. By conformally transforming the Roberts's solution into the Brans-Dicke frame, we find for $ω> -3/2$ that a continuous self-similarity continues and that the critical exponent does depend on $ω$. By conformally transforming the Choptuik's solution into the Brans-Dicke frame, we find for $ω> -3/2$ that at the critical solution shows discrete self-similarity, however, the critical exponent depends strongly on $ω$ while the echoing parameter we…
We provide proofs of some assumptions recently made by F. O. Minotti to conclude on the possibility that an additional scalar field minimally coupled to gravity may help to reconcile a Brans-Dicke coupling constant $ω$ of the order unity with solar system bounds.
