The Large Numbers Hypothesis and a Relativistic Theory of Gravitation

1986 ◽  
Vol 39 (3) ◽  
pp. 339 ◽  
Author(s):  
YK Lau ◽  
SJ Prokhovnik
Keyword(s):  
Scalar Field ◽  
Scalar Potential ◽  
Cosmological Term ◽  
Time Dependent ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Tensor Theory ◽  
Large Numbers ◽  
Dependent Form ◽  
Theory Of Gravitation

A way to reconcile Dirac's large numbers hypothesis and Einstein's theory of gravitation wasrecently suggested by Lau (1985). It is characterized by the conjecture of a time-dependentcosmological term and gravitational term in Einstein's field equations. Motivated by thisconjecture and the large numbers hypothesis, we formulate here a scalar-tensor theory in terms of an action principle. The cosmological term is required to be spatially dependent as well as time dependent in general. The theory developed is applied to a cosmological model compatible with the large numbers' hypothesis. The time-dependent form of the cosmological term and the scalar potential are then deduced. A possible explanation of the smallness of the cosmological term is also given and the possible significance of the scalar field is speculated.

scholarly journals Non-Riemannian description of Robinson–Trautman spacetimes in Brans–Dicke theory of gravity

2019 ◽  
Vol 28 (04) ◽  
pp. 1950070
Author(s):  
Muzaffer Adak ◽  
Tekin Dereli ◽  
Yorgo Şenikoğlu
Keyword(s):  
Scalar Field ◽  
Differential Forms ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Exterior Differential ◽  
Tensor Theory ◽  
Theory Of Gravitation ◽  
Theory Of Gravity ◽  
Future Reference

The variational field equations of Brans–Dicke scalar-tensor theory of gravitation are given in a non-Riemannian setting in the language of exterior differential forms over four-dimensional spacetimes. A conformally rescaled Robinson–Trautman metric together with the Brans–Dicke scalar field are used to characterize algebraically special Robinson–Trautman spacetimes. All the relevant tensors are worked out in a complex null basis and given explicitly in an appendix for future reference. Some special families of solutions are also given and discussed.

scholarly journals Plane Symmetric Solutions of a Scalar-Tensor Theory of Gravitation

1977 ◽  
Vol 30 (1) ◽  
pp. 109 ◽  
Author(s):  
DRK Reddy
Keyword(s):  
General Relativity ◽  
Empty Space ◽  
Scalar Fields ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Plane Symmetric ◽  
Zero Mass ◽  
Tensor Theory ◽  
Special Cases ◽  
Theory Of Gravitation

Plane symmetric solutions of a scalar-tensor theory proposed by Dunn have been obtained. These solutions are observed to be similar to the plane symmetric solutions of the field equations corresponding to zero mass scalar fields obtained by Patel. It is found that the empty space-times of general relativity discussed by Taub and by Bera are obtained as special cases.

scholarly journals HIGHER DIMENSIONAL SZEKERES' SPACE–TIME IN BRANS–DICKE SCALAR TENSOR THEORY

2004 ◽  
Vol 13 (06) ◽  
pp. 1073-1083
Author(s):  
ASIT BANERJEE ◽  
UJJAL DEBNATH ◽  
SUBENOY CHAKRABORTY
Keyword(s):  
Turning Point ◽  
Coupling Parameter ◽  
Big Bang ◽  
Space Time ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Tensor Theory ◽  
Higher Dimensional ◽  
Theory Of Gravitation ◽  
The Big Bang

The generalized Szekeres family of solution for quasi-spherical space–time of higher dimensions are obtained in the scalar tensor theory of gravitation. Brans–Dicke field equations expressed in Dicke's revised units are exhaustively solved for all the subfamilies of the said family. A particular group of solutions may also be interpreted as due to the presence of the so-called C-field of Hoyle and Narlikar and for a chosen sign of the coupling parameter. The models show either expansion from a big bang type of singularity or a collapse with the turning point at a lower bound. There is one particular case which starts from the big bang, reaches a maximum and collapses with the in course of time to a crunch.

A brief note on the limit ω →∞ in Weyl geometrical scalar–tensor theory

2021 ◽  
Author(s):  
A. Barros ◽  
C. Romero
Keyword(s):  
Scalar Field ◽  
Cosmological Constant ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Tensor Theory ◽  
Vacuum Solutions ◽  
Working Out

We obtain vacuum solutions in the presence of a cosmological constant in the context of the Weyl geometrical scalar–tensor theory. We investigate the limit when [Formula: see text] goes to infinity and show by working out the solutions that in this limit there are some cases in which the scalar field tends to a constant (with the implicit consequence of the geometry becoming Riemannian), although the solutions do not reduce to the corresponding Einstein solutions. We have also extended a previous result, known in the literature, by showing that in the case of vacuum with cosmological constant the field equations of the Weyl geometrical scalar–tensor theory are formally identical to Brans–Dicke field equations, even though these theories are not physically equivalent.

scholarly journals Anisotropic Bulk Viscous String Cosmological Model in a Scalar-Tensor Theory of Gravitation

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
D. R. K. Reddy ◽  
Ch. Purnachandra Rao ◽  
T. Vidyasagar ◽  
R. Bhuvana Vijaya
Keyword(s):  
Equations Of State ◽  
Momentum Tensor ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Physical Conditions ◽  
Bulk Viscous Fluid ◽  
Tensor Theory ◽  
Highly Nonlinear ◽  
Bulk Viscous ◽  
Theory Of Gravitation

Spatially homogeneous, anisotropic, and tilted Bianchi type-VI0model is investigated in a new scalar-tensor theory of gravitation proposed by Saez and Ballester (1986) when the source for energy momentum tensor is a bulk viscous fluid containing one-dimensional cosmic strings. Exact solution of the highly nonlinear field equations is obtained using the following plausible physical conditions: (i) scalar expansion of the space-time which is proportional to the shear scalar, (ii) the barotropic equations of state for pressure and energy density, and (iii) a special law of variation for Hubble’s parameter proposed by Berman (1983). Some physical and kinematical properties of the model are also discussed.

scholarly journals EXACT SOLUTIONS FOR COSMOLOGICAL MODELS WITH A SCALAR FIELD

2002 ◽  
Vol 17 (03) ◽  
pp. 375-381 ◽  
Author(s):  
H. MOTAVALI ◽  
M. GOLSHANI
Keyword(s):  
Scalar Field ◽  
Exact Solutions ◽  
Cosmological Models ◽  
Coupling Function ◽  
Noether Symmetry ◽  
Scalar Tensor Theory ◽  
Frw Cosmology ◽  
Field Equations ◽  
Tensor Theory ◽  
Cosmological Solutions

We consider the existence of a Noether symmetry in the scalar–tensor theory of gravity in flat Friedman–Robertson–Walker (FRW) cosmology. The forms of coupling function ω(ϕ) and generic potential V(ϕ) are obtained by requiring the existence of a Noether symmetry for such theory. We derive exact cosmological solutions of the field equations from a point-like Lagrangian.

scholarly journals Cosmological Solutions for the Geometrical Scalar-Tensor with the Potential Determined by the Noether Symmetry Approach

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1110
Author(s):  
Adriano B. Barreto ◽  
Gilberto M. Kremer
Keyword(s):  
Scalar Field ◽  
Scalar Potential ◽  
Noether Symmetry ◽  
Jordan Frame ◽  
Scalar Tensor Theory ◽  
Symmetry Approach ◽  
Tensor Theory ◽  
Dark Energy Component ◽  
Frw Cosmological Model

The aim of this work is to study a scalar-tensor theory where owing to Palatini’s variational method the space-time is endowed with a geometrical structure of Weyl integrable type. The geometrical nature of the scalar field is related to the non-metricity so that the theory is known as geometrical scalar-tensor. On the framework of Weyl transformations, a non-minimally coupled scalar-tensor theory on the Jordan frame corresponds to a minimally coupled Einstein–Hilbert action on the Einstein frame. The scalar potential is selected by the Noether symmetry approach in order to obtain conserved quantities for the FRW cosmological model. Exact solutions are obtained and analyzed in the context of the cosmological scenarios consistent with an expanding universe. A particular case is matched in each frame and the role of scalar field as a dark energy component is discussed.

Neutron stars in the bimetric Scalar-Tensor theory of gravitation. I. new solutions of the field equations

Astrophysics ◽  
1997 ◽  
Vol 40 (3) ◽  
pp. 252-259
Author(s):  
L. Sh. Grigorian ◽  
P. F. Kazarian ◽  
H. F. Khachatrian
Keyword(s):  
Neutron Stars ◽  
Scalar Tensor Theory ◽  
Field Equations ◽  
Tensor Theory ◽  
Theory Of Gravitation
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