scholarly journals Hamilton–Jacobi Equation for a Charged Test Particle in the Stäckel Space of Type (2.0)

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1289 ◽  
Author(s):  
Valeriy Obukhov
Keyword(s):  
Test Particle ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Killing Vector ◽  
Field Equations ◽  
Tensor Fields ◽  
Charged Test Particle ◽  
Complete Sets ◽  
Charged Test ◽  
Hamilton Jacobi Equation

All electromagnetic potentials and space–time metrics of Stäckel spaces of type (2.0) in which the Hamilton–Jacobi equation for a charged test particle can be integrated by the method of complete separation of variables are found. Complete sets of motion integrals, as well as complete sets of killing vector and tensor fields, are constructed. The results can be used when studying solutions of field equations in the theory of gravity.

scholarly journals Separation of variables in Hamilton–Jacobi and Klein–Gordon–Fock equations for a charged test particle in the stackel spaces of type (1.1)

2021 ◽  
pp. 2150036
Author(s):  
Valeriy Obukhov
Keyword(s):  
Test Particle ◽  
Separation Of Variables ◽  
Parabolic Type ◽  
Complete Separation ◽  
Integrals Of Motion ◽  
Klein Gordon ◽  
Charged Test Particle ◽  
Charged Test ◽  
The Given ◽  
Hamilton Jacobi Equation

All equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces provided that Hamilton–Jacobi equation and Klein–Gordon–Fock equation for a charged test particle can be integrated by the method of complete separation of variables are found. The separation is carried out using the complete sets of mutually commuting integrals of motion of type (1.1) whereby in a privileged coordinate system, the given equations turn into parabolic type equations. Hence, these metrics can be used as models for describing plane gravitational waves.

scholarly journals Separation of variables in Hamilton–Jacobi equation for a charged test particle in the Stackel spaces of type (2.1)

2020 ◽  
Vol 17 (14) ◽  
pp. 2050186
Author(s):  
Valeriy Obukhov
Keyword(s):  
Jacobi Equation ◽  
Separation Of Variables ◽  
Equations Of Motion ◽  
Type Equation ◽  
Parabolic Type ◽  
Complete Separation ◽  
Test Particles ◽  
Charged Test Particle ◽  
Charged Test ◽  
Hamilton Jacobi Equation

We can find all equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that the equations of motion of the classical charged test particles are integrated by the method of complete separation of variables in the Hamilton–Jacobi equation. Separation is carried out using the complete sets of mutually-commuting integrals of motion of type (2.1), whereby in a privileged coordinate system the Hamilton–Jacobi equation turns into a parabolic type equation.

scholarly journals The spacetime models with dust matter that admit separation of variables in Hamilton–Jacobi equations of a test particle

2016 ◽  
Vol 31 (06) ◽  
pp. 1650027 ◽  
Author(s):  
Konstantin Osetrin ◽  
Altair Filippov ◽  
Evgeny Osetrin
Keyword(s):  
Velocity Field ◽  
Energy Density ◽  
Test Particle ◽  
Jacobi Equation ◽  
Functional Form ◽  
Separation Of Variables ◽  
Complete Separation ◽  
Coordinate Systems ◽  
Jacobi Equations ◽  
Hamilton Jacobi Equation

The characteristics of dust matter in spacetime models, admitting the existence of privilege coordinate systems are given, where the single-particle Hamilton–Jacobi equation can be integrated by the method of complete separation of variables. The resulting functional form of the 4-velocity field and energy density of matter for all types of spaces under consideration is presented.

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

Equilibrium of a charged test particle in the Kerr - Newman spacetime: force analysis

1996 ◽  
Vol 13 (8) ◽  
pp. 2179-2189 ◽  
Author(s):  
J M Aguirregabiria ◽  
A Chamorro ◽  
K Rajesh Nayak ◽  
J Suinaga ◽  
C V Vishveshwara
Keyword(s):  
Test Particle ◽  
Force Analysis ◽  
Charged Test Particle ◽  
Charged Test

scholarly journals Shapovalov Wave-Like Spacetimes

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1372 ◽  
Author(s):  
Konstantin Osetrin ◽  
Evgeny Osetrin
Keyword(s):  
Jacobi Equation ◽  
Eikonal Equation ◽  
Separation Of Variables ◽  
Complete Classification ◽  
Complete Separation ◽  
Einstein Equations ◽  
Coordinate Systems ◽  
Test Particles ◽  
Hamilton Jacobi Equation

A complete classification of space-time models is presented, which admit the privileged coordinate systems, where the Hamilton–Jacobi equation for a test particle is integrated by the method of complete separation of variables with separation of the isotropic (wave) variable, on which the metric depends (wave-like Shapovalov spaces). For all types of Shapovalov spaces, exact solutions of the Einstein equations with a cosmological constant in vacuum are found. Complete integrals are presented for the eikonal equation and the Hamilton–Jacobi equation of motion of test particles.

scholarly journals Spinning black holes with a separable Hamilton–Jacobi equation from a modified Newman–Janis algorithm

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Haroldo C. D. Lima Junior ◽  
Luís C. B. Crispino ◽  
Pedro V. P. Cunha ◽  
Carlos A. R. Herdeiro
Keyword(s):  
Black Holes ◽  
Jacobi Equation ◽  
Plasma Frequency ◽  
Conformal Factor ◽  
Matter Content ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Original Procedure ◽  
Hamilton Jacobi Equation

AbstractObtaining solutions of the Einstein field equations describing spinning compact bodies is typically challenging. The Newman–Janis algorithm provides a procedure to obtain rotating spacetimes from a static, spherically symmetric, seed metric. It is not guaranteed, however, that the resulting rotating spacetime solves the same field equations as the seed. Moreover, the former may not be circular, and thus expressible in Boyer–Lindquist-like coordinates. Amongst the variations of the original procedure, a modified Newman–Janis algorithm (MNJA) has been proposed that, by construction, originates a circular, spinning spacetime, expressible in Boyer–Lindquist-like coordinates. As a down side, the procedure introduces an ambiguity, that requires extra assumptions on the matter content of the model. In this paper we observe that the rotating spacetimes obtained through the MNJA always admit separability of the Hamilton–Jacobi equation for the case of null geodesics, in which case, moreover, the aforementioned ambiguity has no impact, since it amounts to an overall metric conformal factor. We also show that the Hamilton–Jacobi equation for light rays propagating in a plasma admits separability if the plasma frequency obeys a certain constraint. As an illustration, we compute the shadow and lensing of some spinning black holes obtained by the MNJA.

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