EXACT SOLUTIONS IN BRANS-DICKE MATTER COSMOLOGIES

1996 ◽  
Vol 05 (01) ◽  
pp. 85-98 ◽  
Author(s):  
S. CAPOZZIELLO ◽  
R. DE RITIS ◽  
C. RUBANO ◽  
P. SCUDELLARO
Keyword(s):  
Exact Solutions ◽  
Perfect Fluid ◽  
State Equation ◽  
The State ◽  
Nonminimal Coupling ◽  
Ordinary Matter ◽  
Fluid Matter

We investigate Brans-Dicke cosmology with perfect-fluid matter and give a method for selecting exact solutions parametrized by the constant γ of the state equation p=(γ−1)ρ and the parameter ξ of the nonminimal coupling in which the Brans-Dicke theory can be recast. In this sense, we can classify the solutions having and not having inflationary behavior in the presence of ordinary matter.

NONMINIMAL COUPLING, QUARTIC POTENTIAL AND PERFECT FLUID COSMOLOGIES

1995 ◽  
Vol 04 (06) ◽  
pp. 767-779 ◽  
Author(s):  
S. CAPOZZIELLO ◽  
R. DE RITIS ◽  
C. RUBANO ◽  
P. SCUDELLARO
Keyword(s):  
Scalar Field ◽  
Equation Of State ◽  
Exact Solutions ◽  
Perfect Fluid ◽  
Einstein Gravity ◽  
Nonminimal Coupling ◽  
Stiff Matter ◽  
Quartic Potential ◽  
Fluid Matter

Perfect-fluid matter, satisfying the equation of state p=(γ−1)ρ, is considered in cosmologies where the geometry is nonminimally coupled with a scalar field ɸ and the potential of ɸ is λɸ4+Λ. Exact solutions are found when γ is a constant describing the ordinary forms of matter (γ=1, dust, γ=4/3, radiation, γ=2, stiff matter and γ=0, scalar field matter) and a discussion is done in order to recover Einstein gravity and the Newton constant observed today. The various solutions can be classified according to the different values of γ, λ and Λ.

scholarly journals STRING DILATON FLUID COSMOLOGY

1999 ◽  
Vol 08 (02) ◽  
pp. 213-227 ◽  
Author(s):  
S. CAPOZZIELLO ◽  
G. LAMBIASE ◽  
R. CAPALDO
Keyword(s):  
Exact Solutions ◽  
Perfect Fluid ◽  
Spatial Dimension ◽  
State Equation ◽  
Einstein Gravity ◽  
Asymptotic Freedom ◽  
Spatial Curvature ◽  
Effective Coupling ◽  
Fluid Matter ◽  
Dimension Number

We investigate (n+1)-dimensional string–dilaton cosmology with effective dilaton potential in presence of perfect-fluid matter. We get exact solutions parametrized by the constant γ of the state equation p=(γ-1)ρ, the spatial dimension number n, the bulk of matter, and the spatial curvature constant k. Several interesting cosmological behaviours are selected. Finally we discuss the recovering of ordinary Einstein gravity starting from string dominated regime and a sort of asymptotic freedom due to string effective coupling.

scholarly journals Control Systems and Number Theory

2012 ◽  
Vol 2012 ◽  
pp. 1-28
Author(s):  
Fuhuo Li
Keyword(s):  
Zeta Functions ◽  
Feedback System ◽  
State Equation ◽  
The State ◽  
Point Of View ◽  
Pid Controllers ◽  
Primary Concern ◽  
Feedback Connection ◽  
Proper Understanding ◽  
Natural Way

We try to pave a smooth road to a proper understanding of control problems in terms of mathematical disciplines, and partially show how to number-theorize some practical problems. Our primary concern is linear systems from the point of view of our principle of visualization of the state, an interface between the past and the present. We view all the systems as embedded in the state equation, thus visualizing the state. Then we go on to treat the chain-scattering representation of the plant of Kimura 1997, which includes the feedback connection in a natural way, and we consider theH∞-control problem in this framework. We may view in particular the unit feedback system as accommodated in the chain-scattering representation, giving a better insight into the structure of the system. Its homographic transformation works as the action of the symplectic group on the Siegel upper half-space in the case of constant matrices. Both ofH∞- and PID-controllers are applied successfully in the EV control by J.-Y. Cao and B.-G. Cao 2006 and Cao et al. 2007, which we may unify in our framework. Finally, we mention some similarities between control theory and zeta-functions.

scholarly journals On a type of spacetimes

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4251-4260
Author(s):  
Young Suh ◽  
Uday De
Keyword(s):  
Perfect Fluid ◽  
State Equation ◽  
Symmetric Spacetimes ◽  
Petrov Types ◽  
Perfect Fluid Spacetime ◽  
Physical Consequences ◽  
Codazzi Type

In the present paper we characterize a type of spacetimes, called almost pseudo Z-symmetric spacetimes A(PZS)4. At first, we obtain a condition for an A(PZS)4 spacetime to be a perfect fluid spacetime and Roberson-Walker spacetime. It is shown that an A(PZS)4 spacetime is a perfect fluid spacetime if the Z tensor is of Codazzi type. Next we prove that such a spacetime is the Roberson-Walker spacetime and can be identified with Petrov types I, D or O[3], provided the associated scalar ? is constant. Then we investigate A(PZS)4 spacetimes satisfying divC = 0 and state equation is derived. Also some physical consequences are outlined. Finally, we construct a metric example of an A(PZS)4 spacetime.

scholarly journals Isotropic exact solutions in $$F(R,Y,\phi )$$ gravity via Noether symmetries

2021 ◽  
Vol 81 (2) ◽  
Author(s):  
Saira Waheed ◽  
Iqra Nawazish ◽  
M. Zubair
Keyword(s):  
Scalar Field ◽  
Exact Solutions ◽  
Field Potential ◽  
Noether Symmetries ◽  
Dynamical Equations ◽  
Curvature Invariant ◽  
Gauge Symmetries ◽  
Cosmic Evolution ◽  
Fluid Matter ◽  
Alpha Beta

AbstractThe present article investigates the existence of Noether and Noether gauge symmetries of flat Friedman–Robertson–Walker universe model with perfect fluid matter ingredients in a generalized scalar field formulation namely $$f(R,Y,\phi )$$ f ( R , Y , ϕ ) gravity, where R is the Ricci scalar and Y denotes the curvature invariant term defined by $$Y=R_{\alpha \beta }R^{\alpha \beta }$$ Y = R α β R α β , while $$\phi $$ ϕ represents scalar field. For this purpose, we assume different general cases of generic $$f(R,Y,\phi )$$ f ( R , Y , ϕ ) function and explore its possible forms along with field potential $$V(\phi )$$ V ( ϕ ) by taking constant and variable coupling function of scalar field $$\omega (\phi )$$ ω ( ϕ ) . In each case, we find non-trivial symmetry generator and its related first integrals of motion (conserved quantities). It is seen that due to complexity of the resulting system of Lagrange dynamical equations, it is difficult to find exact cosmological solutions except for few simple cases. It is found that in each case, the existence of Noether symmetries leads to power law form of scalar field potential and different new types of generic function. For the acquired exact solutions, we discuss the cosmology generated by these solutions graphically and discuss their physical significance which favors the accelerated expanding eras of cosmic evolution.

scholarly journals II. Observations on Granite

1794 ◽  
Vol 3 (2) ◽  
pp. 77-85 ◽  
Author(s):  
James Hutton
Keyword(s):  
Natural History ◽  
The State ◽  
Hard Materials ◽  
The Earth ◽  
History Of ◽  
Fluid Matter

Since reading the paper upon the theory of the earth, I have been employed in examining many parts of this country, in order to enquire into the natural history of granite. In this undertaking, I have succeeded beyond my most flattering expectations; and I am now to communicate to this Society the result of my observations.In the paper just referred to, it was maintained, from many different arguments, that all the solid strata of the earth had been consolidated by means of subterraneous heat, softening the hard materials of those bodies; and that in many places, those consolidated strata had been broken and invaded by huge masses of fluid matter similar to lava, but, for the most part, perfectly distinguishable from it. Granite also was considered there as a body which had been certainly consolidated by heat; and which had, at least in some parts, been in the state of perfect fusion, and certain specimens were produced, from which I drew an argument in support of this conclusion.

Thermodynamic of the charged AdS black holes in Rastall gravity: P − V critical and Joule–Thomson expansion

2020 ◽  
Vol 35 (14) ◽  
pp. 2050113
Author(s):  
Sen Guo ◽  
Yan Han ◽  
Guo Ping Li
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Critical Temperature ◽  
Critical Exponents ◽  
State Equation ◽  
The State ◽  
Thermodynamic Quantities ◽  
Critical Temperatures ◽  
Ads Black Holes ◽  
And Inversion

In this paper, we study the thermodynamic of the charged AdS black holes in Rastall gravity. Firstly, the thermodynamic quantities of the charged AdS black holes in Rastall gravity are reviewed and the state equation of this black hole is obtained. Then, we investigate the [Formula: see text] critical and the Joule–Thomson expansion of the charged AdS black holes in Rastall gravity in which the critical temperature and the critical exponents are obtained. In addition, we get the inversion temperature and plot the isenthalpic and inversion curves in the [Formula: see text] plane, and also determine the cooling-heating regions of this black hole through the Joule–Thomson expansion. Finally, we investigate the ratio between the minimum inversion and critical temperatures, and find that the Rastall constant [Formula: see text] does not affect of this ratio.

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