A variational principle for stationary, axisymmetric solutions of Einstein’s equations
نویسندگان
چکیده
Stationary, axisymmetric, vacuum, solutions of Einstein’s equations are obtained as critical points of the total mass among all axisymmetric and (t, φ) symmetric initial data with fixed angular momentum. In this variational principle, the mass is written as a positive definite integral over a spacelike hypersurface. It is also proved that if an absolute minimum exists then it is equal to the absolute minimum of the mass among all maximal, axisymmetric, vacuum, initial data with fixed angular momentum. Arguments are given to support the conjecture that this minimum exists and is the extreme Kerr initial data. PACS numbers: 04.70.Bw, 04.20.Dw, 04.20.Ex, 04.20.Fy
منابع مشابه
Stationary and Axisymmetric Perfect Fluids with one Conformal Killing Vector
We study the stationary and axisymmetric non-convective differentially rotating perfect-fluid solutions of Einstein’s field equations admitting one conformal symmetry. We analyse the two inequivalent Lie algebras not exhaustively considered in [1] and show that the general solution for each Lie algebra depends on one arbitrary function of one of the coordinates while a set of three ordinary dif...
متن کاملApplications of He’s Variational Principle method and the Kudryashov method to nonlinear time-fractional differential equations
In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...
متن کاملEinstein’s Field Equations for the Interior of a Uniformly Rotating Stationary Axisymmetric Perfect Fluid
We reduce Einstein’s field equations for the interior of a uniformly rotating, axisymmetric perfect fluid to a system of six second order partial differential equations for the pressure p the energy density μ and four dependent variables.Four of these equations do not depend on p and μ and the other two determine p and μ. PACS number(s): 04.20.Jb, 04.20.-q
متن کاملBäcklund Transformations of Einstein’s Field Equations for the Interior of a Uniformly Rotating Stationary Axisymmetric Perfect Fluid
Clairin’s method of obtaining Bäcklund transformations is applied to Einstein’s field equations for the interior of a uniformly rotating stationary axisymmetric perfect fluid. It is shown that for arbitrary pressure p and mass density μ the method does not give non-trivial Bäcklund transformations, while if μ+3p = 0 it gives the transformation of Ehlers. PACS number(s): 04.20.Jb, 04.20.Ex
متن کاملOptimal Control of Hand, Foot and Mouth Disease Model using Variational Iteration Method
In this paper, the optimal control of transmission dynamics of hand, foot and mouth disease (HFMD), formulated by a compartmental deterministic SEIPR (Susceptible-Incubation (Exposed)- Infected - Post infection virus shedding - Recovered) model with vaccination and treatment as control parameters is considered. The objective function is based on the combination of minimizing the number of infec...
متن کامل