scholarly journals Spherically symmetric T-solution of the equations of 5-dimensional Kaluza–Klein theory

2020 ◽  
Vol 28 (2) ◽  
pp. 51-56
Author(s):  
V. D. Gladush
Keyword(s):  
Cauchy Problem ◽  
Cosmological Model ◽  
Configuration Space ◽  
Jacobi Equation ◽  
Spherically Symmetric ◽  
Klein Theory ◽  
The Cauchy Problem ◽  
Hamilton Jacobi Equation ◽  
Hilbert Action ◽  
Kaluza Klein

A geometrodynamical approach to the five-dimensional (5D) spherically symmetric cosmological model in the Kaluza–Klein theory is constructed. After dimensional reduction, the 5D Hilbert action is reduced to the Einstein form describing the gravitational, electromagnetic, and scalar interacting fields. The subsequent transition to the configuration space leads to the supermetric and the Einstein–Hamilton–Jacobi equation, with the help of which the trajectories in the configuration space are found. Then the evolutionary coordinate is restored, and the Cauchy problem is solved to find the time dependence of the metric and fields. The configuration corresponds to a cosmological model of the Kantovsky–Sachs type, which has a hypercylinder topology and includes scalar and electromagnetic fields with contact interaction.

scholarly journals ON REPRESENTATION FORMULA FOR SOLUTIONS OF HAMILTON‐JACOBI EQUATION FOR SOME TYPES OF INITIAL CONDITIONS

2001 ◽  
Vol 6 (2) ◽  
pp. 241-250
Author(s):  
G. Gudynas
Keyword(s):  
Cauchy Problem ◽  
Jacobi Equation ◽  
Initial Function ◽  
Initial Conditions ◽  
Representation Formula ◽  
Fundamental Solutions ◽  
The Cauchy Problem ◽  
Hamilton Jacobi Equation

This article investigates the representation formula for the semiconcave solutions of the Cauchy problem for Hamilton‐Jacobi equation with the convex Hamiltonian and the unbounded lower semicontinous initial function. The formula like Hopf ‘s formula is given by forming envelope of some fundamental solutions of the equation.

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.

A static spherically symmetric gravitational field in the kaluza-klein theory

Astrophysics ◽  
1995 ◽  
Vol 38 (3) ◽  
pp. 269-273
Author(s):  
R. M. Avakyan ◽  
E. V. Chubaryan
Keyword(s):  
Gravitational Field ◽  
Spherically Symmetric ◽  
Symmetric Gravitational Field ◽  
Klein Theory ◽  
Kaluza Klein

scholarly journals Variational and viscosity operators for the evolutionary Hamilton–Jacobi equation

2019 ◽  
Vol 21 (04) ◽  
pp. 1850018 ◽  
Author(s):  
Valentine Roos
Keyword(s):  
Jacobi Equation ◽  
A Priori ◽  
Initial Condition ◽  
First Order ◽  
Momentum Variable ◽  
Lipschitz Estimates ◽  
The Cauchy Problem ◽  
Local Lipschitz Estimates ◽  
Variational Operator ◽  
Hamilton Jacobi Equation

We study the Cauchy problem for the first-order evolutionary Hamilton–Jacobi equation with a Lipschitz initial condition. The Hamiltonian is not necessarily convex in the momentum variable and not a priori compactly supported. We build and study an operator giving a variational solution of this problem, and get local Lipschitz estimates on this operator. Iterating this variational operator we obtain the viscosity operator and extend the estimates to the viscosity framework. We also check that the construction of the variational operator gives the Lax–Oleinik semigroup if the Hamiltonian is convex or concave in the momentum variable.

scholarly journals On weak KAM theory for N-body problems

2011 ◽  
Vol 32 (3) ◽  
pp. 1019-1041 ◽  
Author(s):  
EZEQUIEL MADERNA
Keyword(s):  
Configuration Space ◽  
Jacobi Equation ◽  
Kam Theory ◽  
Kam Theorem ◽  
Invariant Solutions ◽  
Weak Kam Theory ◽  
Minimal Action ◽  
Newtonian Case ◽  
Critical Action ◽  
Hamilton Jacobi Equation

AbstractWe consider N-body problems with potential 1/r2κ, where κ∈(0,1), including the Newtonian case (κ=1/2). Given R>0 and T>0, we find a uniform upper bound for the minimal action of paths binding, in time T, any two configurations which are contained in some ball of radius R. Using cluster partitions, we obtain from these estimates the Hölder regularity of the critical action potential (i.e. of the minimal action of paths binding two configurations in free time). As an application, we establish the weak KAM theorem for these N-body problems, i.e. we prove the existence of fixed points of the Lax–Oleinik semigroup, and we show that they are global viscosity solutions of the corresponding Hamilton–Jacobi equation. We also prove that there are invariant solutions for the action of isometries on the configuration space.

scholarly journals Monopole in the Dilatonic Gauge Field Theory

2000 ◽  
Vol 53 (5) ◽  
pp. 653
Author(s):  
D. Karczewska ◽  
R. Manka
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Extra Dimensions ◽  
Numerical Study ◽  
Large Extra Dimensions ◽  
Gauge Field Theory ◽  
Spherically Symmetric ◽  
Dilaton Field ◽  
Klein Theory ◽  
Kaluza Klein

A numerical study of static, spherically symmetric monopole solutions coupled to the dilaton field, inspired by the Kaluza–Klein theory with large extra dimensions is presented. The generalised Prasad?Sommerfield solution is obtained. We show that the monopole may also have the dilaton cloud configurations.

Spherically symmetric solution in the nonsymmetric Kaluza–Klein theory

1984 ◽  
Vol 25 (1) ◽  
pp. 117-130 ◽  
Author(s):  
M. W. Kalinowski ◽  
G. Kunstatter
Keyword(s):  
Symmetric Solution ◽  
Spherically Symmetric ◽  
Spherically Symmetric Solution ◽  
Klein Theory ◽  
Kaluza Klein
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