Exact solutions of the field equations for Charap’s chiral invariant model of the pion dynamics

Pramana ◽  
1999 ◽  
Vol 52 (3) ◽  
pp. 245-256 ◽  
Author(s):  
Susanto Chakraborty ◽  
Pranab Krishna Chanda
Keyword(s):  
Exact Solutions ◽  
Field Equations ◽  
Invariant Model

scholarly journals Some nozzle flows found by the hodograph method

1959 ◽  
Vol 1 (1) ◽  
pp. 80-94 ◽  
Author(s):  
T. M. Cherry
Keyword(s):  
Exact Solutions ◽  
Two Dimensions ◽  
Nozzle Design ◽  
Perfect Gas ◽  
Field Equations ◽  
Rigid Boundary ◽  
Hodograph Method ◽  
Isentropic Flow ◽  
Fixed Boundaries ◽  
Nozzle Flows

For investigating the steady irrotational isentropic flow of a perfect gas in two dimensions, the hodograph method is to determine in the first instance the position coordinates x, y and the stream function ψ as functions of velocity compoments, conveniently taken as q (the speed) and θ (direction angle). Inversion then gives ψ, q, θ as functions of x, y. The method has the great advantage that its field equations are linear, so that it is practicable to obtain exact solutions, and from any two solutions an infinity of others are obtainable by superposition. For problems of flow past fixed boundaries the linearity of the field equations is usually offset by non-linearity in the boundary conditions, but this objection does not arise in problems of transsonic nozzle design, where the rigid boundary is the end-point of the investigation.

Investigating cosmology with equation of state

2019 ◽  
Vol 97 (7) ◽  
pp. 752-760 ◽  
Author(s):  
M. Farasat Shamir ◽  
Adnan Malik
Keyword(s):  
Equation Of State ◽  
Exact Solutions ◽  
Scalar Potential ◽  
State Parameter ◽  
Field Equations ◽  
Equation Of State Parameter ◽  
Radiation Universe ◽  
Modified Formula ◽  
Friedmann Robertson Walker ◽  
Dust Universe

The aim of this paper is to investigate the field equations of modified [Formula: see text] theory of gravity, where R and [Formula: see text] represent the Ricci scalar and scalar potential, respectively. We consider the Friedmann–Robertson–Walker space–time for finding some exact solutions by using different values of equation of state parameter. In this regard, different possibilities of the exact solutions have been discussed for dust universe, radiation universe, ultra-relativistic universe, sub-relativistic universe, stiff universe, and dark energy universe. Mainly power law and exponential forms of the scale factor are chosen for the analysis.

scholarly journals Generating solutions to the Einstein field equations

2016 ◽  
Vol 25 (02) ◽  
pp. 1650022 ◽  
Author(s):  
I. G. Contopoulos ◽  
F. P. Esposito ◽  
K. Kleidis ◽  
D. B. Papadopoulos ◽  
L. Witten
Keyword(s):  
Exact Solutions ◽  
Killing Vector ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Physical Interest ◽  
Axisymmetric Solutions

Exact solutions to the Einstein field equations may be generated from already existing ones (seed solutions), that admit at least one Killing vector. In this framework, a space of potentials is introduced. By the use of symmetries in this space, the set of potentials associated to a known solution is transformed into a new set, either by continuous transformations or by discrete transformations. In view of this method, and upon consideration of continuous transformations, we arrive at some exact, stationary axisymmetric solutions to the Einstein field equations in vacuum, that may be of geometrical or/and physical interest.

scholarly journals SPIN-1 GRAVITATIONAL WAVES: THEORETICAL AND EXPERIMENTAL ASPECTS

2006 ◽  
Vol 03 (03) ◽  
pp. 451-469 ◽  
Author(s):  
F. CANFORA ◽  
L. PARISI ◽  
G. VILASI
Keyword(s):  
Physical Properties ◽  
Exact Solutions ◽  
Gravitational Waves ◽  
Lie Algebra ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Gravitational Fields ◽  
Killing Fields

Exact solutions of Einstein field equations invariant for a non-Abelian bidimensional Lie algebra of Killing fields are described. Physical properties of these gravitational fields are studied, their wave character is checked by making use of covariant criteria and the observable effects of such waves are outlined. The possibility of detection of these waves with modern detectors, spherical resonant antennas in particular, is sketched.

scholarly journals On f(R) Theories in Two-Dimensional Spacetime

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
M. A. Ahmed
Keyword(s):  
Exact Solutions ◽  
Ricci Scalar ◽  
Two Dimensional ◽  
Field Equations ◽  
Dimensional Spacetime ◽  
Set Up

In recent years, theories in which the Einstein-Hilbert Lagrangian is replaced by a function f(R) of the Ricci Scalar have been extensively studied in four-dimensional spacetime. In this paper we carry out an analysis of such theories in two-dimensional spacetime with focus on cosmological implications. Solutions to the cosmological field equations are obtained and their properties are analysed. Inflationary solutions are also obtained and discussed. Quantization is then carried out, the Wheeler-DeWitt equation is set up, and its exact solutions are obtained.

Relativistic modeling of Vela X-1 using the Karmarkar condition

2019 ◽  
Vol 34 (20) ◽  
pp. 1950157 ◽  
Author(s):  
Satyanarayana Gedela ◽  
Ravindra K. Bisht ◽  
Neeraj Pant
Keyword(s):  
Neutron Star ◽  
Physical Properties ◽  
Exact Solutions ◽  
Density Ratio ◽  
Stellar Model ◽  
Energy Conditions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Parametric Class ◽  
Surface Redshift

The objective of this work is to explore a new parametric class of exact solutions of the Einstein field equations coupled with the Karmarkar condition. Assuming a new metric potential [Formula: see text] with parameter (n), we find a parametric class of solutions which is physically well-behaved and represents compact stellar model of the neutron star in Vela X-1. A detailed study specifically shows that the model actually corresponds to the neutron star in Vela X-1 in terms of the mass and radius. In this connection, we investigate several physical properties like the variation of pressure, density, pressure–density ratio, adiabatic sound speeds, adiabatic index, energy conditions, stability, anisotropic nature and surface redshift through graphical plots and mathematical calculations. All the features from these studies are in excellent conformity with the already available evidences in theory. Further, we study the variation of physical properties of the neutron star in Vela X-1 with the parameter (n).

Sign in / Sign up

Export Citation Format

Share Document