scholarly journals A New Class of Almost Ricci Solitons and Their Physical Interpretation

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
K. L. Duggal
Keyword(s):  
Physical Model ◽  
Dynamic Properties ◽  
Fluid Velocity ◽  
General Relation ◽  
Ricci Soliton ◽  
Field Equations ◽  
Open Problems ◽  
Matter Tensor ◽  
Imperfect Fluid ◽  
Almost Ricci Soliton

We establish a link between a connection symmetry, called conformal collineation, and almost Ricci soliton (in particular Ricci soliton) in reducible Ricci symmetric semi-Riemannian manifolds. As a physical application, by investigating the kinematic and dynamic properties of almost Ricci soliton manifolds, we present a physical model of imperfect fluid spacetimes. This model gives a general relation between the physical quantities (u,μ,p,α,η,σij) of the matter tensor of the field equations and does not provide any exact solution. Therefore, we propose further study on finding exact solutions of our viscous fluid physical model for which it is required that the fluid velocity vector u be tilted. We also suggest two open problems.

Generalized Ricci recurrent spacetimes and GRW spacetimes

2021 ◽  
pp. 2150209
Author(s):  
Sudhakar K. Chaubey ◽  
Young Jin Suh
Keyword(s):  
Vector Field ◽  
Cosmological Constant ◽  
Perfect Fluid ◽  
Ricci Soliton ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Einstein's Field Equations ◽  
Almost Ricci Soliton ◽  
Perfect Fluid Spacetime ◽  
Fluid Spacetimes

The main goal of this paper is to study the properties of generalized Ricci recurrent perfect fluid spacetimes and the generalized Ricci recurrent (generalized Robertson–Walker (GRW)) spacetimes. It is proven that if the generalized Ricci recurrent perfect fluid spacetimes satisfy the Einstein’s field equations without cosmological constant, then the isotropic pressure and the energy density of the perfect fluid spacetime are invariant along the velocity vector field of the perfect fluid spacetime. In this series, we show that a generalized Ricci recurrent perfect fluid spacetime satisfying the Einstein’s field equations without cosmological constant is either Ricci recurrent or Ricci symmetric. An [Formula: see text]-dimensional compact generalized Ricci recurrent GRW spacetime with almost Ricci soliton is geodesically complete, provided the soliton vector field of almost Ricci soliton is timelike. Also, we prove that a (GR)n GRW spacetime is Einstein. The properties of (GR)n GRW spacetimes equipped with almost Ricci soliton are studied.

scholarly journals GEOMETRY AND MATTER REDUCTION IN A 5D KALUZA–KLEIN FRAMEWORK

2009 ◽  
Vol 24 (20) ◽  
pp. 1565-1575 ◽  
Author(s):  
V. LACQUANITI ◽  
G. MONTANI
Keyword(s):  
Dimensional Reduction ◽  
Source Term ◽  
Scalar Fields ◽  
Conservation Equation ◽  
Maxwell System ◽  
Field Equations ◽  
Bianchi Identities ◽  
Matter Tensor ◽  
Consistent Approach ◽  
Kaluza Klein

In this paper we consider the Kaluza–Klein field equations in the presence of a generic 5D matter tensor which is governed by a conservation equation due to 5D Bianchi identities. Following a previous work, we provide a consistent approach to matter where the problem of huge massive modes is removed, without relaxing the compactification hypotheses; therefore we perform the dimensional reduction either for metric fields and for matter, thus identifying a pure 4D tensor term, a 4D vector term and a scalar one. Hence we are able to write down a consistent set of equations for the complete dynamics of matter and fields; with respect to the pure Einstein–Maxwell system we now have two additional scalar fields: the usual dilaton one plus a scalar source term. Some significant scenarios involving these terms are discussed and perspectives for cosmological applications are suggested.

scholarly journals Evolution of cosmological horizons of wormhole cosmology

2020 ◽  
Vol 29 (12) ◽  
pp. 2050079
Author(s):  
Sung-Won Kim
Keyword(s):  
Light Cone ◽  
Dynamic Properties ◽  
Field Equations ◽  
The Past ◽  
Particle Horizon ◽  
Proper Distance ◽  
Apparent Horizons ◽  
Spatial Coordinates ◽  
Causal Structures ◽  
Past Light Cone

Recently, we solved Einstein’s field equations to obtain the exact solution of the cosmological model with the Morris–Thorne-type wormhole. We found the apparent horizons and analyzed their geometric natures, including the causal structures. We also derived the Hawking temperature near the apparent cosmological horizon. In this paper, we investigate the dynamic properties of the apparent horizons under the matter-dominated universe and lambda-dominated universe. As a more realistic universe, we also adopt the [Formula: see text]CDM universe which contains both the matter and lambda. The past light cone and the particle horizon are examined for what happens in the case of the model with wormhole. Since the spatial coordinates of the spacetime with the wormhole are limited outside the throat, the past light cone can be operated by removing the smaller-than-wormhole region. The past light cones without wormhole begin to start earlier than the past light cones with wormhole in conformal time-proper distance coordinates. The light cone consists of two parts: the information from our universe and the information from other universe or far distant region through the wormhole. Therefore, the particle horizon distance determined from the observer’s past light cone cannot be defined in a unique way.

scholarly journals Balancing Energy Processes in Turbine Engines

2015 ◽  
Vol 21 (4) ◽  
pp. 48-56
Author(s):  
Włodzimierz Balicki ◽  
Paweł Głowacki ◽  
Stefan Szczeciński ◽  
Zbigniew Korczewski ◽  
Adam Kozakiewicz ◽  
...  
Keyword(s):  
Physical Model ◽  
Dynamic Properties ◽  
Turbine Engines ◽  
Combined System ◽  
Long Distance ◽  
Turbofan Engines ◽  
Marine Propulsion ◽  
Balancing Energy ◽  
Marine Applications ◽  
Energy Processes

Abstract The article discusses the issue of balancing energy processes in turbine engines in operation in aeronautic and marine propulsion systems with the aim to analyse and evaluate basic operating parameters. The first part presents the problem of enormous amounts of energy needed for driving fans and compressors of the largest contemporary turbofan engines commonly used in long-distance aviation. The amounts of the transmitted power and the effect of flow parameters and constructional properties of the engines on their performance and real efficiency are evaluated. The second part of the article, devoted to marine applications of turbine engines, presents the energy balance of the kinetic system of torque transmission from main engine turbines to screw propellers in the combined system of COGAG type. The physical model of energy conversion processes executed in this system is presented, along with the physical model of gasodynamic processes taking place in a separate driving turbine of a reversing engine. These models have made the basis for formulating balance equations, which then were used for analysing static and dynamic properties of the analysed type of propulsion, in particular in the aspect of mechanical loss evaluation in its kinematic system.

scholarly journals On the h-almost Ricci soliton

2017 ◽  
Vol 114 ◽  
pp. 216-222 ◽  
Author(s):  
J.N. Gomes ◽  
Qiaoling Wang ◽  
Changyu Xia
Keyword(s):  
Ricci Soliton ◽  
Almost Ricci Soliton

Implementing the Extended Reduced Order Physical Model Into Commercialized Software Packages: Implementing Modal Constraints Into Software Packages

2003 ◽  
Author(s):  
Takahito Sagane ◽  
Takao Kinoshita ◽  
Hiroshi Tajima ◽  
Kazuto Seto
Keyword(s):  
Physical Model ◽  
Dynamic Properties ◽  
Flexible Structures ◽  
Rigid Bodies ◽  
Elastic Deformations ◽  
Reduced Order ◽  
Constraint Equations ◽  
Software Packages ◽  
Augmented Formulation ◽  
Value Decomposition

In this paper, the extended reduced order physical model, which is developed to represent dynamics of flexible structures in multibody systems, is implemented to general multibody formulations. The elastic deformations are described using vibration modes associated with the rigid bodies that are effectively defined using dynamic properties of the system in this reduced order modeling method. The recursive formulation and the augmented formulation are used to develop the constraint equations associated with the connections between the reference body and the several rigid bodies in the modal representations used to modal elastic deformations. For this purpose, the n-body constraint is developed for the recursive formulations, while these constraint equations are transformed into the form that is suitable for the augmented formulation using the singular value decomposition or QR decomposition. The use of the formulations in this paper allows for the implementation of the extended reduced order physical model into the commercial multibody codes such as SIMPACK, ADAMS, and DADS.

HOMOGENEOUS ANISOTROPIC COSMOLOGICAL MODELS WITH VISCOUS FLUID AND HEAT FLOW IN LYRA'S GEOMETRY

2009 ◽  
Vol 24 (23) ◽  
pp. 1847-1856 ◽  
Author(s):  
SHRI RAM ◽  
M. K. VERMA ◽  
MOHD ZEYAUDDIN
Keyword(s):  
Power Law ◽  
Bianchi Type ◽  
Big Bang ◽  
Field Equations ◽  
Type Singularity ◽  
Exponential Expansion ◽  
Imperfect Fluid ◽  
Lyra’S Geometry ◽  
Type V ◽  
The Universe

In this paper, a spatially homogeneous and anisotropic Bianchi type V model filled with an imperfect fluid with both viscosity and heat conduction is investigated within the framework of Lyra's geometry. Exact solutions of the field equations are obtained by applying a special law of variation for Hubble's parameter which yields a constant value of the deceleration parameter. Two different physically viable models of the universe are presented in two types of cosmologies, one with power-law expansion and other one with exponential expansion. Cosmological model with power-law expansion has an initial big-bang type singularity at t = 0 whereas the model with exponential expansion has a singularity in the infinite past. The physical and dynamical properties of the models are discussed.

Two-fluid Friedmann–Robertson–Walker cosmologies and their numerical predictions

1986 ◽  
Vol 64 (2) ◽  
pp. 204-209 ◽  
Author(s):  
A. A. Coley ◽  
B. O. J. Tupper
Keyword(s):  
Cosmic Microwave Background ◽  
Perfect Fluid ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Microwave Background ◽  
Two Fluids ◽  
Numerical Predictions ◽  
Imperfect Fluid ◽  
State Formula ◽  
Friedmann Robertson Walker

Friedmann–Robertson–Walker models satisfying the Einstein field equations for a combination of two fluids, one of which is a comoving perfect fluid with the radiation equation of state [Formula: see text], representing the cosmic microwave background, are discussed. Existing models, in which the second fluid is a comoving perfect fluid, are reviewed and their numerical predictions calculated. These models are generalized by considering the case in which the second fluid is an imperfect fluid. This fluid is necessarily noncomoving, the tilt representing the motion of the local supercluster of galaxies relative to the cosmic microwave background. The numerical predictions of one such model are calculated and are found to be in excellent agreement with observation.

scholarly journals Gradient almost Ricci solitons on multiply warped product manifolds

2021 ◽  
Vol 13 (2) ◽  
pp. 386-394
Author(s):  
S. Günsen ◽  
L. Onat
Keyword(s):  
Potential Field ◽  
Warped Product ◽  
Einstein Manifold ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Product Manifold ◽  
Rigidity Result ◽  
Warped Product Manifold ◽  
Almost Ricci Soliton

In this paper, we investigate multiply warped product manifold \[M =B\times_{b_1} F_1\times_{b_2} F_2\times_{b_3} \ldots \times_{b_m} F_m\] as a gradient almost Ricci soliton. Taking $b_i=b$ for $1\leq i \leq m$ lets us to deduce that potential field depends on $B$. With this idea we also get a rigidity result and show that base is a generalized quasi-Einstein manifold if $\nabla b$ is conformal.

Sign in / Sign up

Export Citation Format

Share Document