scholarly journals Generating solutions for charged stellar models in general relativity

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
B. V. Ivanov
Keyword(s):  
Differential Equations ◽  
Generating Functions ◽  
Maxwell Equations ◽  
Radial Pressure ◽  
Tangential Pressure ◽  
First Order ◽  
Embedding Class One ◽  
Stellar Models ◽  
Linear Differential ◽  
First Order Differential Equations

AbstractIt is shown that the expressions for the tangential pressure, the anisotropy factor and the radial pressure in the Einstein–Maxwell equations may serve as generating functions for charged stellar models. The latter can incorporate an equation of state when the expression for the energy density is also used. Other generating functions are based on the condition for the existence of conformal motion (conformal flatness in particular) and the Karmarkar condition for embedding class one metrics, which do not depend on charge. In all these cases the equations are linear first order differential equations for one of the metric components and Riccati equations for the other. The latter may be always transformed into second order homogenous linear differential equations. These conclusions are illustrated by numerous particular examples from the study of charged stellar models.

scholarly journals Application of The Riccati Method to The Adiabatic Oscillations of Stars

2004 ◽  
Vol 193 ◽  
pp. 483-486
Author(s):  
M. Takata ◽  
W. Löffler
Keyword(s):  
Differential Equations ◽  
Riccati Equation ◽  
Shooting Method ◽  
Relaxation Method ◽  
Linear Differential Equations ◽  
Matrix Riccati Equation ◽  
First Order ◽  
Nonlinear Matrix ◽  
Linear Differential ◽  
First Order Differential Equations

AbstractThe eigenmodes of the adiabatic oscillations of stars are usually calculated numerically by solving the system of the four linear first-order differential equations using either the relaxation method or the shooting method. Finding some shortcomings in these conventional methods, we adopt another method, namely the Riccati method, in which it is not the system of the linear differential equations but the nonlinear matrix Riccati equation that is solved numerically. After describing the method, we discuss its advantages and give some demonstrations.

Oscillation of first-order differential equations with several non-monotone retarded arguments

2020 ◽  
Vol 27 (3) ◽  
pp. 341-350 ◽  
Author(s):  
Huseyin Bereketoglu ◽  
Fatma Karakoc ◽  
Gizem S. Oztepe ◽  
Ioannis P. Stavroulakis
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Order Linear Differential Equation ◽  
Oscillation Criteria ◽  
Order Linear ◽  
First Order ◽  
Linear Differential ◽  
First Order Differential Equations

AbstractConsider the first-order linear differential equation with several non-monotone retarded arguments {x^{\prime}(t)+\sum_{i=1}^{m}p_{i}(t)x(\tau_{i}(t))=0}, {t\geq t_{0}}, where the functions {p_{i},\tau_{i}\in C([t_{0},\infty),\mathbb{R}^{+})}, for every {i=1,2,\ldots,m}, {\tau_{i}(t)\leq t} for {t\geq t_{0}} and {\lim_{t\to\infty}\tau_{i}(t)=\infty}. New oscillation criteria which essentially improve the known results in the literature are established. An example illustrating the results is given.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

The Wave Theory of the Electron

1928 ◽  
Vol 24 (4) ◽  
pp. 501-505 ◽  
Author(s):  
J. M. Whittaker
Keyword(s):  
Wave Function ◽  
Differential Equations ◽  
Fourth Order ◽  
Commutative Algebra ◽  
Wave Theory ◽  
Wave Functions ◽  
Linear Differential Equations ◽  
Wave Mechanics ◽  
First Order ◽  
Linear Differential

In two recent papers Dirac has shown how the “duplexity” phenomena of the atom can be accounted for without recourse to the hypothesis of the spinning electron. The investigation is carried out by the methods of non-commutative algebra, the wave function ψ being a matrix of the fourth order. An alternative presentation of the theory, using the methods of wave mechanics, has been given by Darwin. The four-rowed matrix ψ is replaced by four wave functions ψ1, ψ2, ψ3, ψ4 satisfying four linear differential equations of the first order. These functions are related to one particular direction, and the work can only be given invariance of form at the expense of much additional complication, the four wave functions being replaced by sixteen.

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