On the weak field approximation of the Brans-Dicke theory of gravity

Barros, A.; Romero, C.

doi:10.1016/s0375-9601(98)00382-x

Cited by 34 publications

(34 citation statements)

References 9 publications

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“…Since, as we will discuss in the next section, this generalization can be made, at least, in two different ways, we will consider both cases, separately. There are many works considering weak field solutions, properties of these solutions and astrophysical implications for different modified gravity theories [24][25][26][27][28][29][30][31][32][33][34][35][36]. However, in most of the works, except for example [30][31][32], asymptotic flatness is assumed.…”

Section: Introductionmentioning

confidence: 99%

Linearized modified gravity theories with a cosmological term: advance of perihelion and deflection of light

Özer

Delice

2018

Class. Quantum Grav.

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Two different ways of generalizing Einstein's general theory of relativity with a cosmological constant to Brans-Dicke type scalar-tensor theories are investigated in the linearized field approximation. In the first case a cosmological constant term is coupled to a scalar field linearly whereas in the second case an arbitrary potential plays the role of a variable cosmological term. We see that the former configuration leads to a massless scalar field whereas the latter leads to a massive scalar field. General solutions of these linearized field equations for both cases are obtained corresponding to a static point mass. Geodesics of these solutions are also presented and solar system effects such as the advance of the perihelion, deflection of light rays and gravitational redshift were discussed. In general relativity cosmological constant has no role on these phenomena. We see that for the BransDicke theory the cosmological constant has also no effect on these phenomena. This is because solar system observations require very large values of the Brans-Dicke parameter and the correction terms to these phenomena becomes identical to GR for these large values of this parameter. This result is also observed for the theory with arbitrary potential if the mass of the scalar field is very light. For a very heavy scalar field, however, there is no such limit on the value of this parameter and there are ranges of this parameter where these contributions may become relevant in these scales. Galactic and intergalactic dynamics is also discussed for these theories at the latter part of the paper with similar conclusions.

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Section: Introductionmentioning

confidence: 99%

Linearized modified gravity theories with a cosmological term: advance of perihelion and deflection of light

Özer

Delice

2018

Class. Quantum Grav.

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“…Where φ is the scalar field, ω is the BD parameter and T denotes the trace of the energy momentum tenosr T µ ν [9]. In the weak field approximation in BD theory one can assume g µν = η µν + h µν where |h µν | << 1 and φ(r) [14], that in the weak field approximation the solutions of the BD equations are related to the solutions of linearized equations in GR with the same T µ ν in the follwing way: if g gr µν (G, x) is a known solution of the Einstein's equation in the weak field approximation for a given T µ ν , then the BD solution corresponding to the same T µ ν , in the weak field approximation, is given by…”

Section: )mentioning

confidence: 99%

“…In doing so, we have followed the method of Barros and Romero [14] which has been suggested recently. For both global and gauge vacuumless strings, the spacetimes are conformally related to that obtained earlier by Cho and Vilenkin in GR [7].…”

Section: Gauge Stringmentioning

confidence: 99%

Vacuumless Cosmic Strings in Brans–dicke Theory

Sen

2001

Int. J. Mod. Phys. D

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“…11 Indeed, if g µν (G, x) is a known solution of the Einstein equations in the weak field approximation for a given T µν , then the Brans-Dicke solution corresponding to the same T µν will be given in the weak field approximation by 11 Indeed, if g µν (G, x) is a known solution of the Einstein equations in the weak field approximation for a given T µν , then the Brans-Dicke solution corresponding to the same T µν will be given in the weak field approximation by…”

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confidence: 99%

“…(11) reduces to Eq. (10) and (11). [11][12][13][14] It should also be noted that when the source of the gravitational field is nonrelativistic, then |P i | ρ and both equations become identical to ∇ 2 Φ = 4πGρ, which is usually regarded as the Newtonian limit of Einstein equations.…”

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confidence: 99%

Topological Defects and Gravitational Forces in Brans–dicke Theory

Barros

Romero

2001

Mod. Phys. Lett. A

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The nature of gravitational forces exerted by topological defects on surrounding matter in the frame of Brans-Dicke theory of gravity (BD) is investigated. Comparison is made with the corresponding cases in General Relativity (GR). The role of the scalar field as a weakener agent of the strength of gravitational forces due to pressure terms is discussed. PACS Nos.: 04.20Jb, 98.80.Cq Amongst the most curious properties of space-time generated by the so-called topological defects (vacuum domain walls, strings, monopoles and textures) lies the appearance of repulsive gravitational forces arising from negative pressure terms, present in the energy-momentum tensor of these structures. 1 The gravitational interaction of vacuum domain walls, strings, monopoles and textures with surrounding matter has been studied both in the frameworks of general relativity 2-5 and Brans-Dicke theory. 6-8 In most of these cases the results have been obtained for weak gravitational fields. It is well known that in the weak field approximation the metric tensor may be written in Galilean coordinates as g µν (x) = η µν + h µν (x), where η µν = diag(1, −1, −1, −1) and |h µν | 1. In the case of Brans-Dicke theory of gravity it is also assumed that the scalar field φ is to be written as1, ω is a dimensionless parameter and G is the Newtonian gravitational constant. 9 On these assumptions, the linearized field equations of general relativity and Brans-Dicke theory are given, respectively, by − h µν + h γ µ,ν,γ + h γ ν,µ,γ − h ,µ,ν = 16πG T µν − η µν 2 T ,

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On the weak field approximation of the Brans-Dicke theory of gravity

Cited by 34 publications

References 9 publications

Linearized modified gravity theories with a cosmological term: advance of perihelion and deflection of light

Linearized modified gravity theories with a cosmological term: advance of perihelion and deflection of light

Vacuumless Cosmic Strings in Brans–dicke Theory

Topological Defects and Gravitational Forces in Brans–dicke Theory

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